text
stringlengths 0
190k
|
|---|
solv-int9810013.txt |@word represent:1 concept:2 partial:1 consider:7 results:1 leads:1 roy:1 generalize:1 consists:1 expressions:2 gj:1 compact:1 inverse:1 calculate:2 passage:1 rg:1 th:2 mod2π:2 stochastic:14 td:1 quasienergy:1 case:8 kπ:2 g2:1 very:2 wave:4 lyapunov:1 eiλj:1 dubrovin:5 riemann:2 presented:1 positions:1 solution:3 large:1 vector:5 math:9 relation:1 anal:1 challenge:1 work:1 sturm:1 disordered:2 intial:1 haar:1 consistent:1 zg:1 estimates:1 measurable:1 second:2 normed:1 ode:1 linear:5 spectral:2 will:1 what:1 nonlinear:1 section:1 expressed:1 agrees:1 lifshitz:1 new:2 principal:1 method:1 full:6 notions:1 honour:1 realizations:1 here:9 following:4 magnetism:1 lev:2 represented:1 along:1 equations:3 appears:1 change:1 obtained:1 remark:5 weinstein:1 institute:1 shift:2 study:2 studied:2 allows:1 step:1 pastur:2 periodic:8 poisson:2 fourier:3 changes:1 crdf:1 useful:1 gurevich:2 private:1 modulated:4 feller:1 clockwise:1 unit:2 use:2 takes:1 usa:1 probabilities:1 next:1 ψj:3 calculation:2 ψi:1 call:3 therefore:3 characteristics:2 bochner:1 means:1 type:1 more:2 nauka:5 subcases:1 solitons:4 operators:1 under:3 stone:1 normalized:1 particular:3 known:5 central:2 analogous:1 must:1 logarithm:1 mg:1 recall:2 equation:6 averaged:1 det:4 preliminaries:1 itself:1 values:6 freedom:1 canonically:1 arrive:1 example:2 def:1 proof:1 lφ:1 f1:1 give:1 process:9 states:10 νg:20 o:5 sense:1 terrestrial:1 information:1 csf:2 iλ1:1 forest:2 pure:4 ensemble:1 modulations:1 product:1 r2l:6 description:5 algebra:1 modulation:2 birthday:1 lax:2 fg:7 mah:1 fj:7 choice:1 data:2 levitan:1 natural:3 dynamical:1 effective:1 explicit:1 correlation:1 definitions:1 ito:1 quasiperiodic:2 ϕj:2 report:1 ffm:12 paper:2 cuts:1 y1:4 kinetic:1 still:1 its:2 before:1 supplemented:1 du:1 group:2 thank:2 ln:2 ll:4 lj:9 degrees:1 systems:4 jacobi:1 mail:2 dq:3 holomorphic:1 zybin:2 yj:4 civilian:1 ya:1 φg:2 processes:2 introduce:6 scaling:2 band:1 rotation:8 now:2 yu:3 nor:1 deift:1 term:3 2g:3 each:2 mean:7 el:4 multiphase:1 square:1 ei:2 gennady:1 generation:1 journ:1 isospectral:1 ξj:5 frequency:2 measure:4 ionosphere:1 our:1 really:1 ru:2 matrix:1 space:2 research:4 r2g:8 ajk:2 formula:3 rj:7 foundation:2 temporal:2 lebesque:1 theory:7 surveys:2 possibility:1 admits:1 completely:1 estimate:1 definition:2 fixed:1 r1:2 r2:1 r3:1 geometry:1 v2:2 noted:1 motion:1 iλ2:1 length:2 fomin:1 βj:2 first:2 there:1 probability:6 waves:2 number:14 xx:2 dispersive:1 stochastics:1 given:5 introduction:4 adjoint:1 πi:1 system:1 their:1 appl:5 realization:4 siam:1 hyperelliptic:1 gives:4 2ag:1 kolmogorov:1 relationship:1 sl:10 centered:1 moscow:9 whitham:5 correspondent:1 coefficients:1 mclaughlin:2 johnson:2 dy:1 see:5 crossroads:1 matter:1 determined:2 were:1 powers:1 russia:2 rewrite:1 direct:1 krylov:2 say:1 ras:2 keller:1 any:4 angle:1 lim:2 self:1 note:2 k1:1 potential:5 jacobian:3 canonical:1 formulas:2 multiple:1 trace:1 opposite:1 object:1 most:1 connected:2 representation:1 phase:7 intrinsic:1 αt:1 soliton:9 kg:1 especially:1 kj:16 torus:4 coincides:1 proceedings:2 part:1 exp:2 physics:2 notion:1 fact:1 probabilty:1 rozanov:1 pril:1 random:9 dy1:1 radio:1 solutions:2 earth:1 uniform:3 d2:2 find:1 d1:4 slow:1 parameters:1 distributed:8 should:1 only:1 quasimomentum:2 integrable:1 moser:2 oct:1 dn:8 do:1 get:1 µj:6 ssl:17 international:2 combinations:1 lattices:2 dyg:1 neither:1 dp:6 alexander:1 closure:1 evolution:8 conditions:1 arxiv:1 troitsk:2 prokhorov:1 hydrodynamic:1 qk:1 cycles:4 4πi:2 set:4 modulo:1 constructing:1 smooth:1 δjk:1 differentials:1 namely:4 sec:1 result:1 arg:1 discussions:1 close:1 dµ:4 ergodicity:1 phases:7 interacting:1 µl:1 various:1 µk:1 simplest:1 theta:1 αk:1 αj:2 approach:1 wg:2 rm1:1 terms:1 wk:2 however:1 incommensurate:2 jm:5 comm:5 solv:1 amer:1 distribution:6 topology:2 both:1 limits:1 many:1 region:1 equal:1 propagation:1 connection:1 berry:1 genus:1 expression:1 schroedinger:2 cj:4 cm:1 point:6 simple:3 asymptotically:2 corresponds:3 dimensional:3 figotin:1 considers:1 conference:1 jetp:1 described:6 basis:2 union:1 due:2 been:1 hitting:2 defined:1 zpj:1 pf:4 r2j:2 basic:6 pj:5 pk:2 define:1 θj:2 ergodic:3 arises:1 corresponding:1 quantities:1 covariance:2 gap:11 lives:1 func:1 lgp:3 denote:1 former:1 present:3 applied:1 frequences:1 value:11 aim:1 invoking:1 suppose:3 ǫt:3 ǫx:8 taking:2 almost:7 averaging:1 vj:1 wkb:1 surprisingly:1 surface:1 according:1 flaschka:2 uxxx:1 rfbr:1 different:1 grant:2 make:1 problems:1 same:2 bands:3 φj:3 finite:7 development:2 independent:3 used:2 hand:1 v1:3 moment:3 v3:2 yg:4 potentials:4 normalization:2 weakly:1 center:1 whole:1 well:6 obviously:1 de:1 components:1 sets:2 soviet:1 usual:1 proposed:1 slowly:1 moments:4 dφ1:1 obtain:1 aspect:1 turbulence:2 λk:1 ams:1 integer:1 density:11 zakharov:3 lattice:5 conjugated:1 theorem:6 dµ1:1 iφ:1 real:4 bij:1 big:1 sums:1 possible:1 cf:1 qj:1 know:1 using:2 dφg:1 meaning:1 semiclassical:1 mir:1 follows:1 dµg:1 korteweg:1 arbitrary:2 dµq:1 stationary:5 fulfil:1 right:1 2iλ:2 some:4 transaction:1 deduce:1 oscillations:2 kdv:10 generates:1 describing:1 normal:2 per:2 does:2 decomposition:4 venakides:5 proc:1 pr:2 obey:1 bm:1 expansion:1 bk:2 evolve:1 substitution:2 imaginary:2 ηj2:2 properties:4 asymptotic:1 about:2 rare:1 novikov:4 dependence:1 surround:2 posess:1 ξk:1 mixed:2 introduced:2 considerations:1 soc:2 communication:1 into:3 ηl:1 integral:8 ηj:1 variable:1 references:1 sov:1 operator:1 financial:1 essen:1 additional:1 support:2 initial:7 transform:2 u2:1 borel:2 institue:1 m1:1 was:1 sinai:1 asymptotics:1 function:19 form:7 but:1 hj:4 construction:1 russian:4 line:2 considerable:1 made:1 2πib:1 ut:1 inside:1 6uux:1 up:1 us:1 liouville:1 ωj:5 limit:1 levermore:1 sum:1 problem:2 similar:1 clear:1 ωg:1 ac:1 constant:1 ag:2 int:1 abstract:1 generating:4 general:3 transl:1 dλ:5 ug:19 formulation:1 functions:4 no:1 when:1 valid:1 lpi:1 zhou:1 separate:1 uniformly:5 generated:2 important:6 included:1 structure:2 implies:1 vries:1 interval:1 gredeskul:1 dvz:2
|
solv-int9810014.txt |@word gs:1 consider:4 yasuhiro:1 particular:1 desirable:1 results:1 four:1 33e:1 scalar:20 grateful:1 partial:1 research:3 localized:1 row:2 inverse:4 const:2 calculate:1 re:5 iii:1 should:1 containing:1 tn:1 γj:2 γh:1 tj:2 preserved:2 th:5 under:12 analogous:2 circumstances:1 norm:2 applied:5 straightforward:1 very:1 wave:11 every:2 additional:1 lecture:1 discretizations:10 difference:4 exact:7 adaptive:2 condition:6 34a:3 34b:1 presented:2 t2:8 solution:48 t1:12 travels:1 discrete:26 vector:42 science:1 small:4 optics:1 slower:1 consistent:1 direct:1 pulse:2 cosh:2 matrices:2 second:1 traveling:1 gn:19 notwithstanding:1 dynamics:1 substitute:2 linear:11 even:1 nonlinear:12 plays:1 appear:2 electronics:2 sum:1 supplied:1 reminiscent:1 version:1 above:4 sup:1 ˆj:2 increasing:2 hb1:2 method:4 contrast:2 hb2:2 satisfy:1 27a:2 27b:2 nonlinearly:1 policies:1 respectively:4 component:11 water:1 asymmetry:1 compose:1 governing:1 sinh:13 represented:1 strong:1 equations:7 z1:2 change:6 obtained:10 naval:1 technical:1 shift:6 study:3 studied:2 example:2 suggests:1 resulting:1 lightwave:1 tables:2 birefringent:2 studies:3 appropriately:2 via:4 useful:2 family:2 9a:2 substitution:2 unitary:3 total:1 unit:1 wise:1 eiωt:1 use:2 asymptotic:6 usa:2 remains:4 positive:6 give:2 ψj:1 comparing:3 program:1 call:1 therefore:9 taken:2 until:1 more:6 separated:3 solitons:34 eiφ2:1 envelope:1 odinger:4 herein:1 interaction:18 excellent:1 known:8 hold:2 effort:2 must:1 ibj:1 collision:5 recall:1 equation:13 london:1 reproduce:1 column:3 itself:2 values:2 following:4 making:1 hiroshima:2 proof:1 meant:1 38c:1 figure:3 2rn:2 december:1 table:4 purposes:1 states:1 indicates:1 14b:5 numbers:2 14a:5 david:1 end:1 decaying:1 turn:1 travel:1 get:1 feature:2 far:1 nontrivial:1 plus:1 parameter:1 sin:5 gordon:1 product:1 maxj:1 replacing:3 max:1 after:4 derived:2 different:8 applications:1 lax:1 faculty:1 date:2 choice:5 data:5 compatibility:4 fn:21 natural:4 clarkson:1 computations:1 sech:7 approximation:1 uqn:1 june:1 correspond:2 garnier:1 so:2 sn:1 suggest:2 acknowledges:1 order:7 superscript:1 holds:2 office:3 indeed:3 kluth:1 years:1 experiments:2 through:1 mentioned:1 japan:2 satisfies:1 still:1 ieee:2 its:3 before:2 solitary:22 derive:1 rapidly:1 forwards:1 qˆ:2 kagamiyama:1 interesting:2 conjugation:1 actually:1 forms:2 absence:2 distinguishing:1 systems:10 eη2:3 eη1:4 main:1 13c:1 13b:1 non:2 13e:2 13d:1 numerically:1 polarizations:5 reflected:1 pfaffians:1 they:3 now:1 yu:2 discuss:2 possess:1 term:1 hallmarks:1 2q:2 january:1 university:4 34c:3 kerr:1 hermitian:1 hqn:1 each:6 found:5 referred:4 subset:2 24a:2 eh:8 24b:2 series:1 reduce:3 society:1 investigated:1 obtains:1 changed:1 quantum:3 our:2 reprints:1 eq:16 special:3 out:1 shown:1 matrix:5 solved:1 furthermore:3 since:3 squared:1 chaos:2 denotes:4 may:3 contained:1 longtime:1 formula:3 rn:22 size:1 supports:1 integrated:2 rj:2 shows:2 foundation:1 theory:3 interactions:7 2h1:2 possibility:1 quite:1 clarify:1 approaches:3 care:2 backwards:3 derivation:1 r2:2 ministry:1 could:1 ist:12 motion:1 introduction:1 length:1 derivations:1 hence:5 retain:3 undergo:1 iβ2:2 speeds:3 first:3 there:9 symmetry:6 variables:1 waves:18 number:7 preservation:1 comprised:1 restrict:1 set:2 specifically:1 another:1 indices:4 open:2 separation:1 given:8 necessarily:1 publication:1 similarly:2 manakov:5 interact:9 1z:2 system:58 construct:2 their:3 constants:1 calculations:1 siam:2 scheme:5 2fn:3 recovered:1 gives:2 free:1 grant:3 relationship:1 asymmetric:19 cˆ:3 relative:3 exactly:2 17b:3 17a:3 transverse:2 forward:11 segur:2 somewhat:1 manifestation:1 explained:1 july:1 sign:2 representing:1 than:3 modes:1 wide:1 quantitative:1 showed:1 log10:4 require:2 integrability:3 final:6 classes:1 intensities:1 amplitude:7 were:3 shifted:3 symmetries:3 bhn:1 arg:2 qˆ1:3 generalization:2 korepin:1 discussions:1 manner:4 conjugate:2 bound:1 constrained:3 any:8 accounted:2 lie:1 strength:1 self:4 mechanism:1 converges:1 polarization:20 ih2:1 materials:1 take:1 analogy:1 finding:2 command:1 n00014:1 modulus:1 reversed:1 bilinear:4 play:1 continuous:1 elastically:5 electric:2 though:1 most:1 qˆn:4 errors:4 sponsored:1 significant:2 formulae:6 pair:19 analytically:1 measured:1 class:5 trapping:1 soliton:88 kf:1 considered:2 calculated:1 proceedings:1 points:2 ohta:2 distinctive:2 typical:2 physics:6 section:1 fact:4 nls:46 particularly:1 phenomenon:1 intensity:6 show:3 reductions:1 rtn:7 converge:2 focusing:2 relation:2 solutions:39 substituting:1 d2:4 indicate:1 d1:3 q1:3 q2:5 parameters:9 claude:1 less:1 reverses:1 analytic:1 only:6 modulation:1 integrable:21 constant:4 oct:1 centrally:1 boulder:4 pℓ:2 move:1 closed:1 notation:1 means:1 routine:1 overall:2 cannot:1 nearly:1 despite:1 combinations:1 lattices:1 dt:9 interpreted:1 dr:1 dp:1 areas:1 evolution:2 determinants:2 continuum:6 54e:1 exchanged:4 conditions:6 arxiv:1 yield:1 acknowledgments:1 qe:1 filled:1 qf:1 analytical:2 scott:1 qj:5 qn:52 user:1 38a:2 38b:2 multiplying:1 physically:2 undergoes:1 frame:4 correlations:1 thereby:1 up:2 observed:2 see:6 individual:8 merits:1 result:1 existence:2 qtn:1 close:2 subject:2 phases:1 fn2:2 speed:9 review:4 consequence:2 symmetric:37 outside:1 determined:2 ladik:2 between:6 invariant:2 approach:1 expressed:1 multiplied:1 comparable:2 terms:1 shabat:1 nature:2 attention:2 transpose:1 however:7 thereon:1 hypothesis:1 key:1 solv:1 31b:2 31a:2 jetp:2 distribution:3 both:11 cos:2 limits:24 many:1 taking:2 conclusions:1 36b:3 equal:4 36a:3 propagation:4 admit:1 pde:5 expression:1 ck:7 among:2 relevant:1 extent:1 asymptotically:2 cf:4 16b:3 height:1 dimensional:5 visually:1 simply:1 confirmed:1 associated:8 considering:1 ensures:1 described:2 transformations:1 basis:7 addition:1 due:2 been:1 mark:1 defined:2 reduction:13 f49620:1 slowly:2 interest:1 certain:1 pj:4 slavnov:1 meeting:1 direction:1 arises:1 corresponding:2 scalars:1 sufficient:1 implied:1 qˆ2:1 decreased:2 c2:19 c1:16 general:12 those:4 case:14 multi:9 p1:7 look:2 gnt:2 pacs:1 5a:13 single:1 air:3 will:2 p2:7 behavior:1 error:4 dms:1 iφ:1 temperature:1 discretize:1 force:3 vectors:9 coupled:1 molecular:1 im:1 thus:2 13a:2 vn:2 ii:3 ih:2 examined:1 vt:1 33a:1 foreign:1 technology:1 higashi:1 35b:3 35a:3 fibers:4 generic:1 media:2 make:1 views:1 radiation:2 qfn:1 same:9 complex:6 runge:1 finite:1 φn:5 kutta:1 independent:4 used:4 peaks:2 pfaffian:1 numerical:15 upon:2 effect:1 counterparts:1 authors:2 moving:4 purpose:1 brussels:2 ablowitz:6 contribution:1 identity:2 recent:1 schr:4 center:1 makes:2 possessed:1 well:4 tsujimoto:1 analysis:2 thought:1 33b:1 without:3 solve:2 machinery:1 components:9 simulated:1 coordinate:4 position:2 model:2 ωj:3 soviet:2 possesses:1 researchers:1 left:1 eilbeck:1 just:1 cj:20 when:4 distribute:1 obtain:4 valuable:1 vanishes:1 shape:2 ch:1 identify:1 alternative:1 scattering:6 letting:1 note:6 hpj:1 zakharov:1 character:1 except:1 mathematically:1 governmental:1 interested:1 location:1 plasma:1 transformation:3 ought:1 5b:13 real:7 9b:2 march:2 eigenfunction:1 government:2 read:1 february:1 16a:3 early:1 boxes:2 grid:1 resolves:1 press:1 part:1 fractals:1 multiplexing:1 necessary:1 semi:1 28a:2 follows:1 reduces:7 28b:2 menyuk:2 separately:1 yields:3 either:3 arbitrary:3 ha1:2 qxx:2 stationary:1 spins:1 mathematical:2 deviation:1 because:3 methods:2 some:2 library:1 b1:18 b2:8 moreover:1 2qn:4 suris:1 generates:1 electromagnetic:3 unavoidable:1 integration:3 84e:1 does:2 provides:2 chains:1 refer:3 varying:1 11a:2 scientific:2 11b:2 retains:1 journal:3 bh:2 usaf:1 bj:2 notably:1 broken:1 although:4 eiφ:1 concreteness:2 properties:1 comparison:2 extension:2 constraint:4 dˆ:1 freedom:1 discussed:2 o:5 simulation:3 a2:12 extensions:1 usn:1 peak:2 discretization:9 cambridge:1 letters:2 colorado:4 h2:12 into:3 h1:2 ahn:1 ηj:4 down:1 phase:5 appropriate:1 right:1 references:1 determine:5 operator:13 financial:1 utility:1 log:9 elastic:4 ψk:3 iβ1:4 support:2 initial:7 question:1 transform:1 long:25 width:1 authorized:1 letter:3 was:7 function:4 medium:1 form:21 hp:2 differences:1 but:4 yo:1 zin:1 hn:6 proportionally:1 convergence:1 optical:5 true:1 circumstantial:1 elliptically:1 versions:2 whether:3 iqt:2 official:1 uq:1 ωt:1 us:2 theoretical:1 below:2 iqn:1 limit:12 demonstrate:1 problem:2 similar:2 strongly:1 ae:1 int:1 ah:3 abstract:1 aj:11 deep:1 evidence:2 engineering:1 simulations:5 education:1 combining:1 physical:3 nh:1 again:1 compared:2 nag:1 national:1 no:5 generally:3 detail:1 field:4 other:6 role:2 copyright:1 eiφ1:1 department:3 mathematics:5 nt:1 izergin:1 poor:1 briefly:1 superposition:1 separate:1 preceding:1 hirota:5 describe:1 gaididei:1 variation:1 a1:16 important:4 allowing:1 variable:3 needed:1 structure:2 implies:1 auxiliary:1 hp2:2 hp1:3 required:1 packets:1 zqn:1 correspondingly:1 dot:1 time:33 qˆj:3 n2:2 backward:9
|
solv-int9810015.txt |@word show:1 rubtsov:1 commute:1 λi:5 inverse:1 lm:1 lj:11 palaiseau:1 li:8 analytic:1 th:2 µi:1 circle:3 hamiltonians:1 oct:1 s1:1 around:1 efinition:2 de:1 possible:3 choice:2 fr:1 eµ:1 using:1 aλ:4 yu:1 eme:2 enriquez:1 fields:4 arxiv:1 proposition:1 l2:1 polytechnique:2 each:1 wronskian:1 cnrs:1 benney:3 umr:1 res:1 nλ:2 decomposition:1 email:1 math:1 degree:1 bc:6 equivalent:1 analogues:1 lmu:1 free:1 solv:2 equations:2 ker:9 definition:1 vectors:4 periodic:3 proof:1 first:1 family:1 ca:1 bound:1 lk:1 ab:3 references:1 operator:4 bλ:1 there:1 question:1 injectivity:4 defined:1 ψi:2 zeros:2 type:7 gives:1 commutativity:2 corresponding:1 form:2 ecole:1 operators:8 cedex:1 eλ:1 lµ:9 translation:1 must:2 showed:3 deg:3 aa:1 mathematiques:1 proved:1 give:1 int:2 abstract:1 generically:1 functions:1 make:1 same:2 write:1 unity:1 other:1 balan:2 φi:2 hierarchies:1 product:3 centre:1 problems:1 lax:8 studied:1 phase:1 identity:1 implies:1 orlov:1 space:1 eor:2 so:1 lλ:22 chosing:1
|
solv-int9810016.txt |@word consider:6 nikita:1 results:1 commute:1 eτ:3 depend:8 calculate:4 tr:6 finally:1 th:4 under:1 must:1 worth:1 confirmation:1 very:3 corollary:1 difference:1 riemann:7 hamiltonian:2 list:1 solution:1 large:9 solved:2 vector:5 equation:14 neighborhood:3 mi:1 estimates:1 direct:3 sign:15 second:2 correlator:1 substitute:1 canonical:1 spectral:2 what:1 nonlinear:9 developed:1 sub:1 section:3 brief:1 expressed:3 uniform:1 goes:2 method:3 here:8 objects:2 possibility:1 separation:2 consideration:1 equations:6 change:1 obtained:4 spite:1 institute:1 study:2 trial:1 permit:1 via:2 useful:1 namely:1 replace:1 apply:2 total:1 use:1 asymptotic:12 would:1 commun:2 remains:3 positive:2 contains:1 negative:1 next:1 explicitly:2 therefore:5 taken:1 associated:2 type:3 bethe:1 more:4 becomes:1 operators:6 odinger:8 appendix:1 particular:2 known:1 fermionic:4 te:1 defines:2 recall:5 originally:1 work:1 det:11 erf:2 fock:2 ρt:3 following:3 arrive:3 example:3 proof:1 abelian:1 calculation:4 december:1 states:1 sense:1 axis:6 goal:2 rather:2 acts:2 chemical:2 how:1 nontrivial:2 parameter:1 product:1 description:1 algebra:1 may:1 thermodynamic:2 after:1 hence:3 drop:2 dynamical:1 explicit:2 korepin:5 provide:2 so:3 correlation:17 representation:5 order:7 holds:1 closely:1 enter:1 indeed:4 thermal:1 paper:2 mentioned:1 steklov:1 its:3 itp:4 derive:1 ln:13 interesting:1 vicinity:1 2λt:4 complex:1 main:2 possessing:1 formulæ:5 them:2 combination:1 powerful:1 framework:2 repulsive:1 they:1 singularity:2 now:3 possess:1 2t:3 term:15 finite:1 presented:3 theory:1 2c:2 found:2 traces:1 characterized:1 arxiv:1 weight:3 series:3 energy:1 reduce:1 related:2 φd1:2 entering:1 quantum:10 our:2 special:1 out:4 ru:1 shown:2 space:2 singular:2 research:1 particles:1 investigation:1 denoted:1 formula:9 evaluation:2 correct:1 math:3 shows:1 foundation:1 linear:1 interactions:1 free:4 standard:2 completely:1 put:1 estimate:3 definition:1 interaction:1 turn:1 corrections:3 first:4 already:1 variables:1 confuse:1 iht:2 restrict:2 set:1 simplified:2 relations:3 illustrate:1 given:4 temperature:3 introduction:1 leading:11 system:1 least:1 their:1 calculations:1 holomorphic:2 moscow:1 exactly:2 contribute:1 off:2 distance:8 depends:3 annihilation:3 were:4 powers:2 russia:1 sb:3 rewrite:2 correction:1 argument:1 say:1 ras:1 any:1 kojima:2 zero:1 depending:2 convenient:1 potential:2 take:1 explanation:1 play:1 trace:1 shall:2 denominator:2 definitions:1 why:2 considered:2 clear:1 later:1 coincides:1 physica:1 yang:4 exp:5 kt:1 sum:1 fact:3 precise:1 show:1 supported:1 relation:1 solutions:1 substituting:1 trivial:1 find:10 principal:1 ratio:3 parameters:2 should:2 lemma:4 only:9 going:1 factor:5 integrable:4 local:2 oct:1 equilibrium:1 dn:2 do:5 dependent:1 expectation:6 dz:1 dx:1 du:5 twobody:1 evolution:1 fields:22 differential:5 remove:1 acknowledgments:1 qa:2 qd:2 contain:1 fixed:3 view:1 kernel:9 dνs:2 exists:1 see:2 result:5 dµ:3 still:1 commutation:3 between:1 fermi:3 d54:1 notice:1 terms:11 attention:1 weak:1 however:7 vanishing:1 solv:1 bose:2 both:1 last:3 equal:4 hψ:1 contribution:1 expression:4 ansatz:1 strongly:2 point:3 reasons:1 asymptotically:1 dimensional:2 respect:6 kernels:4 slavnov:5 described:3 commutative:2 thermodynamics:1 simplification:1 due:4 int:1 describes:2 treat:1 pd:2 basic:3 determinant:33 arises:1 restrictions:1 sufficient:1 gas:3 demand:1 c2:2 c0:2 present:2 case:4 value:6 will:2 while:1 behavior:2 error:3 situation:1 property:1 thus:7 non:3 obeying:1 properties:3 dual:18 ic:2 vanish:1 containing:1 descent:1 grant:1 pay:1 belong:1 connection:1 same:2 clearly:2 φa:22 φb:1 parts:4 φd:20 emphasize:1 proved:1 several:1 difficult:1 independent:1 used:2 infinity:2 i1:6 i0:15 identity:1 mentioning:1 schr:8 nevertheless:2 well:4 analysis:1 obviously:1 position:1 model:4 possesses:4 usual:1 just:3 obtain:3 formulated:1 using:2 scattering:1 λn:2 functionally:1 enters:2 preprint:4 density:2 iϑ:1 seems:1 simple:4 other:1 easy:2 solvable:1 real:7 know:1 vacuum:9 immediately:2 accepted:4 necessary:1 like:2 particle:1 follows:3 izergin:1 separately:1 remind:1 integrals:2 arbitrary:4 become:1 mathematical:1 because:1 methods:2 classical:1 creation:3 some:10 pψ:4 ourselves:2 nonzero:1 cψ:1 describing:1 normal:1 does:4 power:1 each:2 expansion:3 step:2 hilbert:7 eψ:1 impenetrable:1 discussed:1 dependence:1 o:6 dependency:1 plus:1 fredholm:23 act:1 introduced:2 presence:1 into:4 integral:11 functional:2 references:1 operator:4 proportional:1 hep:4 assumed:1 there:1 long:4 pa:2 bosons:2 way:1 was:5 asymptotics:21 function:28 complete:3 form:1 but:4 delta:2 russian:1 coupling:3 applying:1 improved:2 evident:2 2πi:8 vacancies:1 smooth:3 up:1 us:7 φa2:2 below:2 limit:3 steepest:1 problem:8 dudv:1 similar:2 detailed:1 constant:4 defined:4 abstract:1 describe:4 ordering:1 dν:1 dλ:14 regime:1 functions:10 analyticity:1 no:4 when:1 detail:1 field:2 interested:1 role:1 eiht:1 2it:1 excitation:1 models:2 important:5 qψ:4 structure:1 auxiliary:5 original:2 time:10 having:1
|
solv-int9810017.txt |@word subterms:1 partial:3 consider:1 crucial:1 results:3 themes:1 roy:1 proposition:32 consists:1 expressions:2 contributions:1 compact:1 whose:1 preserves:1 terms:9 calculate:1 tv:1 eα:1 acting:1 factoring:2 groundstate:1 quasi:4 preserved:1 under:1 ebres:1 straightforward:3 orthogonal:2 rise:3 springer:2 trigonometric:9 corollary:7 every:1 difference:1 exact:25 leads:2 annihilated:1 eiw:4 hamiltonian:4 turns:1 solution:2 2ki:1 settle:2 gauge:3 div:1 noted:1 a126:1 concluded:1 heckman:3 smaller:1 findings:1 direct:1 groupes:1 second:7 selfadjointness:1 linear:7 will:14 what:1 appear:1 dept:2 sum:6 current:1 subspaces:5 expresses:1 serban:1 codimension:3 coefficient:2 multivariate:1 never:1 isometric:1 understanding:1 desired:3 2kc:1 sogo:1 along:1 standard:1 appears:1 logarithmic:1 obtained:3 remark:3 antisymmetric:2 study:3 allows:1 approaches:1 reports:1 paris:1 resulting:3 action:7 fourier:1 montreal:2 quotient:1 schur:1 useful:1 family:1 f1:1 merely:1 explained:1 diagonalizable:2 assertion:4 aimed:1 sgn:2 apply:1 establish:1 use:4 ρc2:4 proceed:2 prove:4 distinct:2 positive:9 humphreys:1 finally:2 next:2 ψi:1 therefore:3 vi:3 taken:1 type:6 more:2 compositio:1 alcove:3 operators:8 problem:1 hermann:1 flag:8 particular:2 central:1 cases:1 effort:1 must:4 logarithm:1 states:1 ρc:34 valued:1 sheds:1 mc:7 deformed:2 recall:6 equation:2 work:1 kamran:3 values:2 publications:1 following:7 trans:1 root:57 fulton:1 proof:22 claim:5 give:5 calculation:1 numerator:1 preserving:1 2i:1 assumptions:1 hyperplane:1 irreducible:3 spanning:2 verlag:2 recursive:2 rather:1 verify:1 acts:1 recovers:1 write:1 maps:1 ρ2c:3 pair:1 fourth:1 ordinary:1 sin:1 product:6 algebra:2 may:2 orbits:2 collection:1 consequence:1 fd:1 multiplication:4 fi:7 fj:2 choice:1 data:1 constants:10 goal:1 introduced:1 natural:2 outline:1 imply:1 light:1 milson:2 parameterized:1 element:7 hypotheses:1 cannot:2 so:1 fundamental:3 jiα:1 sc:7 representation:3 subsequently:2 order:11 holds:1 indeed:2 over:2 2sc:1 course:2 paper:4 london:1 existence:1 fn:1 roots:17 χd1:2 group:5 fit:1 how:1 chosen:1 interesting:2 sα:8 inclusion:1 conjugation:1 subterm:1 forms:1 systems:25 jacobi:2 olver:2 hidden:1 main:6 defining:1 deformation:1 maximal:4 non:14 combination:3 uhl:1 regarding:1 jα:2 break:1 framework:2 walls:1 wise:1 k2c:1 multidimensional:1 now:12 structural:2 fi2:1 eigenvalue:7 term:3 several:1 invariants:1 university:1 presented:1 csc2:1 l2:18 each:5 side:4 mean:2 subset:9 domain:5 arxiv:1 ei:2 weight:7 series:3 hard:1 related:3 moser:1 used:1 obtains:4 measure:1 quantum:8 our:6 operation:1 out:2 gonzalez:2 factors:4 gradient:4 sutherland:8 furthermore:4 since:8 induces:1 looking:1 re:1 contained:1 vector:7 mα:2 rc:18 denoted:3 formula:17 rn:2 induced:1 suffices:1 math:8 shows:2 theory:4 state:1 divergence:1 quite:1 completely:1 intermediate:1 remainder:2 definition:3 v1:4 phrases:1 turn:1 length:19 harris:1 leading:1 hence:11 generalizations:1 first:12 origin:1 necessity:1 symmetry:1 variables:1 number:7 restrict:1 fh:1 directly:1 ring:1 precisely:2 open:5 alcoves:1 given:13 similarly:2 introduction:2 meaningful:1 adjoint:2 system:11 construct:2 their:1 assumption:4 types:1 statement:2 final:1 gives:2 a31:1 a30:1 2ac:1 using:4 ch:3 exactly:7 proving:1 required:1 short:4 because:1 constituent:1 than:2 coefficients:5 ragoucy:1 finitely:1 divisible:3 see:2 inversely:1 were:1 collecting:1 motivation:1 fashion:1 generality:1 explicit:1 modern:1 argument:2 generalization:2 endomorphism:2 say:1 conjugate:1 need:2 demonstration:1 any:2 lie:6 hypergeometric:1 zero:5 convenient:1 calogero:8 hyperplanes:2 note:12 k1:1 concerns:1 generalized:3 indexed:1 switching:1 formulas:2 play:1 continuous:1 multiple:1 mcgill:4 olshanetsky:16 investigations:1 denominator:3 algebraic:7 involving:1 connected:1 nothing:2 class:1 kc:14 observation:1 kj:1 clear:1 adopt:1 kn:1 dimension:1 reflections:1 quadratic:2 usual:2 physics:1 section:2 fact:5 precise:1 cot2:1 show:6 supported:1 discovered:1 ki:5 ρc1:3 spaces:1 relation:7 substituting:1 analogue:2 brink:2 d0:3 d1:2 bourbaki:1 based:1 parameters:2 hf:1 behind:1 should:6 lemma:2 only:1 explicitly:3 factor:5 integrable:2 constant:1 hamiltonians:17 oct:1 dalhousie:1 dominant:6 above:2 means:1 de:1 straightforwardly:1 obtain:2 self:2 ones:1 words:2 new:2 combinations:2 applying:2 closure:1 qs:1 φi:1 numerous:1 differential:3 factorization:1 nλ:1 common:1 characteristic:1 body:3 set:10 constructing:1 exists:5 physically:1 relative:4 namely:2 alg:1 result:6 chambers:1 fails:1 said:2 eigenfunctions:15 subsequent:1 definite:2 tend:1 symmetric:1 written:2 various:1 permutes:1 invariant:17 boundary:5 approach:3 across:1 preserve:1 recently:1 extend:1 however:1 freudenthal:7 vanishing:1 comm:1 key:1 multiplier:4 solv:1 article:1 lopez:2 nν:1 both:1 essentially:2 2πz:2 cot:5 many:1 taking:2 conclusions:1 equal:2 called:3 present:1 context:3 cµ:1 sense:1 hφ:1 affine:1 necessary:1 point:2 simple:4 ca:2 address:3 corresponds:1 dimensional:7 simply:1 associated:3 actually:1 mc2:1 mc1:1 pp:8 described:2 spanned:1 basis:7 union:1 three:3 been:1 strategy:1 defined:6 change:1 basic:6 algebras:5 trig:48 choose:2 corresponding:13 concerning:2 propositions:1 subspace:10 cos:1 spectrum:1 determination:1 mail:2 c2:5 c1:2 general:1 2ǫi:1 arisen:1 case:3 multi:2 subsets:1 pacs:1 ǫj:1 ǫi:2 ǫn:1 2ρc:1 trick:1 euclidean:1 suppose:2 promising:1 region:1 procedure:2 identical:1 h3a:1 endowed:1 thus:3 iw:1 ii:2 intertwining:5 itself:1 properties:1 dual:1 ready:2 vanish:2 eigenfunction:7 eiµ:2 thereby:1 lengths:5 recursion:5 lett:1 same:1 complex:1 products:1 proved:1 finite:5 four:1 investigated:1 2k6:1 hand:4 usually:1 a2c:9 purpose:1 characters:4 potentials:7 infinite:3 invariance:1 identity:2 recent:1 multiplicities:1 lower:3 suitable:1 sl2:1 reflection:1 mention:2 well:4 phil:1 without:1 flags:1 sets:1 model:4 latter:4 subgroup:1 less:1 half:2 solvability:24 torus:1 underlying:4 identify:3 questions:2 immediately:3 facts:1 eigenstates:1 lebesgue:1 density:1 regarded:1 conclude:1 character:4 lattice:3 potential:2 corollaries:1 treatment:1 theorem:14 mod:1 solvable:7 remaining:1 take:2 real:6 orbit:1 easily:1 iα:3 regard:1 sums:1 possible:1 admitting:1 integer:1 unique:7 formal:2 loss:1 appearing:2 like:1 follows:9 piece:1 serves:1 manifest:1 chamber:1 yields:3 either:1 integrals:1 arbitrary:2 multiplicative:1 become:2 works:1 reduced:7 beltrami:1 mathematical:1 right:4 classical:4 some:5 begin:2 algebraically:1 b1:3 b2:3 moreover:2 halifax:1 reasons:1 eiα:3 solving:1 dense:7 dimensions:1 eiλ:11 ac2:5 ac1:5 does:1 algebraization:1 assuming:1 who:1 power:2 equivalent:1 2c:3 perpendicular:2 step:3 super:1 hilbert:4 takes:1 about:1 actual:1 pλ:15 theorems:1 discussed:1 essential:2 a5:1 referred:1 consequently:9 perelomov:17 soc:1 rev:1 presence:1 into:5 isomorphic:2 negative:1 lies:1 weyl:12 references:1 laplacian:4 determine:2 operator:10 wλ:1 span:1 log:8 there:7 question:4 long:1 noting:2 inner:5 way:2 was:1 naturally:2 function:3 medium:1 complete:2 form:3 converse:1 but:3 construction:1 highest:1 true:1 commun:1 compute:2 evident:2 supp:4 multiplicity:5 chapitres:1 smooth:2 up:2 2πq:1 shifman:1 codomain:1 demonstrate:1 homothetic:4 define:2 similar:1 laplace:1 uc:5 mechanics:1 ac:45 later:1 ordered:2 int:2 certain:4 abstract:2 describe:2 proven:1 denote:14 proves:1 exist:1 gradients:1 commuting:1 reexpress:1 functions:11 completeness:3 integrability:1 no:9 fixing:1 mathematica:1 generally:1 rewriting:1 application:1 other:4 role:1 details:1 conclusion:3 canada:2 elements:3 a10:1 models:3 preceding:4 setting:3 problems:2 polynomials:2 a0:5 generated:2 important:1 bounded:3 variable:1 opdam:3 bcn:2 implies:4 coupling:8 partitioned:1 nµ:7 assume:2 requires:1 space:12 turbiner:4 rule:1 equivalently:1 weights:4 wyllard:2 original:2
|
solv-int9810018.txt |@word represent:1 positions:1 since:4 partial:2 consider:19 pointing:2 funct:1 induces:2 magnetic:2 global:1 rod:6 results:5 gg:2 eds:3 scalar:7 proposition:28 klein:1 consists:1 remarkably:1 preferable:1 gk:198 gi:2 gh:3 devoted:4 whose:2 heller:1 γx:1 depend:1 remarkable:2 tx:4 acts:1 tt:3 tu:3 tr:36 γt:2 γk:14 finally:10 rg:33 indicate:1 present:8 elliptic:2 εijk:5 semenov:1 tg:13 te:4 presentation:3 norm:2 summarizes:1 p2:1 belonging:1 unsatisfying:1 g2:6 g1:6 orthogonal:2 very:3 translations:20 multi:1 geometrical:5 corollary:1 valued:1 putting:1 mps:2 formula:17 discretizations:6 difference:13 matrices:15 condition:4 look:1 generalised:1 hamiltonian:17 turns:6 anisotropy:1 sklyanin:1 list:2 solution:3 t0:12 t1:12 discrete:74 vector:32 fourier:1 small:1 study:1 reyman:2 semidirect:2 commented:1 des:1 consistent:2 direct:3 sign:2 translating:1 elegant:1 integrability:9 equal:2 further:4 defining:1 theories:1 expressions:5 substitute:1 linear:9 even:3 established:1 what:2 nonlinear:5 plays:1 stands:3 invertible:9 brackets:1 giving:2 fact:1 section:8 axes:2 brief:1 expressed:12 version:7 reconstruction:1 new:7 construction:3 d1:8 awk:4 consisting:1 cvk:1 body:30 led:1 notions:6 respectively:5 sommerfeld:1 proc:1 here:12 delivering:7 inverse:1 tangent:18 possibility:1 groups:11 represented:4 const:2 along:6 extrema:4 equations:77 implicit:2 change:1 calculate:3 obtained:2 shansky:1 remark:9 animated:1 weinstein:1 technical:2 shift:1 elaborate:2 larger:1 allows:11 experience:1 resulting:2 loop:1 poisson:26 permutation:1 usually:1 bp:2 suitable:2 makes:2 der:1 ξk:4 langer:1 uniquely:3 remembering:1 via:9 useful:1 viewpoint:1 arbitary:1 pinkall:1 vii:1 ls:4 conjugated:3 href:1 summation:1 apply:1 establish:2 unit:6 derivatives:6 use:8 additive:1 takes:3 working:2 prove:2 remains:4 contains:1 pedagogical:1 cζ:3 comparing:3 assuring:3 m1:6 opposed:2 m3:8 m2:6 e2:3 λmk:3 until:1 more:15 duals:1 introducing:4 equivalence:1 th:6 hermitean:1 points:1 started:1 becomes:3 operators:4 under:31 curvature:9 hirota:1 deserve:1 berlin:5 appendix:7 rigid:14 proceed:1 particular:5 known:10 iv:1 reconstructed:1 account:7 rotational:1 defines:8 announcing:1 integrating:1 deformed:1 recall:3 equation:43 work:6 mi:4 mk:116 mj:2 reviews:1 remain:1 mv:9 obvious:2 era:1 ms:2 mr:3 following:62 arrive:1 example:1 proof:19 beautiful:2 f1:22 f2:16 lectures:1 dual:2 figure:1 give:7 calculation:1 preserving:8 organized:1 purposes:1 accept:1 dependence:1 topic:1 vx:1 pulling:1 want:6 sense:1 every:1 rods:6 lacks:1 conversely:2 tan:1 absolute:1 counterpart:1 end:3 straightforward:1 rather:2 verify:1 get:3 length:1 write:4 maps:5 answer:1 instead:1 flow:15 firmly:1 parameter:4 priori:1 filament:2 map:27 product:11 express:2 ft:4 description:1 algebra:8 may:11 demonstrates:1 after:1 derived:3 different:3 applications:2 produce:1 lax:17 coming:1 multiplication:3 representations:4 choice:2 data:1 parallel:1 hoc:1 interrelations:2 remember:2 third:2 explicit:1 yielding:1 su:53 element:3 fortunately:1 cannot:1 so:33 sect:10 fundamental:4 seems:1 definitions:6 conjugation:2 words:3 order:10 typical:1 integrated:4 holds:3 interpretation:5 help:2 moerbeke:2 indeed:13 move:1 mainly:1 satisfied:2 gravitation:1 interpreted:1 course:5 paper:5 through:17 motions:4 reconstruct:3 mentioned:1 existence:2 kinetic:5 still:3 its:14 discretizing:1 lg:16 derive:11 group:22 τk:4 took:1 how:3 continued:1 fix:2 lk:3 coordinates:2 actually:5 complex:3 choose:1 mail:2 main:2 djm:2 h0:3 ge:1 correspondence:6 them:1 browser:1 pauli:1 combination:2 fragment:1 bernoulli:1 practice:1 fig:1 b2:1 geodesic:1 mention:2 theorie:1 hamilton:7 they:4 oxford:3 rotation:13 now:14 yu:3 discuss:3 continuum:1 easily:3 term:2 φk:22 equality:2 always:6 university:4 identified:4 sin:1 orthonormal:3 sufficiently:1 each:2 found:6 universit:1 trivializations:1 side:2 characterized:3 nonessential:1 homogeneous:1 ann:1 lifted:1 differential:14 another:2 formulate:3 independent:4 ablowitz:1 energy:6 directions:1 reduce:1 stronger:1 related:4 conventions:1 operator:2 m0:1 used:4 poincare:1 proportional:1 our:7 operation:1 differ:1 special:1 out:4 respects:2 shown:1 jimbo:1 matrix:18 involution:7 gradient:4 casimirs:2 lagrangian:26 bls:3 denotes:2 investigation:1 stud:2 denoted:2 rm:4 induced:19 ϕk:2 correct:1 math:14 shows:1 screw:2 uber:1 performing:1 turning:2 theory:14 assured:1 upon:1 encyclopaedia:1 diagonal:1 free:2 standard:9 tian:1 assures:2 completely:3 advantages:1 dynamics:1 ecp:3 put:2 van:3 anal:2 e1:3 qk:2 e3:13 rewritten:6 definition:7 chose:1 bates:1 derivation:5 language:1 r3:25 geometry:10 real:1 could:2 omit:1 motion:79 turn:3 technische:1 tempting:1 cos:1 consequence:1 inst:2 think:1 ℓk:10 first:13 origin:1 ℓx:1 features:2 symmetry:12 iη1:2 reprint:1 variables:4 pgk:2 thereof:1 twisted:1 restrict:2 date:1 spinning:6 done:1 directly:1 carry:1 precisely:4 seiler:3 angular:6 commun:2 equating:1 given:11 reference:5 similarly:4 introduction:4 πk:19 top:45 system:20 relations:2 their:3 brevity:1 statement:4 siam:1 variational:7 structures:2 gives:4 elasticity:1 calculations:1 explanation:1 continuous:19 2ak:1 supply:1 reflecting:1 differentiate:2 somewhat:7 consult:1 hε:5 convinced:1 than:10 dynamical:1 alternative:1 baxter:1 scheme:1 last:1 accordance:1 sections:1 distinguishes:1 capel:1 see:23 contemp:1 nevertheless:1 applet:2 future:1 contrary:1 str:1 were:2 naturally:2 distinguished:1 result:2 motivation:4 fashion:1 symmetries:1 rewrite:5 solitons:1 die:1 modern:1 argument:3 curves:15 departure:1 extremals:6 factorizations:1 manner:2 binormal:1 close:2 need:3 recover:1 any:3 viewed:1 underlines:1 lie:39 constructions:4 angle:2 built:1 zero:4 presents:1 check:1 convenient:6 latter:9 able:1 gravity:4 note:2 εl:5 k1:7 k0:6 square:1 generalized:1 analogy:6 finding:1 coincide:4 analogs:2 tool:1 εc:2 ulrich:1 heisenberg:10 gζ:25 exactly:2 cushman:1 allow:2 shall:7 relation:2 σj:1 sequence:6 systems:14 compare:1 preserve:2 most:2 connecting:1 germany:1 kk:3 representation:16 phase:2 intrinsic:1 class:3 appear:5 approximates:1 soliton:2 teubner:1 constructed:1 gk1:3 gk0:2 later:2 coincides:6 physica:2 traditional:1 bracket:31 principle:2 mechanical:4 velocity:5 left:29 physics:3 notion:1 came:1 applied:1 science:1 bending:3 simulate:1 show:2 reductions:1 text:1 authors:2 anyway:1 notations:9 developed:1 miwa:1 spaces:5 gauge:1 visualisation:1 substituting:1 d2:12 find:17 principal:2 rev:1 satisfies:3 ha:2 proofs:1 graded:1 λt:3 minus:1 state:1 should:2 moments:1 only:10 explicitly:1 coadjoint:2 subsection:3 rich:1 equipped:1 integrate:1 integrable:29 moser:4 local:2 oct:1 merged:1 do:3 legendre:10 ladik:1 notation:1 means:4 df:3 dg:17 de:3 fluid:1 famous:2 closely:1 ones:3 dx:9 suris:4 dw:23 dt:8 kk2:2 admissible:6 ds:3 quispel:1 unfortunately:1 πg:1 evolution:14 precession:1 initial:1 thg:3 textbooks:1 fields:1 arxiv:1 arclength:5 yield:3 method:1 rotationally:2 twice:2 underlying:5 schemes:1 common:1 ut:1 those:6 fixed:12 discussing:1 view:4 satisfy:2 set:6 computed:1 observer:1 achieved:1 physically:1 smooth:7 frame:38 differentials:2 j1:4 j2:4 j3:3 edition:1 namely:4 arc:1 descriptions:1 japan:3 terms:10 connected:2 bobenko:10 analog:4 subject:1 surfaces:1 instance:1 satisfying:2 tensor:2 ways:1 subsequent:1 cλ2:1 symmetric:3 web:2 written:5 determined:3 various:1 closed:2 between:11 invariant:25 geometric:3 before:1 conditions:2 verification:2 knowing:1 notice:11 recently:1 iterated:1 extend:1 nature:1 originated:1 literally:1 wm:3 adjoint:5 wk:169 veselov:6 however:1 ww:1 comm:1 algebraic:1 multiplier:2 solv:1 come:2 inertia:4 factorization:1 both:8 essentially:1 vrule:1 prescription:1 many:1 taking:3 patrick:1 hence:3 declare:1 mathematical:3 connection:2 symplectic:9 context:4 casimir:7 futher:2 attributes:1 summarizing:1 expression:3 comes:1 detailed:2 relevant:1 elaborating:1 pendulum:5 point:14 simple:4 cb:2 ca:3 moscow:1 cf:2 dimensional:2 distinguish:2 adaptation:1 lattices:1 lagrange:114 respect:22 tgh:3 writing:1 cu:1 torsion:6 nijhoff:1 described:3 publishing:1 second:18 λtk:1 addition:2 trajectory:1 invert:1 three:2 been:3 appears:1 ai:1 reduction:15 describes:2 axis:13 pg:2 basic:2 pj:2 pk:38 pi:1 ak:195 define:11 generating:3 corresponding:6 finishes:3 commutes:1 cotangent:8 quantities:2 concerning:1 hasimoto:1 protect:2 hmr:3 gap:1 extremum:5 observe:2 generalization:1 systematic:2 gag:2 c2:2 worked:1 denote:4 manifolds:2 instructive:1 case:22 p3:1 exception:1 p1:1 reparametrization:3 splits:1 unlike:1 rotations:2 might:1 shkoller:1 arnold:1 will:4 euclidean:4 while:1 suppose:2 momentum:3 pictures:1 situation:2 ǫy:1 property:3 0x:1 procedure:4 multivalued:1 inherits:1 identical:2 vectors:9 γn:1 almost:2 ctx:2 consecutive:1 vk:7 thus:2 non:1 according:7 reads:4 itself:4 exterior:1 claimed:1 ib:7 id:7 amended:1 containing:1 develop:1 considerable:1 variations:8 formulations:1 same:3 clearly:4 unity:2 parts:2 widely:1 units:1 products:3 proved:3 several:3 φn:2 development:1 fairly:1 finish:2 http:1 dǫ:10 solved:4 again:1 trajectories:1 tops:2 flows:3 hand:3 parametrized:3 action:39 moment:1 edges:1 moving:3 introduce:1 necessity:2 opinion:1 wk1:1 invariance:3 interested:2 opportunity:1 identity:1 task:1 delivers:1 center:2 java:1 k22:1 formulated:2 usual:2 well:11 obviously:3 concrete:1 solve:1 0l:3 components:2 fixing:1 coordinate:6 audin:1 subgroup:3 spherical:5 unified:1 manifold:3 background:1 just:2 less:5 being:6 resp:1 obtain:1 rest:14 golubev:1 λa:2 poinsot:3 identify:6 correspondences:1 immediately:4 love:1 k2:6 scattering:1 underline:1 λm:2 previous:4 adv:2 heuristic:1 bibliography:1 application:1 auser:1 characterization:1 character:1 parametrization:1 lattice:1 other:6 combine:1 easy:9 theorem:17 skl:2 extensive:1 transformation:10 euler:42 take:4 noether:8 aspects:2 around:5 depends:2 read:13 possible:2 corresponds:7 early:1 pairing:4 appendices:1 press:4 using:4 unique:1 moreover:1 εg:1 string:1 necessary:3 like:1 semi:1 identifying:2 systematically:2 follows:13 isomorphism:1 velocities:1 isotropy:1 specific:3 collect:1 vortex:2 santini:1 yields:1 starting:1 integrals:9 arbitrary:14 recalls:1 conclusion:1 reduced:14 terminology:1 framed:8 gη:3 www:1 right:23 integrators:2 methods:4 classical:10 formulas:7 absolutely:1 sequences:3 some:14 back:8 mech:1 understood:2 choosing:1 table:3 proper:2 ijk:1 τk2:2 ourselves:2 throughout:1 describing:4 lead:1 unreduced:1 fachbereich:1 though:1 integration:4 whole:1 defined:14 does:5 exposition:2 provides:1 ct:2 imply:3 tk:117 demonstrated:1 faddeev:1 problems:1 equivalent:13 plugging:1 cλ:1 viewpoints:1 variation:1 renders:1 trivialize:1 approximating:3 birkh:1 properties:4 simpler:4 deriving:1 about:3 trivialization:22 actual:2 would:1 constraint:1 basis:1 meaning:2 o:19 page:1 practical:1 recalling:1 important:5 nothing:2 stand:1 soc:4 insufficient:1 introduced:2 slightly:4 skew:1 ηg:1 considerations:1 discretization:14 cambridge:2 statements:1 polynomials:1 doliwa:1 into:16 multisymplectic:1 integral:28 functional:25 due:2 lies:2 because:1 references:2 lemma:13 sov:1 frames:8 factor:1 next:3 width0pt:1 k12:1 computer:1 additional:2 elastic:20 a0:2 springer:4 there:4 live:1 zamp:1 start:1 accordingly:1 appl:4 way:4 waw:1 call:1 ξg:2 was:3 therefore:10 function:80 complete:6 form:16 converse:1 denoting:2 singer:1 but:11 somehow:1 ratiu:4 properly:1 link:1 yang:1 agk:1 dy:1 inverted:1 pdes:1 hg:3 marsden:6 pull:7 algebras:3 applying:2 adler:1 versions:2 characteristic:1 gravitational:1 attached:2 up:2 us:14 theoretical:1 discretized:1 v1:3 limit:1 jω:4 uk:16 demonstrate:5 problem:2 similar:5 called:6 ωg:1 mechanics:15 linden:1 mrw:1 constant:8 ad:82 item:1 int:2 certain:1 abstract:1 aj:2 am:3 direction:2 general:9 twist:2 proves:2 au:3 aw:1 formulation:8 gradients:2 formalism:1 commuting:1 simplest:3 physical:1 ks:3 functions:14 compared:1 entirely:1 no:1 astonishing:1 mathematik:1 when:3 detail:1 multipliers:2 field:8 setting:2 role:1 details:1 normal:1 papers:1 trans:1 holm:1 nice:1 juni:1 elements:3 congress:1 finite:3 elastica:3 time:62 vertex:2 kirchhoff:5 bundle:10 a1:4 commutator:3 a3:2 a2:4 log:11 studied:1 included:1 double:1 2i:3 structure:7 source:1 independently:1 implies:4 assume:4 values:2 space:11 curve:24 orbit:1 rule:1 having:1 correspondingly:1 mass:2 parallelism:1 remarked:1 requires:1 original:2 once:4
|
solv-int9810019.txt |@word gu:1 partial:3 remarkable:1 similarity:1 lack:1 results:2 four:2 quadrature:1 edu:1 consists:1 localized:4 devoted:1 whose:3 depend:1 integral:3 auk:1 tu:1 tr:1 editors:2 finally:1 present:3 elliptic:10 under:8 p2:7 stud:1 very:1 rise:1 translations:2 exception:1 wave:1 putting:1 surprise:1 exact:12 immediately:1 u2x:1 permits:1 t2:10 solution:7 u2y:1 small:1 direct:1 cosh:1 second:14 pass:2 further:2 ode:3 theory:4 nonlinear:10 plays:1 11c:1 invertible:1 section:2 3u:3 3h:1 poles:3 above:1 scientists:1 new:5 method:8 satisfy:1 respectively:1 groups:5 equations:33 appears:1 logarithmic:1 obtained:4 technical:1 study:2 studied:2 allows:1 step:1 leaving:1 periodic:4 pick:1 action:4 suitable:1 classification:5 possessing:1 byrd:1 brought:1 establish:1 use:1 sake:1 next:1 few:1 live:1 type:4 more:4 brings:1 berlin:1 particular:3 known:7 cases:3 must:1 springer:3 integrating:1 science:1 equation:63 constraint:1 theories:1 values:2 codimension:7 following:4 making:1 2yt:2 ρz:1 example:3 bk1:3 dedicated:1 bk2:1 give:3 rodriguez:1 preserving:1 indicates:1 lorentz:2 numbers:1 degenerate:1 sharp:1 rescaling:2 occur:1 axis:2 provide:2 discussion:1 six:1 write:1 far:1 nontrivial:2 ordinary:8 verlag:1 parameter:2 classify:2 product:1 algebra:2 may:7 after:1 singularities:5 orbits:4 collection:1 applications:2 faculty:1 choice:1 constants:2 realized:1 computations:1 rather:2 so:2 sn:1 sl:2 order:16 fζ:1 fη:1 mainly:1 fξ:1 characteristic:1 produced:1 paper:6 through:3 existence:1 itu:1 its:4 boosts:1 solitary:1 derive:1 group:27 schwarz:2 ln:3 interesting:1 solving:3 coordinates:1 actually:2 forms:3 moebius:2 choose:2 jacobi:5 derivative:1 conjugacy:1 them:7 combination:1 bernoulli:1 kumei:1 scaling:2 mention:1 they:15 singularity:3 now:1 possess:1 2t:1 finite:2 invariants:4 university:1 classified:3 sufficiently:1 academic:3 2a:2 2b:3 irreducible:1 found:3 2h:4 referred:1 arxiv:1 another:2 list:2 reduce:4 used:3 t3:2 elementary:5 literature:1 static:1 quantum:4 our:1 summary:1 eq:11 abel:6 special:2 out:1 shown:2 ftt:3 space:12 restricted:1 singular:2 lagrangian:1 denotes:2 u2t:1 transforming:2 rational:2 reader:1 formula:3 ref:2 integrated:4 math:3 zassenhaus:1 linear:4 2h3:1 standard:7 admits:1 approaches:1 york:4 hand:1 noteworthy:1 conformally:3 bl3:2 motion:1 appearing:1 11a:1 gordon:4 hence:4 facilitate:1 first:10 symmetry:27 bluman:1 variables:14 waves:1 restrict:1 intuitively:1 simplified:1 directly:2 precisely:1 passes:2 given:4 similarly:2 introduction:2 leading:1 adopted:1 their:1 zeros:2 listed:2 recent:2 final:1 gives:2 similitude:11 grundland:2 mostly:1 always:1 x2:17 translation:1 than:6 coefficients:1 kind:3 showed:2 painlev:22 aims:1 limiting:1 winternitz:5 whenever:5 classes:1 were:1 treated:3 motivation:1 symmetries:3 rewrite:1 argument:1 manner:2 need:1 any:2 lie:4 fxx:1 zero:1 depending:2 convenient:1 h21:1 note:2 k2:9 k1:11 lectures:1 serov:1 normal:1 friedman:1 algebraic:3 remarks:1 class:2 nonlinearity:1 considered:2 ibort:1 km:1 points:2 physics:3 dot:1 dover:2 precise:1 12a:2 12b:2 12c:2 spaced:1 reductions:11 minimizing:1 solutions:36 substituting:1 find:4 dilation:1 based:1 knowledge:1 parameters:2 ngo:1 analytic:1 only:5 generators:2 subsection:2 integrate:2 integrable:4 achieve:1 dn:1 do:2 klein:4 means:1 dependent:5 kinks:1 ones:2 words:1 applying:1 gen:1 becomes:1 evolution:1 conditions:1 differential:16 2b2:3 3f:7 contain:1 view:1 exists:3 namely:3 individual:1 result:1 subject:1 instance:1 satisfying:1 µz:1 symmetric:1 osungen:1 written:2 determined:1 various:1 roots:4 closed:1 invariant:15 neither:1 numerous:1 publishers:3 terms:6 however:2 jr:1 solv:1 article:1 uφ:1 tractable:1 nlkg:6 conclusions:1 4h3:1 admit:1 und:1 context:1 ung:1 pde:1 otherwise:1 eulerlagrange:1 ch:1 kamke:1 cn:1 point:1 leipzig:1 translationally:1 polynomial:1 respect:2 bξ:1 turkey:1 most:1 described:1 transformations:4 basis:2 addition:3 odes:7 been:3 expressed:3 reduction:7 change:2 interest:1 combine:1 systems:2 conte:1 arises:1 corresponding:3 6f:2 systematic:4 olver:1 c2:3 c1:3 c0:3 those:2 case:4 p0:17 p1:16 pacs:1 value:1 remaining:1 will:11 while:3 property:13 conformal:6 engineers:1 planar:1 exceptionally:1 metric:1 ii:1 itself:1 generic:4 make:1 belong:1 poincar:8 complex:1 ince:1 dilations:3 physical:3 privileged:1 higher:2 independent:9 investigated:1 see:1 i1:2 i3:1 i2:2 multiplicity:2 moving:1 purpose:1 invariance:1 subgroups:13 lower:2 task:2 well:3 davis:1 analysis:6 barut:1 gambier:1 arising:1 dimension:2 subgroup:33 unified:1 among:2 being:2 obtain:10 transforms:2 spherically:1 rotation:1 boccara:1 kluwer:3 density:1 except:1 quadratures:2 setting:2 transformed:5 treatment:1 extensive:1 solvable:1 transformation:4 real:3 depends:1 possible:4 test:5 netherlands:2 using:4 fyy:3 dimensional:6 necessary:1 semi:1 obvious:1 reduces:1 performing:1 separately:1 either:3 integrals:1 arbitrary:4 essential:1 mathematical:3 satisfactory:1 often:3 classical:3 formulas:1 some:4 wwz:2 examples:1 b2:10 extended:4 ourselves:1 provided:1 dimensions:5 lead:1 integration:4 2xy:2 does:2 provides:1 2xt:2 l3:11 bf:1 run:2 power:1 11b:1 equivalent:1 host:1 substitution:4 periodically:1 tanh2:2 patera:1 package:1 discussed:2 meaning:2 o:1 reduced:12 distinct:2 transitive:1 book:1 ηf:1 transcendents:2 differentialgleichungen:1 h2:21 h3:15 into:7 h1:21 obtaining:1 h4:1 three:2 references:1 operator:1 movable:3 reducing:2 methods:2 log:2 fields:1 there:3 transform:4 specifically:1 why:1 appl:1 handbook:1 ξf:6 delocalized:1 was:1 function:5 form:13 hq:1 jun:1 but:1 pdes:1 partially:2 uy:1 ux:1 whether:1 minkowski:1 smooth:2 us:2 dordrecht:1 below:2 books:1 simplifying:1 similar:1 called:3 detailed:1 constant:6 af:19 int:1 abstract:1 general:5 enable:1 aw:1 constructed:1 tedious:1 again:4 functions:12 completeness:1 istanbul:2 no:6 mathematica:1 when:2 arctan:2 field:4 other:4 role:1 branch:2 papers:1 department:1 mathematics:1 verlagsgesellschaft:1 expressible:1 problems:1 generated:2 variable:7 structure:2 implies:1 original:2 4h:1 time:6 4f:3 4a:1 having:3 once:2
|
solv-int9810020.txt |@word unavoidable:1 evidence:1 consider:5 yasuhiro:1 caused:1 varying:1 desirable:1 results:5 pfaffians:1 indicates:3 scalar:19 computation:1 gn:11 research:1 scott:1 inverse:4 depend:1 containing:1 must:2 behave:1 indicate:1 manifolds:6 th:12 under:8 tf:6 analogous:1 pleasing:1 dramatically:1 norm:1 case:9 supported:1 amplitudes:2 jensen:1 straightforward:1 ladik:1 very:5 decreases:1 bilinear:2 ibj:1 induce:1 choice:6 grid:4 novel:1 lecture:1 discretizations:13 affect:2 difference:13 exact:4 adaptive:3 condition:4 internally:1 hamiltonian:2 turns:1 solution:31 large:3 discrete:20 vector:59 small:3 optics:1 round:1 dimer:2 slow:1 force:1 10b:2 10a:2 direct:1 pulse:3 cosh:1 integrators:1 second:1 displays:1 pass:1 dynamics:12 estimated:1 substitute:1 theory:4 even:5 nonlinear:20 appear:2 electronics:2 section:3 localization:1 brief:1 version:3 above:3 roundoff:2 new:2 ˆj:4 increasing:1 hb1:2 preserved:1 filled:1 hb2:2 satisfy:4 27a:2 27b:2 measurements:1 respectively:1 component:13 here:3 water:1 asymmetry:2 compose:1 sinh:5 represented:1 november:1 sine:1 equations:5 change:5 differential:1 obtained:2 shift:7 study:2 studied:2 completely:2 hiroshima:2 suggests:3 periodic:4 products:2 lightwave:1 pick:1 usually:1 suitable:1 studies:3 composed:1 via:7 useful:2 ratios:1 family:1 namely:2 explained:1 plenum:1 highly:2 eiφj:1 analyzing:2 verge:1 unit:7 eiωt:1 reflected:1 usa:2 remains:2 give:1 next:1 call:1 therefore:8 pont:1 associated:6 98e:1 type:3 until:3 more:11 separated:2 solitons:26 envelope:4 odinger:8 visual:1 backwards:2 particular:5 known:7 given:8 circumstances:1 high:1 account:1 valued:1 integrating:2 recall:1 equation:15 work:1 cai:1 values:4 following:4 example:9 proof:1 compare:1 figure:3 solved:1 calculation:1 discussed:5 allowed:1 neglected:1 near:1 generically:1 states:1 effectively:1 14b:6 14a:6 ist:8 occur:1 simple:2 absolute:3 end:1 decaying:2 turn:1 holds:3 feature:2 regions:6 far:1 nontrivial:1 carrier:1 acta:1 ordinary:1 parameter:2 sin:3 exponentially:1 product:1 replacing:1 max:1 earlier:1 derived:4 different:5 reflect:1 applications:5 faculty:1 date:3 wave:25 data:16 response:1 fn:9 times:1 natural:4 clarkson:1 effective:9 light:1 grant:2 correspond:1 perhaps:1 so:3 order:8 superscript:1 restriction:2 indeed:4 over:3 suris:1 vary:1 discretization:21 produced:1 paper:1 through:1 left:1 japan:1 satisfies:3 still:2 ieee:2 its:2 depending:1 before:2 solitary:40 rapidly:2 forwards:1 decay:1 kagamiyama:1 interesting:1 temporal:1 coarser:1 coordinates:1 actually:3 b1:9 previously:1 f49620:1 degrees:1 systems:13 constitutes:1 december:1 eη2:3 eη1:4 menyuk:2 them:2 return:1 thereby:1 ahn:2 polarizations:7 practice:1 22b:2 mention:1 tails:1 effects:5 they:4 now:1 discuss:1 term:5 several:1 hereafter:1 2rn:1 instances:1 fixed:1 always:1 university:5 kerr:1 neutron:1 each:9 crossing:1 found:2 side:1 referred:2 subset:1 kutta:1 schemes:7 ei:2 eh:4 evolve:2 experiment:2 series:1 frequency:2 reduce:1 used:2 applicable:1 constitute:1 society:1 investigated:2 expect:1 measurement:1 navy:1 our:2 eq:9 special:5 out:1 matrix:2 space:9 restricted:2 wise:1 since:1 squared:1 chaos:19 denotes:4 investigation:1 multiply:1 longtime:1 formula:2 rn:10 induced:2 issue:1 integrated:5 tori:1 shows:3 after:2 linear:5 interactions:9 kaup:1 diagonal:1 possibility:1 approaches:2 complicated:1 york:1 estimate:4 definition:1 interaction:22 derivation:1 could:1 david:1 motion:2 manakov:4 gordon:2 hence:6 retain:2 generalizations:1 crossings:2 speeds:1 first:2 there:8 symmetry:1 striking:1 waves:22 number:4 reaches:1 multiplication:1 another:1 impossible:1 open:2 size:3 differ:1 perturbation:7 errors:3 table:8 similarly:1 introduction:1 interact:4 system:55 construct:2 name:1 their:4 perturbations:8 constants:1 tol:2 siam:2 scheme:4 structures:1 2fn:1 recovered:1 inner:2 shifted:3 polarization:21 asymmetric:4 reversed:1 continuous:2 accurately:1 transverse:3 optical:4 manifestation:2 focusing:1 off:1 july:1 than:3 coefficients:1 dynamical:1 18b:1 mclaughlin:1 18a:1 showed:1 log10:2 require:1 integrability:8 final:8 future:1 intensities:1 amplitude:5 sech:4 gives:1 exhibit:3 symmetries:1 generality:1 bhn:1 quantitative:1 arg:3 locations:2 generalization:8 randomly:1 conjugate:1 need:1 seen:1 constrained:2 any:9 iφj:1 lie:1 regime:1 latter:1 propagation:5 mechanism:1 converges:1 onset:1 ih2:1 edge:1 take:2 analogy:1 finding:1 negligible:1 n00014:1 unperturbed:1 spectral:3 begin:1 elastically:2 electric:3 iφ2:1 opposite:1 most:3 qˆn:1 regular:1 significant:2 formulae:2 pair:4 analytically:1 extremely:1 class:6 trapping:2 soliton:73 constructed:2 considered:7 chosen:1 later:2 dod:2 irregularity:2 proceedings:1 points:1 ohta:3 distinctive:2 typical:2 physics:5 notion:1 fact:5 qˆj:4 nls:28 particularly:1 phenomenon:1 intensity:6 show:2 rtn:4 contemporary:1 herbst:4 relation:2 solutions:37 find:2 q1:1 q2:1 based:1 parameters:10 situations:1 less:1 only:8 tolerance:5 candidates:1 intrinsically:1 integrable:27 oct:1 boulder:5 do:5 envelopes:1 get:1 dependent:1 air:1 simplest:1 overall:1 cannot:2 invariant:2 elliptically:1 dt:9 sill:1 routine:4 segur:1 evolution:4 exhibiting:1 continuum:3 covering:1 approach:1 arxiv:1 method:3 investigate:2 experiments:2 qe:1 common:1 though:3 analytical:5 london:1 qj:15 discussing:1 qn:78 ignored:1 set:1 computed:2 physically:1 observed:4 irregularly:1 see:6 computer:1 merits:1 result:4 existence:3 analog:2 subject:1 closer:1 grønbech:1 fn2:1 speed:4 away:1 consequence:2 symmetric:40 numerous:1 outside:1 determined:1 closed:1 between:8 limit:7 boundary:5 conditions:8 multiplied:1 comparable:4 responses:2 nature:2 attention:2 transpose:1 however:11 key:1 solv:1 jetp:1 problem:3 both:5 cos:1 philosophically:1 irregular:3 many:2 taking:3 equal:2 sensitive:1 admit:1 manifestations:1 symplectic:1 distinction:1 pde:12 disappears:1 ck:8 cj:21 hold:1 separation:1 pendulum:1 conclude:2 reasons:1 had:1 asymptotically:2 homoclinic:9 ce:1 dimensional:4 grants:1 simply:1 confirmed:1 moreover:3 cq:1 strong:1 described:1 cqn:3 basis:10 addition:2 19a:5 radiative:1 due:6 been:4 mark:1 ran:2 reduction:9 slowly:2 19c:5 ah:3 expected:1 compatibility:1 19b:1 meeting:1 define:1 θj:5 direction:1 corresponding:2 6e:1 scalars:1 excite:2 fractals:1 observe:1 decreased:2 c2:17 c1:7 careful:1 former:1 present:1 applied:7 multi:5 p1:4 limits:9 unlike:1 value:5 transformation:5 will:8 while:5 p2:4 replaced:1 behavior:7 error:13 dms:2 property:1 unitary:4 coupled:1 chaotic:13 vj:2 non:4 vn:2 ii:5 examined:2 vt:1 january:1 technology:1 encompass:1 acknowledgments:1 higashi:1 fibers:5 generic:4 suggest:1 corresponds:1 radiation:1 same:7 shifts:4 complex:9 emphasize:1 runge:1 resulting:2 finite:9 prerequisite:1 development:1 independent:6 literature:1 peaks:3 numerical:24 upon:2 hand:1 average:1 levels:2 user:1 infinite:1 brussels:2 ablowitz:10 prescribed:1 birefringent:3 schr:8 whereby:2 whole:2 nonetheless:1 well:7 analysis:1 thought:2 without:5 57e:1 components:8 position:1 model:3 soviet:1 dimension:2 usual:1 eilbeck:1 distances:1 surveys:1 manifold:2 ae:1 among:1 being:1 generally:1 proximity:2 applicandae:1 obtain:1 pfaffian:1 shape:1 underlying:1 identify:2 part:1 campbell:1 scattering:8 yet:1 note:5 rapid:1 preprint:1 hpj:1 seems:1 mathematically:2 lattice:1 other:5 location:2 16e:1 iπ:1 apart:1 plasma:1 excited:1 ought:1 inelastic:1 march:1 depends:2 read:1 spatial:4 february:1 cf:2 boxes:2 were:3 21b:4 makes:2 21a:4 press:2 accurate:1 2q:1 multiplexing:1 loss:2 nsf:1 necessary:1 like:1 sizes:1 splitting:1 reduces:4 noted:1 unstable:1 either:2 arbitrary:3 qxx:2 stationary:1 mathematical:1 shed:1 because:7 methods:2 classical:1 mathematicae:1 phenomena:1 play:1 library:2 self:3 examples:1 b2:8 specified:1 2qn:6 chakravarty:1 iφ1:1 electromagnetic:2 shall:2 integration:5 conservative:2 waveform:1 defined:1 does:4 yields:1 moderate:2 kenkre:2 demonstrated:1 refer:5 june:1 equivalent:3 bh:2 bj:17 although:1 eiφ:1 properties:4 transformations:1 chapter:1 comparison:1 would:1 extension:1 constraint:2 column:1 freedom:1 quasilinear:1 introduces:1 o:2 simulation:9 compatible:1 range:1 a2:4 schober:3 bloch:1 tsironis:1 perturbed:1 cambridge:1 letters:3 colorado:5 computes:1 82e:1 h2:10 numerically:3 ηj:1 22a:2 down:1 phase:11 appropriate:3 right:2 references:1 determine:5 operator:1 proportional:1 tabulated:1 often:1 log:2 elastic:3 interacted:1 measured:2 support:1 initial:17 question:1 transform:1 long:13 review:6 width:1 low:1 salerno:1 forward:9 was:9 function:3 considerably:1 medium:1 form:19 some:7 differences:2 but:2 volume:1 pj:2 hn:4 proportionally:2 line:3 manifests:1 true:2 truncation:3 directed:1 october:1 compute:1 whether:2 iqt:2 uq:1 ωt:1 us:1 ωj:9 those:3 sum:1 demonstrate:3 distribution:5 similar:1 clear:1 regimes:2 strongly:3 constant:4 af:1 int:1 certain:4 abstract:1 aj:16 deep:1 general:17 oscillations:1 engineering:1 exist:3 physica:1 simulations:12 journal:4 floating:1 whiskered:1 bishop:1 computational:2 physical:9 nh:2 again:2 compared:2 nag:3 garnier:1 no:5 individual:9 when:6 detail:1 field:5 priori:1 role:2 papers:1 department:3 mathematics:7 arithmetic:1 briefly:2 denote:1 superposition:1 separate:2 subspace:1 hirota:3 drift:1 variation:1 a1:4 important:5 peak:2 vectors:5 variable:4 structure:3 implies:2 assume:3 hp2:2 hp1:2 packets:1 having:1 equivalently:1 write:1 dot:1 time:31 push:1 backward:7 requires:1 original:2 quantum:2
|
solv-int9811001.txt |@word minoru:1 partial:1 desirable:1 results:1 four:1 gl:1 whose:1 calculate:1 iii:2 tp:2 tq:2 tl:3 elliptic:2 γl:1 include:1 2γi:1 far:1 witten:1 dim:1 school:1 esα:1 presented:1 yamada:1 irreducible:3 notes:1 t2:2 vector:3 science:2 zn:3 says:1 zi:1 eλn:2 zero:3 mj:3 odd:1 canonical:2 bilinear:22 what:1 stands:2 eδt:3 section:2 expressed:1 current:2 above:5 ˆg:1 new:2 method:3 coefficient:1 respectively:2 realizations:1 here:7 modular:1 situation:1 equations:17 z1:3 obtained:4 remark:6 kanno:2 hiroshima:1 action:3 t22:1 schur:1 via:3 useful:1 projection:1 apply:1 univ:1 research:1 virasoro:2 use:1 chf:1 contains:1 γi:3 next:4 rao:2 few:1 linear:5 approach:1 call:2 chv:1 m2:1 associated:3 type:10 theoretical:1 more:1 flat:2 becomes:1 operators:1 under:1 odinger:1 particular:5 known:7 eα:3 eβ:3 ajν:1 ml:2 equation:4 mi:2 mh:1 preliminaries:1 klt:1 obvious:1 kls:1 following:9 root:9 example:2 deg:2 dxi:5 give:2 dxs:3 dxr:2 saito:4 dxl:1 cartan:2 degenerate:4 yang:1 end:2 discussion:2 acts:5 how:1 pure:1 frenkel:1 simplicity:1 express:1 algebra:27 derived:1 orbits:1 lax:2 faculty:2 representations:13 sy:2 sr:3 sp:4 element:6 sk:4 sj:3 gtor:19 so:3 sn:3 sm:1 sl:6 representation:6 satake:1 least:1 interpretation:1 dx:8 hierarchy:6 developed:1 over:1 y1:1 japan:3 satisfies:5 still:1 its:7 roots:2 τn:14 laced:1 τm:3 group:4 symmetry:8 affine:9 li:2 forms:11 systems:3 lp:1 derivative:2 might:2 image:1 yi:3 non:6 yj:1 yn:4 introduce:6 they:2 ys:3 bigger:1 invariants:1 university:3 2y:3 orthonormal:2 x21:1 toroidal:11 each:2 2m:3 2n:2 kyushu:1 2h:1 lorentzian:1 homogeneous:8 el:5 arxiv:1 weight:2 series:3 functor:1 toda:1 our:4 special:5 category:2 shown:2 acknowledgment:1 3rd:1 space:2 gˆs:2 furthermore:1 since:3 gradation:3 denotes:1 gˆ:1 geom:1 denoted:3 rh:3 math:5 theory:3 standard:1 base:1 τn2:1 put:1 e0:2 definition:2 pairs:2 zjl:2 ahler:2 signature:1 hence:2 first:1 xj:8 xk:1 xi:1 xn:2 xl:2 variables:4 number:1 rank:1 system:2 restrict:1 relations:2 given:1 dedekind:1 tor:24 twisted:2 construct:5 their:2 realization:10 exponents:1 gpr:2 progr:1 ch:1 exactly:2 realized:1 part:1 j2:1 htα:1 authors:1 x2:3 dx2:1 believe:1 pne:2 showed:1 kenji:1 namely:1 preparation:1 classes:1 decompose:1 hz:5 ueno:1 epr:5 topics:2 generalization:3 recover:1 ω1a:5 any:2 lie:37 petviashvili:1 self:1 mills:1 note:3 k1:3 εn:2 εi:1 generalized:3 coincide:1 kac:4 even:1 gα:1 shall:1 birkh:1 algebraic:1 regular:1 letter:3 pair:1 subset:1 class:2 appear:1 indu:1 soliton:8 kk:1 ki:1 kh:1 kn:3 kl:1 kp:1 kw:4 kv:1 ku:1 physics:1 nls:1 show:1 purely:1 relation:1 solutions:13 pke:1 centralizer:1 d4:1 principal:7 completion:2 dls:2 finally:1 wzw:2 topological:1 lemma:4 only:1 candidates:1 inami:2 integrable:2 oct:1 hope:1 do:1 dl:6 dk:1 means:1 df:1 dg:1 de:1 da:3 ϕl:2 ϕk:7 dw:10 dt:3 gel:3 fields:1 differential:4 common:1 view:2 set:16 exists:1 j1:1 module:6 mentioned:1 see:4 theoretic:1 commutation:2 ul:1 representatives:1 symmetric:2 written:1 future:1 dlt:1 αi:5 invariant:2 αj:1 conditions:1 deformation:1 x22:1 terms:2 hecke:1 dxj:1 jr:1 ika:1 comm:1 solv:2 thank:1 both:1 essentially:1 eta:1 casimir:2 comment:1 coxeter:1 point:2 simple:3 character:1 dimensional:10 simply:1 moreover:2 pr:9 lect:1 duk:3 transformations:2 dun:6 basis:2 union:1 mey:1 locally:2 sl2:8 int:2 much:1 interest:1 basic:4 pk:1 algebras:15 pn:2 abstract:1 choose:3 cambr:1 generating:3 arises:1 corresponding:1 concerning:1 general:1 xiong:1 kashiwara:1 present:1 case:4 look:1 exponential:2 τs:1 will:1 suppose:1 du1:1 vj:1 vk:1 thus:2 vn:5 iv:2 ii:3 cocycle:1 dual:1 make:1 lett:1 hierarchies:2 finite:4 subalgebra:4 φn:7 higher:2 independent:2 zumino:1 extended:1 wakimoto:3 t21:1 auser:1 infinite:2 invariance:1 2u1:1 schr:1 nevertheless:1 well:2 coordinate:1 model:2 arising:3 possesses:1 posses:2 resz:1 yoshihisa:1 obtain:4 actions:1 sdym:2 facts:1 λn:3 adt:1 preprint:1 ads:1 fukuoka:1 regarded:3 seems:1 lattice:1 setting:1 treatment:1 theorem:6 moody:2 transformation:1 gave:1 spanned:1 know:1 press:1 mod:2 like:1 follows:6 δt:3 δp:2 collect:1 ai:1 δm:1 korteweg:1 either:1 because:2 iohara:2 some:5 understood:1 examples:3 respect:7 kdv:4 2d:2 2φn:2 everything:1 compute:1 proc:1 numbers:1 kyoto:2 step:1 symp:1 liouville:1 cε:4 central:2 would:1 extension:2 o:1 compatible:1 stand:2 2x1:1 idg:1 em:2 primitive:1 into:2 references:1 wess:1 operator:1 yokonuma:1 log:50 there:2 yoshii:2 jsps:1 way:1 ed:1 m1:1 exceptional:1 was:2 suzuki:1 naturally:1 function:4 form:12 regard:1 but:3 introduction:1 construction:1 related:2 delta:2 highest:3 dus:3 applying:1 embedded:1 up:1 us:6 considered:1 ωk:1 un:4 uk:4 uj:1 define:6 similar:1 called:3 constant:1 prepotential:1 defined:3 universal:1 describe:2 fellow:1 2dw:1 graduate:1 rewriting:1 field:1 other:1 zαi:1 department:2 mathematics:3 nice:1 elements:6 denote:1 exp:25 vertex:10 polynomials:1 a1:2 generated:4 eφn:2 variable:1 structure:4 dvn:1 hiroshi:1 vries:2 modules:1 eαi:1 hirota:15
|
solv-int9811002.txt |@word neighbors:5 consider:8 chain:4 global:1 results:6 four:1 roy:1 gl:2 contributions:1 causes:1 depend:4 tl:12 tk:1 under:4 include:2 applied:3 presently:1 straightforward:1 zhang:6 very:2 choice:2 electron:8 every:1 emphasized:1 matrices:1 encounter:1 annihilated:2 solves:2 presented:6 guk:1 positions:2 sklyanin:1 solution:8 try:1 solved:1 vector:1 phase:4 math:4 pbc:2 eigenvalues:4 superalgebras:1 attracting:1 employing:1 sℓ:1 direct:1 past:1 fold:1 imply:1 deutscher:1 arrachea:1 substitute:2 established:1 plays:1 section:6 3p:2 expressed:1 version:2 above:2 new:9 increasing:1 method:1 contrast:1 satisfy:1 condensed:1 wavefunctions:7 exchange:1 respectively:2 here:8 bariev:1 them:3 ansatz:17 groups:1 along:1 equations:24 obtained:2 instituto:1 institute:1 shift:4 vectors:2 pi:1 periodic:18 products:2 ξ2n:8 action:13 hospitality:1 involves:1 formulated:1 highly:2 translational:1 total:3 unit:1 use:2 eψ:1 would:2 ψr:2 supergroups:1 contains:2 finally:1 angela:1 next:2 distributing:1 comparing:1 nucl:2 ξl2:3 call:1 therefore:2 assistance:1 type:8 bethe:17 more:3 separated:6 sigaud:1 operators:1 ti:2 everywhere:1 particular:1 cases:4 iii:2 must:1 gℓ:1 permits:1 deformed:2 recall:1 equation:15 work:1 modified:1 ufrgs:1 values:3 following:15 meet:1 arrive:3 example:2 links:7 give:1 calculation:1 arise:1 organized:1 states:21 numbers:1 degenerate:1 sense:2 occur:1 guarantee:1 verify:1 breaking:1 feature:1 b408:1 far:3 nontrivial:1 parameter:4 product:4 proc:1 mat:1 algebra:16 may:2 derived:3 containing:1 alegre:1 applications:1 plane:4 amparo:2 physik:1 waves:1 representations:5 law:1 types:1 sz:1 calves:1 caixa:1 sectors:3 spectra:2 lines:1 korepin:3 si:5 so:2 grande:1 sl:1 representation:2 order:3 acts:2 a27:2 subtracting:1 developed:1 move:2 satisfied:3 produced:2 course:1 paper:3 through:6 gould:2 statistical:1 satisfies:1 its:3 before:2 derive:1 group:6 thank:1 maps:1 energies:1 interesting:2 fix:2 vicinity:1 systems:2 kuniba:1 main:1 deformation:1 correspondence:1 austauschdienst:1 non:4 within:1 combination:2 janeiro:1 framework:1 they:5 bazhanov:1 employed:1 brasileiro:1 now:10 nor:1 aligia:1 porto:1 term:4 2p:9 2q:8 temperley:4 classified:1 identified:1 fs:1 orthonormal:1 each:1 2n:1 carlos:2 baxter:1 ei:1 another:1 weight:1 doing:1 series:1 energy:10 related:1 gun:2 used:1 expect:1 quantum:14 our:1 eq:2 frappat:1 special:2 out:2 batchelor:1 shown:3 gon:1 matrix:1 rs:1 since:3 rev:5 denotes:1 acting:2 investigation:1 adapt:1 denoted:1 akademischer:1 get:10 ref:2 rj:1 shows:1 arnaudon:2 linear:3 interactions:1 ısica:1 fisica:1 departamento:1 quite:1 reason:1 e4:3 e6:7 e3:6 publication:2 definition:3 pairs:1 could:2 keep:1 prester:2 isotropic:2 qn:1 generalizations:1 essler:2 first:5 already:1 symmetry:1 wave:3 number:1 twisted:1 peculiarity:1 utilized:1 directly:1 electronic:1 between:2 affords:1 interchange:2 given:5 rewritten:1 similarly:1 introduction:1 interact:1 system:4 construct:3 their:2 convention:1 potts:1 gives:3 free:4 a30:1 exactly:1 reflecting:1 translation:1 operates:1 kind:1 kulish:1 jumps:1 was:9 require:1 zero:2 annihilation:1 matter:1 determined:2 amplitude:1 were:2 stz:3 exhibit:1 sees:1 2πl:1 acknowledged:1 spectrum:2 acknowledgment:1 hoppings:1 recover:1 seek:4 lie:2 multiparametric:2 convenient:1 isolated:1 k2:96 k1:92 potential:1 generalized:3 alcaraz:1 calculus:1 play:1 shall:2 consistency:1 centro:1 impurities:7 algebraic:3 propagate:1 pair:2 karowski:4 class:3 tensor:2 exact:1 parametrize:2 b419:1 neighboring:2 ki:1 later:1 traditional:2 yang:1 electrons:2 xavier:1 left:2 physics:2 sum:3 fact:3 sector:14 incorporate:1 sul:1 particularly:1 tecnol:1 implying:1 spaces:1 relation:2 solutions:1 substituting:5 superalgebra:1 trivial:3 find:6 occupation:1 believe:2 parameters:4 eigenspace:1 written:1 should:1 only:2 writen:1 integrable:2 mechanics:1 hamiltonians:4 local:2 oct:1 do:8 notation:2 means:3 de:10 da:1 ones:1 combinations:1 applying:2 dr:1 neither:1 itzhak:1 conditions:24 arxiv:1 summary:1 qc:1 bae:2 she:1 mapped:1 including:1 view:2 set:7 computed:1 exists:1 chryssomalakos:1 module:2 grosse:2 relative:1 cbpf:1 see:5 result:1 terms:4 ur:1 prototypical:1 brazil:3 satisfying:1 imposition:1 federal:1 funda:2 sites:3 underline:1 boundaries:6 state:5 closed:19 simplest:1 invariant:11 boundary:33 approach:5 notice:2 recently:4 hecke:1 extend:2 however:1 pseudoparticle:15 gratefully:1 unnormalized:1 solv:1 configuration:1 both:2 last:3 biquadratic:1 many:1 according:1 ısicas:1 contribution:1 expression:1 among:1 ci:14 co:1 point:2 simple:3 corresponds:1 parametrization:4 dimensional:1 respect:2 appeared:1 kp:6 described:1 basis:3 addition:3 simplification:1 due:2 been:3 int:1 cient:1 describes:1 treat:1 interest:1 anisotropic:4 algebras:1 define:3 arises:1 supersymmetric:2 xxz:2 bulk:10 observe:1 systematic:1 demand:1 general:2 spin:16 case:11 solvable:1 will:10 near:5 fub:1 behavior:1 ıfico:1 situation:1 procedure:3 a21:5 larger:2 a24:1 coupled:2 a29:4 thus:3 site:1 iv:2 ii:2 rio:2 cond:1 susy:1 different:1 santos:3 hubbard:2 generic:1 same:6 paulo:1 shifts:2 complex:1 split:1 diagonalize:2 modification:1 investigated:1 singapore:2 again:1 effect:1 zapletal:2 parametrized:2 invariance:3 estado:2 reference:1 correspondent:1 hopping:2 well:3 solve:5 easily:1 coordinate:6 position:1 model:13 dimension:1 usual:4 distances:1 world:2 graded:5 proposed:2 being:5 boer:1 obtain:7 via:1 thanks:2 integer:1 ogico:1 momenta:2 eigenstates:6 previous:1 accepted:2 conclusions:1 seems:1 except:1 nacional:1 lattice:2 conselho:1 lett:7 diagonalization:2 pseudoparticles:17 eigenstate:3 momentum:1 build:1 real:1 eigenfunction:1 eigenvalue:14 read:1 possible:2 spanned:1 know:1 using:8 variants:1 postal:1 mod:1 translationally:1 theor:1 appearing:1 like:1 follows:2 reduces:1 manifest:1 ai:3 pesquisas:1 martin:2 schadschneider:1 parity:1 right:2 methods:2 creation:1 some:1 irrelevance:1 understood:1 examples:1 moreover:3 provided:4 lima:3 theoretische:1 grading:1 bento:1 fapesp:1 subclass:1 ξp:2 does:1 provides:1 chains:5 bd:1 eigenfunctions:1 pesquisa:2 scientific:2 problems:1 equivalent:1 rua:1 analysed:1 relating:1 qni:2 proceed:1 carried:1 extension:2 extending:1 discussed:3 desenvolvimento:1 carries:1 connected:1 introduced:2 projectors:1 automatically:1 lieb:4 soc:1 additionally:1 presence:1 into:13 h1:1 ξ1n:2 down:2 lies:2 hermitian:1 sov:1 operator:12 financial:2 uk2:1 support:2 there:1 u1:3 u0:24 u2:2 start:2 cocommutativity:1 ed:1 sections:1 schoutens:1 daad:1 complete:3 form:2 differences:2 but:3 hk:1 hi:3 hn:2 cnpq:1 highest:1 considerable:1 foerster:5 made:1 compute:1 consist:2 versions:1 uq:5 up:2 us:10 tell:1 un:5 limit:1 uk:17 bracken:1 problem:2 similar:2 called:1 strongly:3 cbc:2 ac:1 adopt:1 associated:7 defined:4 certain:1 aξ:2 describe:1 condition:1 ao:5 denote:1 single:2 av:1 corresponding:5 hamiltonian:10 commuting:1 universidade:1 physical:1 ni:22 no:1 when:10 vanishes:2 other:2 role:2 details:3 er:1 expected:1 generates:1 excitation:1 a12:6 models:13 ξr:8 remarked:1 vertex:3 a1:12 ξi:1 meaning:1 a2:9 ξl:17 allowing:1 ξn:6 ξa:9 ξb:9 impurity:7 building:1 correlated:9 coupling:1 4x:1 space:1 l69:1 interacting:4 rule:1 eiθ:2 starting:1
|
solv-int9811003.txt |@word replacing:1 concept:1 interpret:2 consider:31 remarkable:4 both:5 primed:6 subscripts:1 four:5 eds:1 commute:9 pronko:1 contradict:1 consists:4 gn:27 expressions:2 manipulations:4 contributions:1 row:2 ihep:2 particles:1 inverse:1 depend:4 calculate:4 centres:4 graph:27 equivalence:27 γj:6 uniqueness:2 tj:1 arisen:1 th:6 analogous:2 te:14 tb:17 struik:1 ta:15 p2:2 g4:1 g3:1 summand:1 made:1 very:4 rise:1 cwn:1 geometrical:3 crosses:2 every:2 figs:1 circled:1 formula:1 y1:1 difference:2 matrices:17 condition:8 generalised:4 aσ:2 immediately:4 hamiltonian:1 did:1 positions:1 bσ:2 list:3 solution:8 t1:5 try:1 discrete:7 proposition:4 minimal:1 dealt:1 indices:10 gauge:7 straight:2 related:1 application:1 specially:1 zj:37 zk:3 pass:1 direct:3 sign:2 sergeev:14 surrounding:4 zero:13 proved:1 deutscher:1 j22:1 corner:2 further:9 rectangular:2 zp:8 remarkably:1 substitute:2 canonical:3 bilinear:1 south:1 what:2 nonlinear:1 const:1 appear:8 invertible:1 giving:4 trivial:2 section:7 symbolically:1 d3:6 current:28 above:6 flowing:1 new:4 t2:6 principal:1 method:2 3d:29 body:3 compact:1 outgoing:7 simultaneously:1 chose:1 degree:1 fiz:1 never:2 component:4 equals:1 here:11 diagonal:2 quasimomenta:3 simplices:1 objects:8 ansatz:2 sinh:2 exponent:1 alone:1 path:1 κv:2 invented:1 equations:25 appears:8 change:10 obtained:6 remark:1 property:4 incoming:1 northern:2 structures:1 remarks:2 institute:1 shift:6 changed:2 allows:4 bv:1 mx:1 binomial:1 products:1 permutation:6 usually:3 surely:4 proof:1 changes:4 der:3 uniquely:2 appropriately:3 formulated:3 useful:6 classification:2 extra:4 namely:3 z1:1 planar:3 marked:1 highly:1 visible:1 f3:1 wk:1 protvino:1 summation:1 apply:3 b224:1 imaginary:1 linearly:1 orientation:2 standing:1 use:6 y2:1 takes:2 would:4 prove:2 sake:1 nine:1 contains:3 direction:2 finally:1 next:3 few:5 nucl:1 explicitly:2 call:10 therefore:2 vi:9 taken:4 veb:1 simpler:1 type:11 bethe:1 more:6 sort:4 introducing:2 vk:4 formally:4 integers:1 becomes:5 operators:19 curvature:4 t3:6 tested:2 berlin:2 correspondingly:2 everywhere:1 labelled:2 separates:1 known:4 projective:9 cases:1 hold:1 r1:15 zi:5 obeying:1 valued:4 quantized:2 integrating:2 unessential:3 recall:5 equation:39 work:2 det:26 modified:2 theories:1 alexey:1 remain:1 values:2 columns:2 ms:1 resembles:3 following:20 making:2 example:13 def:3 numbers:4 unknown:1 nearest:2 f2:2 omit:1 korepanov:21 figure:12 give:15 relativistic:1 permutations:2 demands:1 hexagons:1 states:5 something:3 sense:5 triangle:7 yβ:1 algebraical:1 ratio:1 normalize:1 needs:1 vanish:2 end:1 dilogarithm:9 rather:2 verify:1 divided:1 means:13 feature:4 makes:2 maps:5 nontrivial:2 commutative:9 pair:1 connect:2 adjacent:1 instead:4 constraints:1 parameter:1 classify:1 stand:4 map:40 product:9 express:1 description:1 algebra:23 may:21 thermodynamic:1 after:1 derived:5 connects:1 fa:1 fb:1 fc:1 considers:1 fj:4 choice:2 data:3 parallel:2 refuse:1 natural:5 dynamical:21 resemble:1 invariants:1 maybe:1 δi:1 lines:17 correspond:2 su:1 element:6 provide:1 switch:1 sh:1 so:38 expression:3 fundamental:5 s2:2 representation:5 sw:1 superscript:1 xj:10 six:4 interpretation:8 help:4 produces:1 hierarchy:1 over:3 spectral:6 mainly:1 conserving:3 interpreted:2 combinations:1 paper:6 through:2 looks:1 statistical:2 signs:2 mentioned:10 existence:2 still:4 pointer:3 its:11 expansion:1 write:6 derive:1 outer:6 symmetry:1 φa:8 jacoby:1 interesting:4 fix:3 solving:3 li:2 initial:1 φc:4 degrees:1 fig:25 mathematicae:1 diagonalize:1 mail:1 hidden:1 main:5 might:1 maillard:1 lx:12 arguments:3 versus:2 homotopy:4 them:15 good:2 return:2 φf:4 descendants:1 integral:4 φg:5 introduce:12 primary:3 scaling:1 mention:3 volkov:2 multiplicative:1 they:5 bazhanov:10 ψf:3 yp:8 singularity:1 now:27 yu:8 discuss:3 nos:1 eigenvalue:2 term:4 several:2 equality:5 dilogarithms:1 always:1 university:1 b3:11 2d:10 theory:3 l2:10 l3:2 toroidal:4 l1:20 repeating:1 degasperis:1 side:19 s1:2 mean:2 baxter:26 domain:2 weyl:21 ei:3 directly:5 formulate:3 series:4 leonard:1 ea:1 ec:1 eb:1 elementary:3 abelian:1 strips:2 obtains:2 ez:1 quantum:23 our:8 along:2 eq:1 xp:8 special:5 out:3 shown:13 papers:1 rp:2 matrix:41 space:12 spectrum:1 restricted:1 tried:1 surrounded:2 semi:1 cancels:1 wholly:1 f1:2 re:2 acting:1 investigation:3 multiply:1 ra:2 rational:5 reader:3 denoted:1 got:1 numeric:1 originally:1 note:16 shows:1 stat:2 commutation:1 linear:21 problems:3 southern:1 acknowledgements:1 given:29 possibility:3 quite:1 clarify:1 approaches:1 complicated:4 j33:1 put:2 dubna:1 ferro:1 additional:3 definition:12 pairs:4 derivation:2 r2:3 r3:2 geometry:1 impose:3 used:3 keep:1 motion:16 thing:4 ten:1 place:1 threat:1 removing:1 consequence:8 teor:1 distinguish:1 assign:10 βj:1 first:13 origin:4 xk:2 xi:6 xn:1 simply:3 xb:7 xc:7 variables:58 xa:7 number:12 exact:1 done:1 relations:17 another:15 enumerate:1 impossible:1 thick:12 open:6 size:1 take:1 guess:2 suppl:1 reference:2 introduction:2 twenty:1 eqs:2 abp:2 system:41 construct:4 obligatory:1 their:7 intermediate:1 lakshmanan:1 too:1 calculations:3 realization:1 gilbert:1 cycle:2 αk:8 west:1 aims:1 gives:16 free:1 mentioning:1 lot:1 relationship:1 exactly:4 za:2 xδ:2 part:6 western:1 manipulation:2 parameterisation:1 quasiclassical:1 translation:1 x1:4 coefficients:6 18b:1 kind:6 unfortunately:1 18d:1 cyclic:1 sections:3 integrability:11 summands:1 limiting:2 bi:5 nevertheless:1 classes:1 contrary:1 supposed:1 were:1 geometrically:1 entries:3 providing:1 powers:1 russia:1 decompose:1 w2:60 gathering:1 vector:3 rewrite:3 bosonic:1 explicit:3 zamolodchikov:10 argument:2 already:1 say:1 variable:1 intertwining:1 north:2 obviously:1 border:1 any:33 k33:3 depending:3 convenient:2 genus:1 aa:1 oriented:2 k2:1 k1:1 internal:8 square:2 amusing:1 resembling:2 destroy:1 coincide:4 gains:1 heisenberg:1 even:1 electric:1 trace:4 investigations:3 ıve:2 who:2 systems:4 most:3 regular:4 connected:8 locality:3 comparing:1 definitions:1 phase:3 analytically:1 φk:3 stands:2 forever:2 don:1 observation:2 consequences:2 considered:4 torus:8 partition:3 coincides:3 vertices:38 physica:1 order:4 graphs:15 proceedings:2 yang:16 verlag:1 principle:1 exp:1 subsequent:1 communication:1 hietarinta:1 usual:19 physics:4 notion:5 repeatedly:1 ambiguities:2 follow:1 phenomenon:1 supplements:1 supported:1 xap:5 ambiguously:1 functionals:3 notations:6 x2:4 miwa:1 spaces:2 relation:16 solutions:4 x3:4 keywords:1 substituting:1 careful:1 uniform:2 d2:6 find:6 d1:4 suw:1 κi:1 based:4 proposed:1 parameters:11 ψj2:1 kagome:17 written:1 topological:1 should:4 failed:1 only:14 going:2 generators:2 subsection:6 ambiguity:20 qx:2 integrable:10 local:18 oct:1 hope:2 κj:3 do:9 move:2 dj:6 3m:10 notation:4 get:9 simplest:5 assumed:2 solvability:1 aα:2 aim:2 ones:1 tbm:3 words:4 invariant:11 dv:1 applying:2 aλ:1 maillet:3 boundary:4 evolution:33 αj:3 stroganov:5 places:2 conditions:12 arxiv:1 fixes:1 remove:3 sum:5 twice:1 investigate:2 factorisation:1 roger:1 common:1 contain:6 including:1 fixed:9 inside:1 fruitful:1 view:1 set:23 exists:4 clarified:1 frame:2 j1:5 j2:5 j3:5 differs:1 see:9 w3:31 result:4 w1:71 y0:1 discussions:1 touched:2 acts:3 mathematik:1 subject:4 determinants:2 braid:1 tensor:2 ways:2 nuclear:1 inhomogeneous:1 sites:17 artificial:1 state:1 identification:2 chosen:1 closed:10 between:7 lxi:6 probably:1 subscript:1 dilogarithmic:1 approach:13 hence:14 fx:10 jw:4 terms:12 edge:17 uj:34 points:2 wj:49 wi:1 however:1 untouched:1 wv:5 cut:1 hypothesis:1 como:1 multiplier:2 solv:9 group:4 multivariable:1 configuration:1 methods:1 thank:1 σj:4 last:1 reverse:2 limits:2 modular:1 many:4 taking:1 constructive:1 according:4 ybe:2 mathematical:2 etc:3 admit:1 purely:1 symplectic:4 faces:1 contribution:1 ub:1 adapted:1 ll:2 cj:7 torn:1 co:16 necessary:1 cm:1 point:6 simple:8 overview:2 quadrilaterals:1 corresponds:14 ingoing:4 walk:11 dimensional:21 directions:1 non:4 math:10 lattices:2 sequences:2 polynomial:1 moreover:3 actually:5 cw:1 cv:1 appeared:1 bλ:1 considering:2 nijhoff:2 pp:7 xα:1 described:5 perspectives:2 second:1 basis:2 analogies:1 decent:2 igor:1 due:19 mark:2 defined:18 belongs:1 combined:2 interest:2 basic:1 technical:1 algebras:1 ak:1 important:3 choose:3 generating:3 arises:1 corresponding:22 observable:5 painted:1 concerning:6 formed:2 subspace:4 gen:1 else:2 ordering:1 yk:2 fy:9 c3:5 c2:7 c1:11 denote:9 assigning:1 those:1 σn:4 case:35 extracted:2 p0:13 p1:14 classifications:1 look:3 pacs:1 admissibility:7 tetrahedron:21 conserved:2 value:5 transformation:2 will:13 rests:1 while:2 suppose:10 monodromy:4 involved:2 cancelled:1 situation:3 ly:4 procedure:2 dλ:1 understand:1 correspondence:3 layer:3 ve:2 almost:2 trivially:1 vj:27 av:1 thus:23 site:24 surface:1 solved:5 yj:11 properties:5 triple:1 mod:4 quantization:6 conserve:1 currents:33 rfbr:1 wissenschaften:1 different:18 null:2 verified:1 since:2 φv:6 grant:1 make:1 belong:8 determinant:7 cross:3 same:19 intersecting:1 shorter:1 shifts:5 φb:5 complex:3 φd:4 φe:4 widely:1 propose:1 φh:7 resulting:3 φj:16 finite:14 clearness:1 independent:11 investigated:3 rmatrix:1 cubic:3 jα:9 assignment:1 numerical:1 isaev:1 marking:1 counterparts:1 hand:16 triangulation:1 action:7 moment:1 edges:10 infinite:1 frequently:1 invariance:12 identity:1 polygon:3 eigenvectors:2 suitable:1 center:2 scenario:1 k22:4 whole:10 mangazeev:5 well:7 fusion:4 analysis:4 factorises:1 without:4 solve:1 components:4 sets:3 model:23 left:11 restore:3 affine:1 boos:1 manifold:2 just:6 generalisation:2 being:6 newton:2 obtain:10 rest:2 homogeneity:3 assigned:19 λa:17 via:4 transforms:1 using:1 touch:1 λj:2 alternative:1 λh:5 eigenstates:1 z0:1 previous:7 k3:4 alphabetical:1 unique:3 preprint:1 infinitely:3 dashed:2 regarded:3 conclude:2 seems:1 except:1 sometimes:1 lattice:51 valid:3 combine:6 lett:7 easy:3 absorbed:1 east:1 solvable:1 summations:1 euler:3 generalized:1 real:1 acta:1 depends:5 easily:2 rules:10 replaced:1 couple:2 decomposed:2 possible:2 game:7 five:1 know:1 background:1 press:1 world:1 imposed:1 intersection:2 string:13 formal:4 scalars:1 reshetikhin:2 ns:2 appearing:1 like:10 lost:1 sincerely:1 ψk2:1 obvious:2 ψk1:2 private:1 δm:1 δj:1 integrals:16 arbitrary:8 completely:1 become:3 discussion:1 therein:2 twelve:4 right:12 bβ:1 classical:2 sequence:3 kashaev:8 arrows:6 fordy:1 some:26 briefly:1 calculated:1 zcp:3 b1:5 choosing:2 respect:11 small:1 little:3 ferroelectric:1 vol:2 cp:1 multidimensional:2 dimensions:2 absolutely:1 rpl:3 everything:1 does:7 decomposition:1 provides:2 toda:1 proc:1 restoring:1 refer:1 conference:2 faddeev:6 object:4 obey:5 bb:1 bc:1 bm:3 equivalent:18 each:15 aj:15 conventional:2 bj:7 bk:1 cλ:1 bu:1 step:3 substituted:1 bp:21 simplex:4 arithmetical:2 conserves:2 triangulated:1 2n:2 intersects:1 transformations:2 monomials:3 sub:2 actual:1 anything:1 algebraic:24 column:5 freedom:2 theorems:1 discussed:2 a3:5 o:3 recalling:1 must:9 plus:2 obeys:5 act:1 eight:2 introduced:13 consequently:2 automatically:1 graphically:1 applicandae:1 homogeneous:4 primitive:2 letters:1 follows:9 previously:4 visit:2 into:17 formulae:3 numerically:1 functional:28 three:16 down:1 nothing:3 appropriate:1 because:4 references:3 wα:3 strip:1 operator:28 proportional:3 tetrahedral:3 pentagon:2 technically:3 realisation:4 arrow:5 rows:1 hep:1 deal:1 module:4 qcb:1 transfer:8 there:8 u1:47 u3:26 u2:36 ordered:2 start:2 conservation:4 inner:3 way:15 labelling:2 tmf:1 rinat:1 was:13 manchester:1 function:14 arise:1 complete:10 form:16 enough:1 a9:1 regard:4 but:13 mysterious:1 seria:3 laurent:1 line:4 removed:1 considerations:2 strings:2 partially:3 commun:6 submitted:4 october:1 arranged:3 mat:1 consist:1 thanks:1 walks:9 characteristic:1 uw:3 uv:4 up:6 us:3 international:1 connectedness:1 below:1 limit:5 uk:1 planes:3 problem:18 define:6 similar:4 called:8 eigenvector:1 delete:1 mechanics:1 block:2 ab:1 associated:4 b2:4 af:1 int:10 abstract:1 describe:1 am:5 graphical:3 general:25 dξ:1 ap:8 single:5 distinguished:3 rule:1 aw:1 formulation:3 exist:3 check:1 triangles:6 constructed:3 again:3 functions:7 together:1 no:7 na:2 whereas:1 eastern:3 when:15 ne:2 multipliers:3 power:1 field:2 other:12 statement:1 details:4 branch:1 spatial:1 mathematics:1 amusingly:1 really:2 inclined:5 nv:2 nice:1 tam:3 picture:1 draw:2 elements:25 star:1 conventionally:3 separate:2 models:17 pure:3 time:8 vertex:43 outlets:3 polynomials:3 leaving:1 a1:7 class:4 meaning:4 a2:10 bounded:1 allowing:1 included:1 a8:1 sides:3 structure:22 auxiliary:9 monomial:11 practically:1 visits:1 established:1 curve:2 governed:1 original:2 implied:2 weights:4 hirota:3 reached:1 observables:2 having:1 restored:3 once:3
|
solv-int9811004.txt |@word represent:1 partial:1 consider:3 remarkable:1 funct:1 peq:1 lr1:1 scalar:1 proposition:11 follow:1 row:1 devoted:1 preserves:2 inverse:4 depend:1 show:3 tn:17 finally:2 tm:1 th:9 under:3 case:5 straightforward:1 zhang:1 far:1 bilinear:6 conditions:3 wave:30 putting:1 summarized:1 manin:1 deformations:1 condition:4 lφ1:1 leads:2 hamiltonian:1 turns:1 t2:1 solution:7 t1:29 convenience:1 commute:1 math:10 science:2 eigenvalues:1 anal:1 wronskian:4 direct:1 past:1 integrability:1 further:2 khesin:1 linear:9 even:1 established:1 t2k:2 nonlinear:2 plays:1 appear:1 iterating:4 t2n:1 section:3 expressed:5 dbt:40 version:2 goes:2 new:6 ever:1 method:2 satisfy:6 respectively:9 understanding:1 desired:1 compose:1 china:1 concluding:2 equations:8 obtained:4 remark:1 difficulty:1 shift:1 study:1 studied:3 chang:1 suitable:1 relation:1 followed:2 jager:1 tau:7 rφ:1 ai:2 apply:1 schief:1 virasoro:1 use:3 would:2 commun:3 give:2 γi:1 next:3 ψj:2 few:1 ψi:8 call:1 type:5 until:1 more:3 formally:2 solitons:2 operators:10 curvature:2 particular:2 known:1 cases:1 iii:3 logarithm:1 springer:1 deformed:16 recall:1 equation:6 work:1 det:7 hope:1 concepts:1 following:12 example:5 performed:1 lφ:1 f1:6 f2:3 bureau:1 qdeformed:2 council:1 chosen:1 calculation:2 organized:1 effectively:1 chin:1 attain:1 want:1 goal:2 darboux:7 verify:1 s1:11 s0:8 recovers:2 nontrivial:3 pure:1 answer:1 ordinary:5 frenkel:2 mas:1 express:1 blocks:1 begining:1 replacing:1 suppose:2 applications:1 lax:23 representations:2 compatibility:1 fn:6 realized:2 branches:1 clarkson:1 computations:1 pdos:2 perform:6 si:1 so:2 sn:4 definitions:1 order:5 produces:1 hierarchy:36 indeed:1 choose:1 years:1 seco:1 paper:2 through:1 satisfies:3 still:2 its:4 hazewinkel:1 ln:13 solving:1 lt:1 systems:3 derivative:1 τq:20 them:3 nsc:2 motivated:1 combination:1 acklund:5 evolution:2 introduce:3 mention:1 qualified:1 they:2 ls1:1 nov:1 now:2 above:2 eigenvalue:1 term:1 university:3 presented:1 applied:2 reasonable:1 l1:3 differential:5 successively:1 formulate:2 ed:2 hard:1 elementary:7 our:2 operation:1 eq:5 out:3 lt1:1 res:13 furthermore:1 since:3 denotes:2 formula:1 rn:6 announced:1 shows:3 provide:1 theory:4 quite:1 admits:1 nth:3 complicated:3 ask:1 compositions:2 pairs:1 r1:9 starts:1 turn:1 int:2 ism:2 chiao:1 hence:4 βn:2 view:1 generalizations:1 eqs:5 first:4 initial:1 features:1 question:1 variables:1 number:1 simplified:1 another:1 illustrate:2 given:7 similarly:1 introduction:1 adjoint:32 rong:1 system:9 construct:8 appl:1 constants:1 structures:1 gives:3 part:1 natural:1 coefficients:6 covariantly:1 t3n:1 kind:1 capel:1 iteration:3 zero:3 limiting:1 future:1 were:1 powers:1 result:4 rewrite:2 modern:1 ming:1 say:1 ω1n:2 manner:1 conjugate:1 need:1 hsien:1 any:3 viewed:2 form:12 petviashvili:1 convenient:4 s20:1 note:1 potential:6 generalized:2 salle:1 residue:1 though:1 reach:1 what:1 simplify:1 involving:1 letter:1 representation:3 remarks:2 iterate:1 soliton:6 especially:2 considered:1 clear:1 flow:1 physica:1 typeset:1 kp:4 exp:3 vries:3 fact:3 laws:1 oevel:2 dickey:2 reductions:3 supported:1 purely:2 gauge:24 solutions:9 substituting:1 analogue:3 trivial:4 find:1 q2:4 just:6 should:3 analytic:1 only:2 integrable:2 achieve:1 do:5 cheng:2 means:1 de:5 ones:2 preparing:2 words:1 gen:3 regarding:1 kadomtsev:1 qx:2 arxiv:1 acknowledgments:1 investigate:1 roger:1 common:1 contain:1 qi:4 drinfeld:2 qk:1 αn:2 qn:19 coefficient:1 set:3 exists:1 achieved:1 imposing:1 tu1:1 national:4 facts:2 see:5 sec:5 usefulness:1 terms:4 λi:1 subject:1 satisfying:2 ways:1 subsequent:2 written:1 hsinchu:1 µi:1 simplest:1 αi:1 geometric:1 approach:1 discovery:1 preserve:3 recently:1 iterated:1 nature:1 matveev:1 p2i:1 however:3 p2k:1 manakov:1 wq:14 solv:1 last:1 triggers:3 many:4 according:1 pdo:5 etc:2 whole:1 arbitrarily:1 cj:2 key:1 point:1 simple:1 represented:1 moreover:1 throughout:1 considering:1 described:1 transformations:11 equivalent:1 px:2 due:1 been:4 35q53:1 reduction:1 interest:1 basic:1 pj:1 algebras:1 define:4 θk:2 determinant:3 pseudodifferential:3 θn:2 versa:1 concerning:2 func:1 deepen:1 denote:2 p2:5 p1:5 classifications:1 exponential:1 remaining:1 will:7 near:1 replaced:3 property:1 chau:1 thus:2 non:1 iv:2 ii:2 characterize:1 itself:1 binary:18 different:1 shaw:1 grant:1 generic:1 ωn1:2 same:3 parts:1 φi:22 φj:2 several:1 composition:1 φn:16 higher:1 development:1 independent:1 extended:1 horozov:1 flows:2 hand:3 purpose:1 pitaevskii:1 infinite:1 frequently:1 tung:1 expand:1 relies:1 framework:1 jcs:1 well:1 analysis:2 obviously:1 academic:1 ωnn:2 without:2 easily:1 haine:2 justify:1 gelfand:2 proposed:1 yen:1 being:1 obtain:8 identify:1 transforms:1 differentiation:1 taiwan:3 scattering:2 kluwer:2 zakharov:1 except:2 leibnitz:1 valid:1 transformed:15 treatment:1 easy:2 republic:1 sokolov:1 transformation:3 cramer:1 represents:1 february:1 using:10 formal:1 reshetikhin:1 like:3 follows:8 exhausted:2 korteweg:4 become:2 mht:1 works:1 unexplored:1 because:1 old:2 methods:1 formulas:1 phenomena:1 consultants:1 kdv:31 lyubashenko:1 shall:1 integration:1 does:1 ωij:1 inserting:1 process:2 bm:2 bn:13 bi:3 expansion:1 step:14 binomial:1 revtex:1 although:2 properties:1 commutative:1 extension:2 column:2 novikov:1 o:1 compatible:1 multisoliton:1 extensions:2 stand:1 moerbeke:1 into:4 successive:1 integral:1 pair:2 right:1 references:1 sov:1 operator:38 van:1 chung:2 there:4 u1:22 u0:37 conservation:1 way:2 ψn:14 was:1 minors:1 function:28 triggered:10 some:1 but:3 iliev:4 construction:4 adler:1 pi:3 applying:1 whether:1 us:6 dordrecht:2 below:1 un:5 ui:10 backlund:1 similar:2 called:4 associated:10 worthwhile:1 heidelberg:1 defined:5 abstract:1 describe:1 general:3 single:2 exist:1 together:1 formulation:3 supersymmetric:1 identities:1 constructed:9 functions:15 no:1 when:1 detail:1 application:1 tin:1 other:4 role:1 department:3 mathematics:3 elements:1 generates:1 separate:1 radul:1 vertex:1 shown:1 polynomials:1 a0:1 important:2 structure:2 building:1 implies:3 vice:1 corresponding:2 physics:1 required:1 pseudo:1 rule:1 time:1 starting:1 lett:2 once:1
|
solv-int9811005.txt |@word represent:3 since:6 consider:2 gp:1 rev:1 results:6 giving:1 leads:6 scalar:2 commute:1 comments:1 constants:2 dα:3 gr:1 devoted:1 whose:3 inverse:2 quasi:1 tj:1 those:1 under:2 analogous:1 include:1 worth:1 applied:1 conjecture:1 g3:3 rel:1 advantage:2 very:6 translations:1 focus:3 nontrivially:1 inequivalent:1 difference:1 condition:27 common:1 bxy:1 entire:1 2κe:2 obvious:1 2κb:1 hamiltonian:20 turns:1 list:1 solution:10 large:1 solved:7 convenience:1 vector:13 math:6 dealt:1 indices:2 relation:5 anal:1 rk:2 noted:2 des:1 dealing:2 consistent:2 zg:1 coefficient:1 discover:1 integrability:7 zz:19 further:1 dynamics:3 odd:1 ode:1 substitute:1 even:3 index:1 what:1 nonlinear:8 gβγ:1 advantageous:1 3s:2 sum:1 dr2:1 analogously:1 expressed:3 3k:1 cyclic:5 odes:2 above:5 new:12 method:9 contrast:2 satisfy:5 full:3 degree:8 γz:1 respectively:3 component:1 here:4 desired:1 ansatz:2 sinh:2 situation:1 represented:3 consideration:1 standard:5 equations:21 appears:1 interpret:1 box:1 samuelsson:1 2x2:8 institute:1 study:3 studied:1 allows:1 leaving:1 p2:1 poisson:6 usually:1 implement:1 suitable:1 studies:2 via:4 useful:1 projection:4 classification:4 requiring:1 namely:3 vii:1 spz:1 scaled:1 iz:5 names:1 apply:3 weierstrass:1 should:1 tools:1 linearly:3 readily:1 use:8 takes:7 would:5 bilinearity:1 covariant:2 positive:1 kα:6 next:1 comparing:3 explicitly:1 therefore:2 taken:3 themselves:1 simpler:1 type:10 more:6 introducing:2 formally:1 standardized:3 becomes:10 holt:6 om:3 curvature:1 eξ:1 eλ:1 particular:6 known:11 cases:18 hold:3 iii:3 must:6 k00:1 couples:1 keeping:1 quartic:2 equation:15 work:7 oscillator:3 dx2:1 4x2:2 itself:4 values:4 making:4 dec:1 example:2 history:1 wojciechowski:2 f1:10 compare:4 f3:8 give:4 positioning:1 allowed:1 table:8 metamorphosis:6 numbers:1 sense:1 rescaling:7 information:1 end:3 g1:2 cαβγδ:1 turn:2 rather:2 discussion:1 holds:1 feature:1 write:3 how:3 nontrivial:9 criterion:1 fourth:1 instead:2 ordinary:2 constraints:1 parameter:2 sin:8 classify:1 isotropic:1 λz:1 algebra:1 may:1 max:2 after:1 derived:1 mapping:2 demanding:1 2iφ:1 explored:1 lax:1 designed:1 fi:7 choice:3 types:3 stress:1 aαβγ:6 natural:6 dynamical:1 effective:1 explicit:1 correspond:4 element:1 sk:2 generic:1 so:3 realizes:1 allow:1 enter:1 sg:1 se:3 restriction:4 interpretation:1 pw:4 gauges:2 developed:1 dy:1 satisfied:6 utilize:1 course:2 paper:3 including:1 4f:1 thesis:1 signs:1 existence:3 kinetic:1 still:1 its:13 before:1 derive:1 group:1 thank:1 energies:1 interesting:2 fix:2 solving:4 coordinates:6 writing:2 absence:1 drawback:1 degrees:1 systems:17 xyy:1 jacobi:35 mail:2 might:1 setting:3 bω0:1 maximal:1 symmetrization:1 them:2 thereby:2 practice:1 introduce:2 geodesic:3 scaling:3 mention:1 hamilton:1 they:3 now:11 day:1 kαβγ:5 represents:1 term:1 2ey:1 invariants:31 university:3 presented:2 2y:5 correspondence:1 sufficiently:1 iff:3 2g:4 stockholm:4 2b:1 each:2 found:7 difficult:1 2i:4 referred:3 homogeneous:5 lie:1 rosquist:6 differential:1 energy:43 reduce:1 related:4 bradley:1 toda:1 investigated:2 obtains:1 ez:3 separating:1 our:12 happen:1 avoided:1 eq:35 special:4 out:5 try:1 shown:3 fundamentally:1 space:9 restricted:2 furthermore:3 singular:1 parametrizing:1 unknown:2 denotes:2 re:30 acting:2 izv:1 reader:2 print:1 formula:1 goliath:2 2k:1 scalings:1 shows:1 working:1 linear:15 divergence:2 free:11 orbits:2 admits:2 completely:1 complicated:1 members:1 dω0:1 care:1 definition:1 derivation:1 r2:3 tsiganov:3 geometry:12 could:5 impose:1 ds2:4 βz:1 motion:2 ahler:8 6xy:2 physto:3 signature:1 hence:4 onto:1 first:8 origin:1 simplifies:2 encoding:1 variables:4 number:3 rank:20 references:1 xy:3 simplified:2 adopted:1 directly:4 xr:1 impossible:1 given:18 reference:1 similarly:2 introduction:1 leading:2 b2:2 system:16 least:3 indicate:1 xpx:3 master:1 superintegrable:18 calculations:2 convention:1 final:3 gives:7 mentioning:1 commutativity:1 iaz:2 zeroth:1 realized:2 direct:1 2aw:1 part:9 consult:1 x2:17 attempt:1 translation:1 representing:1 than:1 coefficients:3 covariantly:1 2f3:1 dtj:1 gγβ:1 third:12 d00:1 24x2:1 second:9 nakahara:1 sweden:1 determined:2 were:2 identical:1 treated:1 w2:1 er2:3 symmetries:1 generality:3 look:1 turned:1 manner:1 conjugate:5 constrained:1 any:11 lζ:1 dαβ:2 depending:1 convenient:2 ypx:11 ypy:3 able:2 isolated:2 mechanism:3 zq:3 note:3 sciences:1 z1:10 potential:29 take:3 reparametrization:3 finding:2 begin:2 added:1 olshanetsky:3 shall:3 track:1 object:3 3y:6 birkh:1 most:3 exploited:1 reducible:1 nonstandard:1 inserted:1 why:1 involving:1 volume:1 parametrize:1 nonlinearity:1 considered:2 clear:1 later:3 kr:1 bracket:2 principle:1 parenthesis:1 hietarinta:5 typically:1 section:7 fact:11 saying:1 particularly:1 show:2 recipe:2 3x2:2 gauge:5 solutions:9 x3:1 substituting:3 find:6 symmetric:2 satisfies:1 xpy:11 pdes:1 basel:1 separability:2 analytic:11 only:9 going:4 geodesics:3 factor:9 thompson:2 integrable:8 hamiltonians:6 interested:1 his:1 notation:1 means:2 dependent:4 simplest:2 particle:1 soon:1 3x:1 dz:5 closely:1 probably:1 report:1 dt:1 interpreted:2 dr:1 gen:3 approach:8 arxiv:1 grav:2 3f:3 investigate:1 cf:1 noncanonical:1 academie:1 mapped:2 fixed:15 traceless:1 riemannian:2 pµm:2 redefine:1 set:6 exists:2 achieved:2 imposing:1 frame:6 2c:1 lett:2 see:3 computer:1 result:2 terms:5 λi:1 uggla:1 satisfying:4 tensor:36 µm:11 written:2 identification:1 between:4 invariant:54 geometric:8 conditions:4 x4:1 preserve:2 attention:2 recently:1 2px:3 restricting:1 however:11 killing:48 ww:6 ramani:1 vanishing:2 extent:1 solv:2 configuration:5 tensors:5 topology:1 both:6 cos:9 limits:1 taking:2 according:13 ln:12 sketchy:1 context:1 quite:1 pde:8 adapted:2 otherwise:1 mechanics:1 ci:1 words:1 necessary:3 simple:5 harmonic:3 ce:4 parametrization:1 dimensional:7 cz:1 cy:2 simply:2 polynomial:10 associated:4 bξ:1 indefinite:5 considering:1 pq:1 described:1 transformations:8 geometries:1 addition:3 z0:17 px:21 py:19 due:1 been:6 pµ1:3 defined:2 belongs:1 combined:3 interest:1 anzats:1 algebras:1 choose:2 nuovo:1 arises:1 corresponding:12 qc:1 sufficient:4 xxx:1 marklund:1 2gαβ:1 zero:3 systematic:2 maximally:1 irrelevant:1 present:5 case:36 p3:1 p1:1 splits:1 pacs:1 conserved:5 value:6 will:13 euclidean:2 while:2 eib:1 viii:1 applies:1 f2:10 property:1 conformal:27 procedure:3 iy:3 noether:1 vectors:3 pαβγ:4 century:1 vol:1 vi:2 metric:22 thus:10 surprisingly:1 surface:4 iv:1 ii:1 ay:1 ik:1 ij:17 im:5 dual:2 yr:1 ic:4 vanish:1 k0:1 confirmed:1 null:14 perform:1 make:11 geometrization:5 admit:3 same:8 clearly:2 zf:1 complex:12 split:2 several:3 four:3 independent:6 used:6 http:1 bristol:1 trivially:1 cubic:41 9x2:1 hand:3 parametrized:2 action:1 kz:6 auser:1 invariance:1 recent:2 relies:1 weakly:1 off:2 center:1 possibly:1 nevertheless:2 makes:4 failing:1 well:7 obviously:1 without:2 solve:1 components:6 sets:1 coordinate:6 centerof:1 dimension:2 usual:2 unified:5 just:4 less:1 being:6 when:11 grammaticos:1 obtain:5 dφ2:1 identify:1 transforms:7 momenta:3 tables:1 conjugates:1 family:2 workers:2 seems:2 except:1 improvement:1 parts:1 priori:1 transformed:2 treatment:3 theorem:1 transformation:14 gave:1 real:21 rescaled:2 forces:1 easily:2 read:1 decomposed:1 possible:8 admitting:5 corresponds:5 department:3 quest:1 unification:1 press:1 using:11 like:1 9y:1 imposed:3 standardization:1 semi:1 δy:5 follows:5 reduces:1 html:1 admitted:1 separately:2 ai:1 continue:1 steps:1 either:1 integrals:1 always:5 translated:2 colon:1 8x4:1 hαβ:3 mathematical:1 www:2 because:1 old:1 methods:3 classical:4 polar:1 some:11 back:3 b0:2 b1:2 choosing:3 moreover:1 nonzero:1 provided:1 cp:1 fop:1 dimensions:1 2e:2 affects:1 avoid:1 2f:3 kµ1:1 does:2 2pz:3 assuming:1 yields:2 2a:2 pr:4 who:1 zzz:5 rep:2 rescale:2 equivalent:2 arbitrary:22 illustration:1 dropped:1 step:2 although:2 become:4 bx:2 proceed:3 pβ:8 pγ:6 about:1 pα:20 a1:2 carried:1 extension:1 constraint:1 freedom:5 prove:1 discussed:1 dependence:4 reduced:1 pz:11 a2:2 ensure:1 done:2 reads:3 analogy:2 2cf:1 introduced:1 automatically:1 perelomov:4 outset:3 publishing:1 previously:3 noting:1 into:12 rendus:1 rotations:1 functional:4 three:7 down:2 pair:1 hermitian:1 accounts:1 operator:1 often:2 2ax:1 additional:3 a0:2 assumed:3 there:4 philadelphia:1 long:1 class:1 fully:2 start:1 accordingly:1 quadratic:10 way:2 analyze:1 was:6 naturally:1 function:19 2ay:1 complete:2 form:20 bpy:1 but:10 hj:12 lowered:1 rauch:2 ec:1 hc:1 line:1 trying:1 true:1 partially:1 made:1 applying:1 bpx:1 whether:2 wish:1 up:3 us:3 different:4 dφ:3 below:2 2hj:1 pφ:7 homothetic:1 examples:1 strongly:4 constant:15 sight:1 flat:2 int:2 certain:2 abstract:1 general:16 quantum:1 single:3 ar:5 exist:1 formulation:2 trace:15 2iz:2 drach:13 commuting:2 check:1 physical:12 reiφ:1 functions:2 compared:1 cim:1 no:8 fixing:1 whereas:2 generally:1 detail:1 reality:1 field:1 other:10 remarks:1 fokas:3 test:1 standardizing:2 igk:1 concerning:1 picture:3 4i:2 helpful:1 deriving:1 commutator:1 meaning:1 important:1 overdetermined:3 variable:10 rq:2 4e:1 implies:3 coupling:7 algorithm:1 assume:1 physics:5 required:1 original:3 equivalently:1 implied:1 mass:1 time:11 far:1 appl:1 4a:1 requires:1 gαβ:5 once:2
|
solv-int9811006.txt |@word limited:1 func:2 four:2 rˆ:2 consists:4 analiz:1 relationships:2 whose:1 calculate:2 under:14 xtk:3 rise:3 every:7 manin:1 school:2 dubrovin:2 suffices:3 solution:100 convenience:2 vector:17 indices:2 direct:5 nail:1 second:8 invariant:10 even:13 established:1 errors:1 ˆx:2 ak2:2 ak1:2 above:15 new:15 consisting:1 coefficient:4 simultaneously:1 κi:2 κj:5 never:2 here:22 q11:31 q12:22 obtained:30 study:2 mulase:3 fourier:4 changes:1 york:5 divide:2 explained:1 seven:2 deconinck:3 total:10 univ:2 p42:2 linearly:5 derivatives:47 would:5 cohomological:1 bundles:3 negative:3 therefore:5 m3:2 m2:2 until:1 decomposable:1 solitons:1 odinger:1 berlin:1 must:2 mg:7 βr:2 xhk:2 xhj:1 mn:1 mi:6 mt:1 mr:7 example:14 yeshiva:1 indicated:1 give:3 table:9 involve:2 want:6 ni1:1 boussinesq:14 provide:3 how:9 nontrivial:9 significance:2 ordinary:27 sato:3 description:2 oscillators:1 earlier:1 wrong:1 lax:7 constants:11 third:1 summing:1 first:32 order:47 restriction:3 executed:2 over:3 vary:1 satisfied:6 executes:1 thesis:1 satisfies:3 integrands:1 before:3 fix:1 writing:1 harmonics:1 fik:1 maximal:7 them:5 combination:3 they:11 singularity:1 represents:1 alex:1 each:16 side:7 independent:47 list:6 t3:11 used:22 combining:1 jimbo:1 restricted:5 particles:1 newly:1 ri:1 rk:1 trajectories:3 linear:26 surveys:2 standard:1 publ:1 storm:1 generalizations:3 already:3 miura:3 rank:32 relations:4 another:5 immensely:1 illustrate:1 rewritten:1 similarly:1 manakov:1 top:1 needed:7 listed:1 variational:9 rejected:1 finitely:1 grassmann:1 showed:3 msri:1 zero:6 classes:1 powers:2 minus:2 rewrite:5 modern:1 manner:1 seen:3 relatively:1 convenient:4 isolated:1 absorbed:1 shallow:1 foliate:1 extending:1 phase:31 acknowledgements:1 observation:1 flow:22 bracket:23 vries:4 sum:2 reductions:7 solutions:67 keywords:1 substituting:1 d2:4 d1:4 just:1 specify:2 integrate:2 hamiltonians:7 dn:3 do:9 mixture:1 dj:2 dk:18 di:2 de:6 fluid:1 dx:3 reconstruct:1 treatise:1 runs:1 fields:1 greene:1 twice:1 analytical:2 nγ:9 pitaevskii:1 depends:16 w2:1 w1:1 discussions:1 best:1 subject:1 oceanic:1 said:2 tensor:3 rings:1 symmetric:3 simplest:2 drawn:2 approach:11 terms:47 extend:1 however:14 wx:3 essentially:6 casimir:10 exceeds:1 distinction:2 contribution:1 genus:62 0n:3 2ni:1 abhyankar:1 nˆ:1 polynomial:5 commutative:1 puts:1 basis:4 three:14 been:7 much:1 expected:3 quantities:51 θg:4 belfer:2 chur:1 qγδ:11 worked:1 manifolds:1 applied:1 remaining:3 near:1 suppose:1 applies:1 procedure:3 shiota:3 ir:1 iv:1 ii:5 ik:1 im:1 exterior:1 ni2:1 uxxx:7 containing:3 recursion:4 make:1 complex:1 evolve:2 vvx:1 i1:1 i2:1 hand:11 potentials:58 prescribed:1 weakly:1 scenario:1 academic:1 left:6 graded:1 alluded:1 rotated:1 scattering:3 functionally:21 previous:10 burns:1 coordinatized:1 zakharov:4 regarded:1 quadratures:1 transformed:3 easy:3 posed:2 possible:10 spanned:6 unique:1 advanced:1 appearing:6 specific:2 korteweg:11 arbitrary:1 invaluable:1 right:4 consultants:1 confusing:1 steps:6 plot:1 kruskal:3 binomial:2 properties:4 o:3 topologically:4 plus:1 slightly:1 automatically:5 functions:18 δux:1 contains:3 publishing:1 bound:2 down:1 remarks:7 acad:1 sov:4 amsterdam:1 often:1 support:1 initial:49 transform:6 conservation:1 way:12 was:23 minors:3 lowest:4 form:37 converse:1 denoting:1 rauch:1 true:2 inside:2 maximum:1 krichever:17 proved:3 qij:42 abstract:2 conserved:54 proves:2 exist:2 accounting:1 dβ:1 check:3 qis:1 constructed:9 ni:49 nj:6 nk:2 no:6 whereas:1 when:17 vanishes:1 tin:2 interested:1 role:1 tik:7 test:1 nr:12 tig:1 corrected:1 variable:8 qi1:6 qi2:1 assume:5 proposed:2 pseudo:5 ti1:3 ti2:3 time:16 n2:13 n3:8 n4:3 n5:1 llr:1 equalities:1 invent:2 leads:2 computation:1 inverse:10 depend:7 recurrence:3 quasi:1 elliptic:1 analogous:3 frequencies:2 lrk:1 springer:4 seemingly:3 choice:1 coprime:8 entries:2 annihilated:1 riemann:9 presented:10 turns:2 nondynamical:1 involution:13 quick:1 upper:3 work:9 dealing:2 sign:2 spectral:1 t2k:1 adds:2 appear:7 shares:2 wxxx:1 shared:2 satisfy:5 water:1 groups:2 along:9 appears:9 change:1 wait:1 institute:2 vectors:12 simultaneous:1 poisson:30 usually:5 conveniently:1 spatially:3 merely:2 compare:1 working:2 prove:8 positive:8 introducing:2 acceptable:1 validity:3 rigid:1 observations:1 cases:5 easiest:1 valued:5 tokyo:1 modified:1 reviews:1 values:25 following:17 attain:1 degenerate:3 figure:9 performed:1 allowed:8 counting:2 conversely:1 occur:1 verlag:4 pini:15 lemma:3 darboux:2 discussion:1 write:14 criterion:2 pure:2 allowable:3 parameter:3 δvx:1 may:1 needs:5 applications:3 date:2 drastic:1 data:20 compatibility:5 natural:3 dynamical:6 whenever:1 curry:1 explicit:5 st:1 so:18 representation:5 typical:17 indeed:1 pointed:2 mainly:1 stability:1 course:1 argued:5 still:2 solitary:1 interesting:1 jij:2 decreases:2 forms:1 offers:1 constitutes:1 mail:1 main:3 correspondence:1 non:5 views:1 introduce:2 scaling:3 nov:1 now:9 term:21 dikii:7 equality:2 name:1 corank:1 possibilities:4 vt2:1 em:1 square:2 significantly:1 avoided:1 shown:15 space:40 furthermore:12 lagrangian:93 increase:3 contained:1 formula:3 fomenko:1 u2x:3 correct:1 shows:6 after:3 theory:12 possibility:6 quite:3 org:1 remainder:3 care:1 qj:2 language:1 impose:11 motion:11 place:1 u22:1 2p12:1 βj:7 βk:2 origin:1 xk:1 symmetry:6 variables:83 xx:3 simplified:2 u3:25 carry:1 impossible:1 given:35 necessarily:7 indicate:1 types:1 typographical:1 structures:2 speaking:1 gives:11 asymmetric:1 proving:3 x2:3 than:18 coefficients:11 edition:3 require:3 purposely:1 were:7 skewsymmetry:1 eliminating:1 generality:2 dynamically:1 argument:3 generalization:2 winding:1 say:3 any:27 efficient:1 ideas:3 note:19 sciences:2 potential:18 noth:1 formulas:1 multiple:4 trace:1 uyy:2 algebraic:7 pair:4 pages:5 acknowledges:1 especially:2 surprising:1 considered:6 later:4 drive:2 quantity:5 precise:1 arnol:1 q42:1 show:6 leibniz:1 recipe:1 contemporary:1 specifically:2 written:12 analytic:2 only:53 explicitly:13 essence:1 legendre:7 get:4 cannot:3 tk2:2 tk1:2 gel:5 london:1 kernel:4 imposing:17 violated:1 j1:3 j2:3 namely:4 priloˇzen:2 lnk:1 hierachy:1 surfaces:2 fails:2 αr:94 commutation:2 ways:1 definite:2 functionals:8 enough:3 bureau:1 between:8 αi:1 αk:4 αj:16 αm:1 notice:2 foreword:1 comm:2 jetp:2 resides:1 many:6 according:2 called:5 expression:4 vux:3 eulerlagrange:2 affine:1 characterization:3 overview:3 lagrange:18 considers:1 considering:1 skew:1 3u3:2 3u2:3 direction:4 offered:1 previato:2 observe:1 olver:1 weierstrass:1 irrelevant:1 those:2 case:40 situation:3 nonstationary:1 u2xx:3 metric:1 uxx:11 middle:1 good:1 motivated:1 δfr:1 different:21 verified:1 author:2 commuting:4 same:13 arguments:1 physical:2 investigated:1 singapore:2 trivially:1 invariance:3 δf1:1 δf2:1 onedimensional:1 without:2 solve:8 components:2 dimension:14 bodies:2 manifold:3 among:1 rest:1 torus:26 summed:1 differentiation:9 multiples:1 except:4 lett:3 real:2 aspects:1 around:1 topology:1 using:53 reduces:7 either:5 integrals:1 multiplicative:1 stationary:25 reduced:8 specified:2 nonzero:1 provided:2 slice:1 dimensions:1 decomposition:3 provides:3 refer:3 scientific:1 power:1 kyoto:1 equivalent:13 found:13 repeating:1 discussed:10 meaning:2 practical:2 mutually:12 2j:2 2k:2 cambridge:3 communication:1 vogtmann:1 references:2 determine:14 operator:23 assumed:1 strictly:1 there:23 start:1 series:3 equated:2 complete:11 formalisms:1 harwood:1 elimination:1 2vx:2 pdes:1 adler:12 vectorfield:1 mat:1 6uux:3 liouville:11 ωj:4 strongly:1 ab:1 ai:1 certain:5 ak:3 aj:6 general:7 examine:4 governed:2 formulation:1 tedious:1 again:3 completeness:2 stationarity:5 graduate:5 field:2 valid:3 spatial:3 mathematics:5 mccrea:1 important:4 included:1 mass:2 firstorder:1 starting:4 original:2 sci:4 consider:18 scalar:1 commute:9 follow:2 expressions:3 research:2 tr:20 tn:36 tl:1 tm:10 tj:3 tk:107 th:49 ti:2 fax:1 straightforward:1 laws:1 very:3 difference:1 rn:2 condition:21 hamiltonian:108 t4:2 t5:13 t2:28 applicable:1 t1:32 large:5 anal:7 tel:1 integrability:7 further:3 canonical:20 subscripts:1 what:5 nonlinear:15 brackets:7 section:27 version:1 fractional:1 method:11 contrast:3 component:3 operating:1 berkeley:2 directions:1 equations:108 search:1 generalizing:1 divisor:1 allows:2 amount:1 periodic:11 action:4 quotient:4 uuxxx:1 family:4 texts:3 establish:1 readily:1 ψx:1 takes:1 whittaker:1 etc:4 ψt:1 comparing:1 mckean:2 minor:1 more:21 kˆ:2 operators:13 constructs:1 tested:2 vn:1 particular:6 known:9 evolves:3 none:1 tr2:3 science:3 equation:133 remain:1 canonically:1 nonsingular:24 wojciechowski:1 f1:1 f2:1 stated:2 share:1 states:2 numbers:1 sense:12 sharp:1 axis:4 information:4 respective:1 goal:1 acta:1 funkcional:2 simplicity:4 fr:2 algebra:2 derived:3 waves:4 derives:1 shore:1 sect:1 fundamental:3 media:1 helv:1 hierarchy:68 quasiperiodic:5 paper:10 through:3 existence:5 kinetic:1 its:17 continued:2 solving:2 actually:1 resort:1 systems:17 jacobi:4 might:1 skipped:1 return:1 finitedimensional:1 number:33 easily:12 2q:3 2r:7 always:10 2g:2 2m:3 2n:13 2h:5 2i:5 characterized:1 referred:4 multiphase:3 weight:15 energy:3 hard:1 idea:4 recapitulate:1 finish:1 quantum:2 solved:6 robert:1 since:36 induces:1 denotes:3 acting:1 equate:2 denoted:1 occurs:2 members:3 put:1 definition:20 pairs:6 recast:1 american:1 consequence:13 disregarded:1 done:2 construct:2 equating:1 introduction:2 5th:1 least:1 echet:1 assumption:3 vxx:5 statement:3 scheme:2 too:1 holomorphic:3 calculations:3 relationship:7 immediate:2 part:7 authors:1 vxxx:2 determines:3 double:1 determined:19 vx2:2 conjugate:2 null:1 7z:1 lie:1 generalizes:2 3d2:1 petviashvili:4 depending:5 k2:35 k1:42 generalized:3 jacobian:5 finding:2 towards:2 most:7 significant:1 extremely:1 soliton:7 kg:1 kj:7 clear:3 physica:2 kp:141 exp:1 physics:3 multiplicities:1 relation:1 3u:2 carefully:1 find:22 parameters:30 factor:4 integrable:14 circle:2 q4:1 his:1 notation:4 dependent:6 express:2 combinations:4 during:1 reprint:2 spikes:2 arxiv:1 redefined:1 common:3 set:34 achieved:2 vˆx:1 uu2:1 see:10 fand:5 smallest:3 various:3 conditions:45 uux:2 missing:1 veselov:6 vanishing:1 uψ:1 solv:1 both:17 last:10 symplectic:3 pde:2 whole:2 finds:2 point:12 simple:2 lagrangians:7 corresponds:6 dimensional:54 simply:1 raise:1 due:1 reduction:33 describes:2 pk:8 ph:1 pi:11 empty:1 determination:2 nonconstant:1 assigning:2 p2:4 p1:4 look:1 evaluated:2 while:1 replaced:2 2q12:3 engineers:1 exclude:1 vol:1 encountered:1 centennial:2 vanish:1 2uv:2 righthand:1 grant:1 2p21:2 modification:1 survey:2 higher:23 literature:1 flows:24 moving:1 necessity:1 2u2:5 lower:11 kashiwara:1 analysis:1 concrete:2 machinery:1 gsi:1 parametric:2 λg:1 world:2 useful:3 alternative:1 letting:1 conclusions:1 guaranteed:3 theorem:41 guarantees:2 transformation:45 euler:18 φ0j:4 integer:22 formal:1 imposed:1 follows:18 separately:2 imposes:2 indication:2 translated:2 essential:1 terminology:2 mathematical:10 methods:9 discrete:1 some:18 dullin:1 mech:1 added:2 examples:7 uspekhi:1 describing:7 nonsingularity:1 integration:4 providence:1 eliminate:1 ψt1:1 minimal:8 ba:1 gmax:11 bk:2 step:33 rur:1 relating:2 hilbert:1 uxxxx:4 integers:6 novikov:23 bilinearity:1 ψtk:1 colorado:2 into:3 nsf:1 rows:1 span:1 u5:2 u4:10 u1:13 u0:3 long:3 u2:27 ut2:1 ut1:1 forward:1 sections:5 russian:3 segur:4 ux:15 ut:1 uv:2 up:8 us:9 ur:15 ui:1 uk:6 uj:5 autonomous:6 similar:1 ki:1 constant:9 defined:12 single:1 formalism:2 defines:5 amounts:3 rewriting:2 points:4 elements:6 conventionally:1 problems:1 polynomials:3 william:1 generated:3 sides:2 structure:17 implies:4 algorithm:21 required:8 equivalently:1 implied:1 requires:1 having:1 once:2 partial:11 funct:3 results:20 illustrated:2 incommensurable:1 contributions:1 compact:4 tr1:3 include:1 dramatically:1 2rm:1 expressing:3 wave:7 matrices:2 entire:1 notes:1 deals:1 inspection:1 dαj:1 concluded:1 zx:1 dynamics:3 odd:19 index:2 plays:1 invertible:9 analogously:1 expressed:14 3m:1 expresses:2 degree:7 respectively:7 desired:2 separation:1 others:2 remark:7 weinstein:1 involved:2 resulting:7 implement:1 makes:2 examining:2 transformations:1 app:1 integrations:1 private:1 addressed:1 decrease:2 use:16 next:13 few:2 becomes:2 iii:2 integrating:1 unknowns:1 obvious:3 codimension:1 fulfill:1 drops:1 proof:36 calculation:1 purposes:1 assumptions:1 invoke:1 holds:6 instead:4 singular:20 collection:1 abuse:1 fits:1 correspond:4 doklady:2 move:1 interpreted:2 including:3 hypersurface:2 mentioned:1 kp1:2 kp2:3 ln:6 zˆ:2 lj:4 lk:3 lr:30 derivative:19 defining:1 cusp:1 greater:4 outlined:1 practice:1 p11:10 p12:7 spelt:1 p14:1 reconstruction:1 february:1 dirac:1 university:4 identified:1 l2:4 l3:4 constraints:4 related:4 inverted:2 society:1 our:8 special:8 out:11 matrix:22 rev:3 geom:1 stud:1 lecture:1 induction:3 math:14 interactions:1 completely:16 gardner:5 monographs:2 backwards:1 geometry:5 determining:4 times:4 hence:44 reached:1 ψxx:1 dispersive:1 unknown:4 system:91 unspecified:1 their:23 appl:9 zxx:1 final:1 commutativity:2 reversed:1 exactly:3 lists:1 completes:1 varieties:2 holland:2 providing:1 result:11 curves:2 need:10 constrained:2 apparently:1 clearly:10 mij:6 able:2 uuxx:1 instance:5 scientists:1 calculus:1 lectures:1 unless:1 connected:3 class:3 consequences:3 fact:4 oevel:4 supported:1 purely:9 miwa:1 manchester:4 trivial:5 devries:7 q3:2 q2:3 knowledge:5 should:3 bernard:1 inherited:1 local:1 achieve:1 funkt:1 familiar:1 q33:2 ones:1 words:9 evolution:17 kadomtsev:4 determinants:1 densities:1 differential:62 nauk:1 contain:4 qi:17 fixed:6 view:2 requirement:1 multiplying:1 modulo:2 computed:1 exists:2 notational:2 variations:1 p24:2 p21:17 usefulness:1 reconfirm:1 phases:20 state:1 identification:1 closed:1 theta:5 shabat:2 hypothesis:1 hammack:2 taking:2 equal:4 chosen:2 expand:1 otherwise:6 comment:1 relevant:1 tori:4 ca:2 cf:2 coordinates:9 respect:30 addition:3 thanked:1 degrees:1 improve:1 define:7 determinant:1 describe:1 corresponding:9 sufficient:4 covered:2 present:3 value:18 will:10 examines:1 almost:7 vi:1 thus:1 surface:16 vx:7 generic:16 member:8 parts:4 φg:2 φj:3 finite:37 cubic:1 effect:1 parametrized:1 v2:1 v3:1 infinite:10 identity:6 argue:2 schr:1 nevertheless:3 well:9 position:1 soviet:4 less:4 obtain:12 preprint:1 δαi:1 δαj:5 extends:1 identical:5 checking:1 execute:1 know:5 resolves:1 press:3 immediately:4 loss:2 necessary:8 like:2 δx:1 δv:6 δt:1 δu:14 δs:1 δl:32 δh:19 δf:1 become:1 works:1 page:4 because:7 classical:4 sequence:1 library:1 q21:24 choosing:2 kdv:21 happens:2 vt1:1 lead:1 demonstrates:1 avoid:1 parametrizable:1 does:12 assuming:6 chains:1 demonstrated:3 slight:2 although:2 p33:3 fordy:1 simpler:2 about:2 carried:1 extension:2 column:4 introduces:3 dependence:16 compatible:1 involutivity:1 introduced:9 h2:6 h1:5 functional:10 h5:1 restatement:1 additional:1 vˆ:2 quadratic:6 terminates:1 naturally:1 function:18 north:2 triangular:7 but:13 volume:10 hk:79 repeated:2 construction:2 highest:12 count:6 whether:1 smooth:1 below:13 dms:1 limit:2 demonstrate:1 problem:20 vectorfields:1 mechanics:3 pij:48 int:1 geometrical:2 denote:14 nongeneric:2 mutual:3 ingredients:3 wxx:3 detail:2 other:42 details:2 repeat:1 kinds:1 expressible:1 pi1:11 inspiration:1 auxiliary:1 factors:5 rule:1 4q:1 4g:3
|
solv-int9811007.txt |@word partial:1 consider:4 remarkable:1 results:1 eds:2 proposition:3 sci:2 involved:1 gj:3 gi:6 whose:1 inverse:1 chain:1 paris:2 γk:2 quasi:7 γn:1 under:2 applied:1 g3:1 g2:13 g1:14 very:2 geometrical:4 trough:1 anonymous:1 entries:1 difference:1 matrices:2 nijenhuis:14 dim:1 hamiltonian:22 turns:1 solution:2 t0:1 leave:1 involution:2 vector:12 eigenvalues:5 neighborhood:3 b21:1 second:2 concludes:1 dynamics:1 canonical:21 even:1 aim:2 nonlinear:2 invertible:2 diag:3 expressed:1 poles:1 above:3 new:2 acknowledgments:1 body:6 respectively:2 fernandes:1 here:1 provides:1 leeds:2 address:2 concluding:1 along:1 strong:1 equations:10 obtained:3 remark:2 items:1 studied:1 oberwolfach:1 suggests:1 poisson:14 action:3 studi:1 suitable:1 studies:1 classification:2 highly:1 first:1 univ:1 linearly:1 virasoro:1 takes:1 distinct:1 fordy:2 comparing:1 assuring:1 explicitly:2 therefore:3 endowed:1 type:2 entails:1 more:1 zeroes:1 introducing:1 thus:1 operators:1 berlin:1 rigid:2 particular:3 known:3 iii:1 account:2 ρi:3 recall:3 equation:4 work:1 concepts:1 following:2 example:2 proof:1 wojciechowski:1 f1:1 give:1 relativistic:1 hydrodynamic:1 trieste:3 degenerate:3 sense:2 united:1 end:1 afk:4 provide:1 verify:1 s1:5 means:1 feature:1 maps:1 classify:1 r2n:4 product:1 de:2 algebra:1 2g2:1 applications:1 levi:2 plane:2 fi:5 fk:5 fn:1 stress:1 natural:1 dynamical:16 third:1 schneider:2 linear:1 explicit:1 st:1 darboux:6 so:5 sect:2 s2:4 representation:2 order:2 editrice:1 interpretation:1 hierarchy:2 indeed:2 satisfied:1 course:1 through:2 mentioned:1 existence:3 europa:1 still:1 its:11 roots:1 le:1 τj:2 thank:1 acknowledge:1 coordinates:12 actually:1 degrees:4 systems:24 jacobi:4 derivative:1 main:1 into:1 non:11 zakharevich:1 introduce:2 ls2:1 they:4 nov:1 now:2 discuss:1 developments:1 easily:2 gets:1 hereafter:1 invariants:1 university:1 theory:2 2a:1 each:3 found:1 2n:1 2j:1 referred:3 heavy:1 differential:1 arbitrariness:1 map:10 ed:1 ea:2 related:4 owing:1 our:1 eq:2 special:2 out:3 shown:5 matrix:3 solved:1 restricted:1 furthermore:3 since:3 denotes:1 mate:1 geom:1 suffices:1 occurs:2 math:11 shows:1 ackel:1 fisica:1 quite:3 admits:4 completely:7 complicated:1 ruijsenaars:2 geometry:1 could:1 linearized:1 motion:5 top:1 variabili:1 first:1 separable:9 lichnerowicz:1 already:1 peculiar:1 miura:1 variables:3 primary:1 done:1 relations:1 directly:3 clarity:1 open:2 given:15 introduction:3 bologna:1 dipartimento:3 system:19 least:2 locale:1 assumption:1 manifolds:3 realization:1 structures:5 final:1 completed:1 exactly:1 γ1j:1 encompassing:1 separability:3 coefficients:2 metodi:1 marshall:1 cimento:2 integrability:2 project:1 matter:2 were:1 naturally:1 result:3 symmetries:1 murst:1 ann:2 generalization:1 any:3 emes:1 blaszak:2 lie:2 angle:1 depending:3 calogero:6 instance:1 take:3 polimi:1 opposite:1 magri:3 chart:6 compl:1 most:1 gravitation:1 letter:5 formulae:1 phase:1 class:11 soliton:1 considered:5 torus:3 milano:5 qbh:17 occasion:1 fact:5 oevel:1 reductions:1 supported:1 γnj:1 relation:4 solutions:1 civita:2 trivial:2 q1:8 q0:9 enough:1 than:1 only:1 going:1 integrable:18 hamiltonians:2 local:2 preliminaries:1 ratiu:1 characterization:2 dk:2 dh:4 di:9 dependent:1 syst:1 µj:2 da:2 ones:1 gen:1 secondary:1 evolution:1 conditions:1 arxiv:1 involutive:1 mapped:1 fixed:1 riemannian:1 set:4 ser:2 ferrarese:1 clarified:1 topics:1 morosi:10 see:2 differentiable:1 discussions:1 terms:2 subject:1 seminars:1 said:3 tensor:10 enlightening:1 ways:1 marmo:2 yet:1 symmetric:1 written:1 µn:1 µi:6 dynam:1 between:4 invariant:2 approach:2 counterexample:2 recently:2 however:3 gratefully:1 comm:1 solv:1 amer:1 tensors:4 suggested:1 both:6 c21:2 universit:1 equazione:1 many:3 according:1 admit:2 item:1 ete:2 tangent:1 passing:1 whole:1 ck:6 ci:1 cn:3 point:3 simple:1 corwin:1 dimensional:2 analyzed:1 polynomial:3 associated:2 considers:1 ferapontov:1 pp:3 submanifold:1 skew:1 three:2 been:5 strategy:1 int:2 much:1 9jt:1 interest:2 ah:1 algebras:2 ak:1 filippo:1 arises:1 corresponding:4 vinci:2 cotangent:1 scienze:1 matematiche:1 observe:3 angles:2 mail:2 c3:1 c2:2 c1:6 formes:1 those:1 case:3 globally:2 p0:29 p1:20 transformation:1 will:1 kowalevski:1 aij:1 situation:2 property:3 conformal:1 procedure:2 della:1 vi:1 4c2:2 ii:1 exterior:1 2g1:1 different:3 italy:3 dhj:2 recursion:1 formulations:4 connection:1 clearly:1 proved:3 φk:2 independent:2 used:1 singapore:1 functions:5 flows:3 boston:1 birkhauser:1 γij:1 jour:1 ablowitz:1 identity:1 electromagnetism:1 piazza:2 nevertheless:1 symplectiques:1 well:4 s22:1 without:2 coordinate:1 hamilton:7 model:2 dimension:1 dh1:1 dh0:1 gelfand:2 construct:1 manifold:1 graded:1 just:5 being:4 newton:2 obtain:2 valuable:1 world:1 λk:2 λj:11 λi:30 λn:8 functionally:1 previous:2 infinitely:1 conclude:1 seems:3 quadratures:4 other:1 transformed:2 lett:3 solvable:5 remaining:1 euler:2 kingdom:1 lacking:1 couple:1 admitting:3 press:1 immediately:1 collect:1 integrals:4 arbitrary:3 stationary:3 italian:2 mathematical:2 acad:2 classical:1 some:5 searching:2 examples:3 b2:9 kdv:2 dense:1 universita:1 per:1 prop:2 francoise:1 expressing:1 chains:2 minimal:3 bn:2 bh:28 bi:16 bj:1 references:1 properties:1 simpler:1 about:1 algebraic:2 freedom:4 compatible:3 sake:2 introduced:2 consequently:2 perelomov:1 unnoticed:1 h2:2 h0:2 h1:3 integral:2 ut:1 pair:5 en:1 bihamiltonian:3 compatibles:1 landi:1 physical:1 criticisms:1 degli:1 log:8 few:1 strictly:1 there:2 question:1 transform:1 salerno:1 was:5 detγ:1 function:2 complete:2 form:7 regard:2 denoting:1 hj:1 construction:1 politecnico:2 matematica:3 partially:1 cij:1 smooth:4 us:7 theoretical:1 liouville:5 un:1 problem:2 similar:2 b1:13 mechanics:1 aµj:1 constant:2 af:1 defined:1 flow:1 abstract:1 describe:2 condition:2 general:2 dξ:7 examine:1 referee:1 exist:2 formulation:16 constructed:3 mutual:1 completeness:1 when:1 pfaffian:5 arctan:1 aµ1:6 field:12 aµ2:5 remarks:1 details:1 solitons:1 department:1 mathematics:1 ag2:1 ag1:1 differential:1 time:1 problems:2 bundle:1 meaning:2 a2:2 sulla:1 cnr:1 structure:20 searches:1 d21:1 space:1 rather:1 scientific:1 egrabilit:1 remarked:2 starting:1 nuovo:2
|
solv-int9811008.txt |@word consider:4 remarkable:2 depends:1 results:6 existing:1 four:1 eds:3 comments:1 constants:4 centers:3 gi:4 viceversa:1 whose:2 depend:1 reverting:1 quasi:6 investigation:1 restriction:2 manifolds:8 elliptic:3 under:2 details:1 francoise:1 sound:1 diffeomorphic:1 straightforward:1 very:1 springer:3 focus:1 pfaffian:17 anonymous:1 nijenhuis:19 dim:1 dubrovin:1 hamiltonian:26 turns:4 notes:1 solution:2 enon:2 occurs:1 large:1 involution:3 vector:26 bq2:1 λni:1 eigenvalues:6 hospitality:1 specified:1 force:5 literature:1 second:4 concludes:1 further:2 odd:1 editrice:1 canonical:7 even:2 nonlinear:1 appear:1 invertible:6 diag:1 section:2 hereditary:1 birk:1 version:1 fuchssteiner:1 above:11 shared:1 method:1 body:4 simultaneously:1 reflecting:1 respectively:4 fields:3 lichnerowicz:1 2q22:1 tangent:1 separation:6 q12:20 concluding:1 along:1 strong:1 equations:5 change:1 obtained:2 scienze:1 classified:1 study:3 garnier:1 allows:5 p2:10 periodic:1 poisson:19 action:2 opinion:1 studi:1 suitable:2 perelomov:1 quotient:1 heiles:2 wojciechowski:1 useful:1 projection:1 search:1 first:3 pp:5 univ:1 derivatives:1 takes:4 would:1 prove:1 distinct:1 positive:1 bundles:2 uniqueness:1 next:1 few:4 live:1 therefore:2 means:1 type:7 theoretical:1 fokas:1 berlin:4 rigid:1 particular:5 known:4 cases:5 hold:1 iii:4 must:1 account:1 integrating:1 ρi:5 recall:6 equation:6 work:1 oscillator:2 foci:1 values:1 ratiu:1 concepts:1 following:6 example:4 define:2 f1:3 f2:2 give:1 arise:2 degenerate:1 sense:2 standard:8 conversely:1 axis:4 compatible:3 needs:1 boussinesq:2 goal:1 provide:1 verify:3 s1:1 s0:11 ferrarese:1 feature:1 recovers:1 write:2 how:1 nontrivial:1 soliani:1 get:1 symposium:1 field:25 verlag:3 product:1 may:1 after:1 inessential:1 levi:3 plane:4 fi:4 fk:3 fixed:2 fn:1 stress:2 natural:3 dynamical:16 third:1 linear:1 explicit:1 correspond:1 st:3 darboux:10 cannot:1 so:8 sect:2 order:2 origin:1 holds:1 subsections:1 hierarchy:5 indeed:4 novikov:1 influence:1 course:2 xi:3 including:2 mentioned:1 still:3 its:2 roots:1 shorter:1 le:1 thank:1 trieste:3 chosen:1 interesting:1 coordinates:26 actually:1 degrees:4 systems:30 jacobi:10 mail:2 main:1 setting:1 maximal:7 non:6 zakharevich:2 introduce:2 hamilton:9 they:9 nov:1 discuss:1 nor:2 easily:3 term:1 hereafter:2 always:3 presented:4 theory:2 each:4 references:1 universit:2 traces:1 referred:4 homogeneous:3 different:6 arbitrariness:1 ed:1 related:2 owing:1 subsec:1 our:4 eq:6 out:4 living:1 shown:4 benenti:1 matrix:2 space:9 restricted:6 furthermore:2 since:7 denotes:1 mate:1 rational:1 lecture:1 rn:2 integrated:1 math:10 foundation:1 ackel:3 maintains:1 embed:1 quite:2 admits:4 completely:5 flows:5 dimm:1 beginning:1 log:1 recovering:1 geometry:2 inspection:1 could:2 motion:15 bologna:1 hence:2 generalizations:1 separable:11 already:1 variables:10 number:1 rank:3 peculiarity:1 done:1 construct:2 neighborhood:2 clarity:1 given:19 cartesian:2 publication:1 introduction:1 data:1 dipartimento:2 system:18 least:4 their:4 lifting:3 scheme:2 structures:6 recovered:1 completed:1 definitions:1 encompassing:1 believe:1 separability:1 kind:4 marshall:1 cimento:2 integrability:3 submitted:1 seminars:1 matter:3 classes:1 yi2:1 nuovo:2 acknowledged:1 ann:1 pass:1 generalization:2 say:4 kepler:4 conjugate:3 recover:1 any:5 complete:4 lie:1 angle:1 depending:2 calogero:3 instance:2 potential:3 take:2 coincide:1 spectral:1 polimi:1 analyse:1 magri:5 chart:1 birkh:1 most:2 gravitation:1 pair:3 intrinsic:1 class:6 considered:5 torus:2 milano:3 physica:1 proceedings:1 points:2 torun:1 qbh:42 physics:3 notion:1 fact:7 show:1 supported:1 notations:1 relation:1 solutions:2 civita:3 d4:1 q1:22 q0:1 q2:27 based:1 knowledge:2 ellipsoid:4 situations:2 written:4 only:4 experiment:1 factor:1 parabolic:1 integrable:12 constant:2 local:1 achieve:1 characterization:1 do:2 dk:2 dh:5 di:5 de:1 straightforwardly:1 da:1 ones:1 report:1 during:1 dt:2 neither:2 processes:1 transversal:1 fields:1 arxiv:1 preliminarily:1 fulfilled:1 acknowledgments:1 λp0:1 involutive:1 ems:2 through:2 fixed:1 view:1 riemannian:1 satisfy:1 set:7 exists:3 veselov:1 morosi:5 see:4 result:4 p22:2 discussions:1 recently:3 alternative:3 best:2 subject:1 said:3 tensor:22 enlightening:1 ways:2 review:1 marmo:2 symmetric:1 enough:1 µn:2 µi:9 dynam:1 between:1 geometric:4 approach:2 checks:1 europa:1 however:5 killing:1 gratefully:1 comm:1 solv:1 amer:1 tensors:6 originates:1 both:5 essentially:1 pempinelli:1 last:1 many:2 according:3 admit:4 symplectic:12 casimir:1 leeds:1 passing:1 experimental:1 ck:1 ci:1 cn:1 point:4 simple:1 harmonic:2 whatever:1 dimensional:5 exploit:1 lagrange:2 polynomial:3 moreover:3 bλ:1 considering:1 finally:1 described:3 submanifold:1 three:4 been:11 ai:2 reduction:6 4q1:1 interest:1 boston:1 algebras:1 wants:2 filippo:1 aj:2 corresponding:11 vinci:1 cotangent:5 xxx:1 remark:2 matematiche:1 lift:1 recalled:1 representative:1 derivative:1 c2:1 c1:1 developments:1 present:2 case:12 p0:39 p1:48 unlike:1 blaszak:3 arnold:1 transformation:2 will:5 while:1 fernandes:1 situation:4 2q12:1 property:4 conformal:1 procedure:2 subsect:3 real:3 larger:1 coupled:1 vol:2 endowed:1 boiti:1 iv:3 ii:7 reads:1 itself:1 properties:1 exterior:1 riv:1 italy:2 perform:1 make:1 formulations:2 connection:1 member:1 gavrilov:1 proved:3 physical:1 infer:2 independent:4 used:2 yi:2 singapore:1 upon:1 hand:1 usually:1 auser:2 potentials:1 jour:1 identity:1 electromagnetism:1 piazza:1 nevertheless:2 try:1 well:3 analysis:1 obviously:1 concrete:1 solve:1 coordinate:1 arising:1 stating:1 dh1:1 dh0:1 arbitrarily:1 gelfand:3 manifold:13 just:8 being:8 permutationally:1 newton:1 infinitely:1 defined:2 thanks:1 world:1 λk:1 λj:11 momenta:6 briefly:1 λn:7 functionally:1 previous:4 k2:4 conclude:1 neishtadt:1 quadratures:3 belongs:1 lett:4 easy:1 relevance:2 solvable:3 remaining:1 euler:5 generalized:1 fibration:1 aspects:1 lacking:2 read:2 possible:3 admitting:1 immediately:2 unique:1 projectable:1 fixing:1 particle:2 lost:1 contradict:1 loses:1 falqui:1 integrals:8 arbitrary:4 stationary:4 reduced:1 terminology:1 italian:1 mathematical:3 satisfactory:1 classical:4 fordy:2 some:5 searching:2 q22:16 b0:1 examples:7 b2:7 proper:1 kdv:4 cq2:2 happens:2 provided:2 cnr:1 configuration:2 does:2 eliminate:1 minimal:3 λi:32 2q2:2 bn:2 bh:34 bi:14 bj:1 2n:5 kozlov:1 about:1 getting:2 freedom:4 discussed:2 nonvanishing:1 sake:1 recognizes:1 introduced:4 organizers:1 aq2:1 previously:1 h0:1 h1:1 integral:4 due:1 phase:7 coefficients:1 bihamiltonian:2 operator:1 degli:1 x2i:3 elastic:4 comparing:1 there:9 question:1 quadratic:1 way:5 salerno:1 was:1 assumes:1 naturally:1 function:11 elsewhere:1 form:15 regard:1 denoting:2 but:3 somehow:1 construction:1 politecnico:1 matematica:1 evident:1 wish:1 smooth:5 up:2 us:14 krichever:1 liouville:5 those:2 anew:1 problem:8 similar:1 called:1 b1:11 mechanics:2 celestial:1 associated:3 item:2 int:1 corwin:1 abstract:1 describe:1 condition:4 general:10 dξ:1 satisfied:1 referee:1 exist:2 formulation:29 follows:1 constructed:5 ni:1 functions:12 whereas:2 generally:1 pfaffian:1 other:2 remarks:1 multidimensional:1 theor:1 differential:1 problems:2 bundle:3 a1:24 a0:1 a2:28 leaf:3 structure:13 searches:1 geometrical:2 dτ:1 scientific:1 time:1 having:1
|
solv-int9811009.txt |@word gr:5 lack:1 results:3 eds:1 commute:1 6z:2 consider:5 whose:1 compose:1 concerned:1 contained:1 tj:7 those:2 far:1 wave:10 corollary:1 every:1 lecture:4 difference:6 indicate:1 unlike:1 proc:1 notes:4 solution:4 large:1 involution:3 vector:1 annihilates:1 eigenvalues:3 noted:1 zn:3 wronskian:2 ze:1 coefficient:5 integrability:1 eλi:2 reine:1 spectral:11 3z:1 3x:1 appear:2 shares:2 subspaces:3 ˆg:1 increasing:1 ˆm:3 satisfy:3 unbaum:3 respectively:1 here:2 desired:1 groups:1 berkeley:1 alone:2 strong:1 equations:11 change:1 institute:1 loop:1 action:2 quotient:1 useful:1 transformations:3 requiring:1 inverses:1 berest:1 use:1 would:3 commun:1 contains:1 call:2 therefore:1 taken:1 ψc:22 associated:4 type:2 more:4 introducing:1 sharing:1 formally:1 duality:2 solitons:4 operators:32 eλ:1 particular:5 known:5 isomorphism:1 huygens:2 equation:7 des:1 mi:2 publications:1 following:2 bakalov:3 example:2 proof:2 tau:2 involve:1 sense:2 s3:1 s1:1 holds:1 e2x:2 s5:1 write:1 maps:1 pure:3 significance:4 instead:2 ordinary:18 parameter:6 sato:1 map:4 mat:1 singular:1 may:3 earlier:1 multiplication:1 fi:1 physical:1 dynamical:3 whenever:1 explicit:1 element:3 darboux:3 so:3 allow:1 order:5 restriction:1 produces:1 hierarchy:6 over:1 satisfied:5 paper:3 thesis:1 existence:1 satisfies:8 its:3 no3:1 sλ:2 sciences:1 lc:1 chosen:1 interesting:1 lj:1 τc:10 conjugation:1 better:1 systems:7 lp:6 derivative:1 main:1 might:1 non:5 greater:1 acklund:1 chalykh:1 uspekhi:1 band:2 nov:1 now:2 yu:1 easily:1 term:2 alex:4 university:1 2x:2 2z:4 sufficiently:3 l0:9 each:2 found:3 polynomially:1 arxiv:1 sλi:2 idea:1 society:3 used:1 expect:1 tˆ:5 special:1 24z:1 shown:6 space:3 furthermore:1 since:5 adelic:1 research:1 particles:1 collisions:1 acting:2 funcˆ:1 rational:13 formula:1 ri:3 math:6 aˆm:4 theory:1 8z:3 institut:1 ord:1 ruijsenaars:3 generate:1 definition:1 pairs:2 degenerations:1 linearizing:2 american:3 hence:1 formulas:1 already:2 rothstein:2 variables:3 rank:1 xz:4 duistermaat:1 ring:14 precisely:1 sutherland:2 subring:2 given:6 necessarily:1 similarly:3 introduction:1 system:2 relations:1 their:4 airy:2 gives:1 relationship:3 differentiate:1 x2:2 x3:1 translation:2 believe:1 than:2 coefficients:11 finitely:1 likely:1 limiting:2 preparation:1 fˆ:1 were:1 tion:1 result:2 boston:1 20z:1 generalization:2 say:2 angew:1 need:1 seen:1 seem:1 any:10 relatively:1 wilson:4 angle:1 depending:1 self:1 note:11 instance:1 generalized:2 even:1 play:1 though:1 object:1 reach:1 hautes:1 connected:1 class:1 kc:9 soliton:9 especially:3 ke:1 considered:2 physica:1 proceedings:4 kp:26 principle:2 exz:23 fact:5 akhiezer:1 show:1 supported:3 spaces:1 solutions:14 12z:2 trivial:1 find:2 situations:1 should:1 lemma:3 only:7 factor:1 integrable:4 moser:6 local:1 above:1 notation:2 dependent:1 familiar:1 de:1 cannot:2 words:1 prime:1 differential:39 factorization:3 qc:7 nauk:1 common:1 crm:5 kernel:3 etudes:1 set:2 constructing:1 exists:4 achieved:1 observed:1 see:4 differentiable:2 recently:1 λi:4 subject:1 satisfying:1 rings:3 scientifiques:1 written:4 between:2 conditions:1 choose:1 terms:2 segal:1 however:4 veselov:1 comm:3 wr:2 solv:1 distribution:1 both:2 diejen:1 limits:1 many:1 according:1 propagation:1 connection:1 finds:2 comes:1 ci:4 cn:4 point:2 ca:1 cf:2 dimensional:5 anti:2 16z:4 polynomial:8 moreover:3 pp:9 described:2 commutative:3 basis:5 addition:2 due:1 been:5 int:1 much:1 z2:2 inventiones:1 ph:1 pi:6 define:2 determinant:1 corresponding:4 commutes:1 yakimov:3 subspace:6 curves:1 c2:5 c1:6 present:2 case:6 exponential:10 defining:1 will:11 bispectral:27 while:1 suppose:1 applies:1 situation:1 property:3 procedure:1 vol:1 thus:4 them:1 intertwining:1 clearly:1 involutions:1 proved:1 finite:2 difficult:1 literature:1 parametrizes:1 infinite:1 frequently:1 serdica:1 well:4 horozov:4 calogero:7 proposed:1 being:1 questions:1 differentiation:1 shorthand:1 ps0:1 letting:1 adding:1 preprint:1 conclusions:1 conclude:1 had:1 lett:2 theorem:9 adm:4 eigenfunction:5 eigenvalue:6 evaluate:1 spanned:2 know:1 using:1 unique:1 translationally:1 particle:4 follows:3 communications:1 continue:1 arbitrary:1 simply:4 reduced:1 mathematical:5 right:1 methods:1 classical:2 sequence:1 mathematicae:1 translational:13 some:1 examples:1 choosing:1 specified:1 kdv:3 dimensions:1 lead:1 providence:3 bessel:1 demonstrated:1 workshop:1 bm:5 journal:1 wavefunctions:4 properties:1 11z:1 dependence:1 o:1 consequently:1 linearization:1 appropriate:1 references:1 determine:1 operator:24 van:1 additional:2 springerverlag:1 support:3 there:6 question:1 appl:1 way:2 was:3 function:17 form:7 but:4 volume:3 construction:1 grassmannian:3 highest:1 he:1 applying:1 versions:1 whether:1 wish:1 monic:1 up:1 us:1 below:1 vinet:1 problem:4 similar:1 called:1 ex:1 ac:2 mathematiques:1 constant:8 ad:1 defined:3 abstract:1 am:4 general:4 quantum:3 tomography:1 distributions:6 constructed:1 functions:13 no:5 composing:1 application:1 other:3 role:1 elements:4 generates:1 separate:1 models:1 problems:1 polynomials:2 generated:3 important:2 variable:2 4z:2 gr1:1 physics:1 baker:1 factors:1 pseudo:1 together:1 time:3 having:3
|
solv-int9811010.txt |@word results:1 commute:2 edu:1 expressions:1 devoted:1 whose:1 inverse:2 tw:1 γq:3 dickey:7 intensive:1 tk:1 th:2 dressing:2 fay:7 string:1 straightforward:1 zhang:2 wave:4 deformations:1 school:1 hamiltonian:2 solution:2 convenience:1 vector:3 recall:1 anal:1 zm:3 zero:1 further:3 khesin:1 goes:2 residue:1 established:2 nonlinear:1 expressed:2 consistently:1 cheng:1 new:4 contrast:1 satisfy:1 respectively:4 here:1 xλ:4 china:1 address:1 along:1 equations:1 obtained:2 shift:1 study:3 action:2 shifting:2 tu:1 linearly:1 virasoro:1 tn:1 use:1 would:1 commun:3 next:1 linear:2 call:1 therefore:2 more:1 introducing:2 operators:4 ti:4 particular:1 iii:2 integrating:1 deformed:17 ml:9 equation:7 work:1 infinitesimal:6 concepts:1 following:9 under:1 proof:7 tau:10 qdeformed:1 calculation:1 permutations:1 performed:1 council:1 s3:16 s2:11 discussion:1 holds:3 recovers:2 ordinary:7 parameter:1 sato:6 product:1 after:1 residues:1 lax:9 date:1 types:1 lemmas:1 pdos:4 so:2 order:1 s0:4 words:2 iti:1 hierarchy:38 spectral:1 zeq:1 through:2 satisfies:3 still:1 its:4 before:1 ln:14 interesting:2 ll:11 lm:2 lk:7 systems:2 derivative:1 main:1 deformation:1 τq:62 correspondence:1 acklund:4 introduce:2 framework:1 yq:6 nov:1 now:2 yu:1 above:2 easily:1 february:1 equality:1 always:1 university:1 2z:1 2d:1 each:2 s1:15 constraints:1 differential:5 chung:1 series:1 mas:1 literature:1 connect:1 quantum:2 our:4 operation:1 eq:11 special:1 out:2 shown:3 jimbo:2 matrix:1 space:1 res:6 furthermore:1 since:2 induces:1 denotes:1 weightings:1 acting:5 formula:3 ref:1 math:12 shows:1 theory:3 quite:1 admits:1 definition:1 turn:1 int:2 hence:4 qn:3 first:1 variables:2 number:1 xz:5 simplified:2 another:3 carry:1 xq:12 given:1 bracket:1 zω:1 introduction:1 together:1 adjoint:2 system:4 construct:1 too:1 structures:2 gives:1 shifted:1 proving:1 part:5 zθ:1 x2:1 x3:1 peculiar:1 cyclic:1 see:3 preparation:1 symmetries:14 kashiwara:1 ming:1 seco:1 conjugate:1 constrained:3 hsien:1 any:2 viewed:1 petviashvili:2 convenient:1 gravity:1 bilinear:1 ˆq:1 reach:1 horozov:1 connected:1 letter:1 pair:1 xµ:1 soliton:1 orlov:1 flow:1 typeset:1 points:1 ckp:3 exp:7 exq:2 exz:11 fact:1 laws:1 show:4 leibniz:1 supported:1 miwa:2 relation:2 analogue:1 find:1 parameters:1 should:3 lemma:9 explicitly:1 rich:1 integrable:3 do:1 his:1 establishes:1 express:1 closely:1 combinations:1 gen:4 kadomtsev:2 qx:3 arxiv:1 ωq:37 roger:1 contain:1 qi:10 qk:4 view:1 shulman:1 multiplying:1 bts:3 tu1:1 national:2 differentiation:1 depends:1 sec:3 recently:2 dµ:1 λi:1 subject:2 commutation:1 written:1 µi:1 approach:3 notice:1 terms:3 confusion:1 wu:1 key:1 solv:1 both:1 last:1 according:2 pdo:2 etc:2 connection:1 expression:1 fields:1 corresponds:1 maintained:1 simply:1 moreover:1 kp:31 considering:1 described:1 transformations:5 second:2 trajectory:1 moerbeke:7 due:1 been:3 defined:8 reduction:7 basic:1 pi:5 define:5 θk:2 corresponding:1 commutes:1 concerning:1 func:1 mail:1 denote:2 spirit:1 present:1 case:1 classifications:1 exponential:1 value:1 will:1 situation:1 property:2 conformal:1 shiota:5 refs:1 thus:1 iv:2 ii:1 different:1 grant:1 proved:1 several:1 used:1 singapore:2 flows:6 hand:1 parametrized:1 infinite:1 identity:9 relies:1 ccu:1 well:3 without:1 haine:1 resz:8 being:1 obtain:3 world:2 facts:1 taiwan:1 frenkel:2 letting:1 generator:6 belongs:1 combine:1 lett:5 easy:3 theorem:6 mod:1 divided:1 identical:1 using:9 formal:2 reshetikhin:1 like:1 identifying:1 follows:5 serves:1 reduced:1 because:1 classical:1 some:2 understood:2 kdv:1 lyubashenko:1 provides:1 numbers:1 scientific:2 equivalent:2 bi:1 binomial:1 revtex:1 science:1 about:1 carried:1 compatible:3 into:1 nsc:1 integral:1 nothing:1 references:1 operator:19 van:7 additional:16 prepare:2 initial:1 conservation:1 ed:1 resolvent:3 was:1 function:13 form:3 but:2 iliev:3 adler:7 algebras:2 whether:1 us:7 ωi:3 ui:1 backlund:1 called:7 associated:4 ai:3 abstract:1 pseudodifferential:1 general:1 single:1 dλ:1 formulation:2 θn:1 identities:1 constructed:2 ni:1 functions:4 dressed:1 field:2 other:3 republic:1 department:1 mathematics:2 zheng:1 completes:1 separate:1 models:1 setting:1 vertex:5 generated:2 sides:1 structure:1 acknowledgment:1 implies:3 rule:1 35q53:1 time:1
|
solv-int9811011.txt |@word ψ1x:4 darboux:23 partial:2 consider:2 ψ1t:2 results:3 integration:5 four:1 φ1x:3 lakshmanan:2 expressions:1 φ1t:3 devoted:3 whose:1 inverse:6 terms:16 referring:1 paris:1 finally:4 manifolds:3 under:2 te:1 pickering:1 applied:5 advantage:1 returning:1 far:1 rise:1 springer:2 wave:5 summarized:1 resonant:1 condition:1 level:1 list:2 solution:11 inspection:1 sign:1 painlev:15 dynamics:1 substitute:1 ψ2x:4 bilinear:3 aim:2 nonlinear:3 appear:1 giving:1 section:13 tabor:1 version:6 above:2 new:2 solitonic:3 method:18 satisfy:2 simultaneously:1 respectively:2 conte:1 here:2 bi:4 l22:1 eci:2 address:1 represented:1 along:1 coupling:1 equations:17 appears:1 logarithmic:1 calculate:1 obtained:9 property:3 study:5 studied:1 allows:6 example:1 suggests:1 suggestion:1 usually:1 pxy:2 followed:1 merely:1 explained:1 apply:3 total:1 tools:2 derivatives:4 use:7 ψy:14 proceed:1 would:1 prove:1 positive:1 contains:1 negative:2 ψt:8 next:2 call:2 therefore:5 yangmills:1 iteratively:1 ablowitz:1 possible:1 successful:1 fokas:2 odinger:1 appendix:3 encouragement:1 particular:3 known:1 cases:3 iii:6 easiest:2 account:1 defines:1 equation:42 mi:4 modified:3 mj:1 mt:3 interaction:4 following:3 my:20 mx:1 f1:5 f2:4 figure:14 stated:1 calculation:1 βx:4 indicates:1 calvo:1 numbers:1 allowed:1 handle:1 conversely:1 verlag:1 information:1 rather:1 get:1 nyt:2 write:6 how:3 criterion:1 acta:1 product:1 2my:21 singular:39 collection:1 lax:23 φ2t:1 fi:2 summarize:2 φ2x:1 data:2 compatibility:1 constants:5 branches:2 clarkson:1 explicit:3 yielding:1 φx:5 allow:3 definitions:1 af1:1 talk:1 six:1 interpretation:1 indeed:1 satisfied:2 l19:1 paper:5 through:2 its:1 derive:1 thank:1 located:1 ln:5 temporal:1 fruitful:1 forms:1 systems:2 τx:1 relate:1 mail:1 τt:1 correspondence:1 non:11 good:3 return:2 salamanca:2 mxy:14 auto:2 acklund:3 newman:1 they:1 singularity:5 now:4 easily:2 term:2 hereafter:1 university:1 40k:1 identified:1 establishing:1 each:2 2m:3 pb95:1 arxiv:1 ei:4 arbitrariness:1 series:3 idea:1 related:3 society:1 yield:1 combining:2 our:3 es:1 out:1 shown:5 precisely:1 m2y:2 furthermore:1 research:1 smm:6 affords:3 kent:1 lecture:1 integrated:1 math:10 shows:1 linear:11 found:1 ψ2t:2 ısica:2 possibility:1 approaches:1 complicated:1 e1:6 e2:6 pairs:7 perform:3 determining:2 could:2 iterative:3 linearized:1 universidad:1 hence:1 first:6 initial:2 manuscript:1 miura:2 restrict:1 xy:6 4b:1 ψxy:4 ψxx:4 φ2y:1 maple:2 dispersive:5 similarly:1 introduction:1 leading:8 carnevale:1 system:8 construct:5 compulsory:1 their:2 vxx:1 calculations:3 structures:1 adopts:1 relationship:2 alonso:1 part:3 authors:1 attempt:1 believe:1 coefficients:2 require:3 iteration:5 integrability:1 express:1 determined:3 were:1 λut:1 powers:2 result:2 seminal:6 generality:1 rewrite:1 mind:1 qpx:1 manner:1 need:1 seen:1 solitons:4 generalizes:1 jour:1 zero:3 depending:4 self:1 able:1 note:1 potential:1 generalized:6 subject:2 salle:1 shall:6 pyt:1 most:2 plan:1 qxxx:1 pair:17 acknowledgements:1 why:2 soliton:3 laurent:1 considered:8 chosen:1 later:3 χy:1 χx:4 χc:1 χb:1 χa:1 velocity:1 physics:4 χj:3 fact:1 show:2 supported:1 relation:2 solutions:38 x3:1 substituting:4 trivial:2 ae1:1 q0:1 based:1 state:1 should:6 only:6 explicitly:3 rich:1 qx:7 integrate:2 dominant:6 means:6 2mx:8 de:3 ϕi:2 dx:4 despite:1 gen:1 evolution:1 qt:1 qv:6 fields:3 dgicyt:1 differential:2 expansions:2 remove:2 redefined:1 london:1 musette:1 view:2 set:5 constructing:2 respect:2 maximum:1 ωxx:4 w2:1 w0:4 close:1 best:1 techniques:1 said:1 eigenfunctions:16 written:2 various:1 between:9 invariant:1 reading:1 approach:1 choose:1 gives:1 recently:1 importance:1 matveev:1 however:1 2αx:2 conde:1 wv:3 uω:3 solv:1 p2y:2 wy:1 wx:4 both:2 providing:1 many:2 taking:4 according:1 contract:1 etc:1 pde:5 expression:6 among:2 ci:1 point:2 simple:1 corresponds:1 leon:1 analyzed:1 polynomial:3 proved:1 second:3 pp:1 transformations:7 pt:5 basis:1 px:2 py:5 been:10 int:1 reduction:1 describes:1 combined:4 inv:1 define:2 field:7 direction:3 arises:1 sufficient:1 pempinelli:1 determination:1 systematic:1 derivative:1 careful:1 spain:1 case:5 pacs:1 will:7 while:4 behavior:8 orica:1 balance:1 leaves:1 procedure:6 coupled:3 vi:7 boiti:1 thus:3 them:4 uxx:3 iv:3 ii:5 vq:1 n2y:3 itself:2 vt:1 dual:1 vw:1 vx:1 vy:2 2uv:1 different:5 φt:3 mxx:2 author:2 generic:1 φy:3 algorithmically:1 cross:1 same:2 complex:2 1x:2 several:2 difficult:4 used:9 see:3 vvx:1 bonus:1 hand:3 v0:3 v2:1 moving:1 purpose:1 potentials:1 totally:1 identity:1 task:1 schr:1 nevertheless:1 well:6 analysis:10 solve:1 arising:1 manifold:40 proposed:2 obtain:20 rest:1 identify:1 using:5 useful:2 scattering:3 nov:1 previous:5 conclusions:2 except:1 weiss:2 qx2:1 setting:1 easy:1 c13:1 c12:2 c11:2 transformation:23 designate:1 real:3 sonia:1 bij:1 eigenfunction:1 represents:1 showing:1 february:1 reads:1 press:1 necessary:1 loss:1 pertinent:1 like:1 identifying:1 follows:2 unnecessary:1 specific:1 ai:8 yields:3 arbitrary:9 multiplicative:1 mathematical:1 because:3 often:1 deal:1 truncated:6 2x:1 some:4 truncates:1 b1:4 b2:3 moreover:1 chakravarty:1 ourselves:2 est:6 dimensions:18 extensively:1 provides:4 refer:1 algorithmic:3 usal:1 jumps:2 ψx:10 expansion:12 step:1 substitution:3 properties:1 about:2 simplest:1 discussed:1 dependence:1 o:2 konopelchenko:1 introduced:1 consequently:1 cambridge:1 φxx:1 plethora:1 into:1 obtaining:2 martinez:1 references:1 determine:4 ea1:2 ea2:2 methods:1 her:1 area:1 there:6 question:1 u0:1 long:5 class:1 accordingly:3 facultad:1 way:6 m1:4 analyze:1 was:4 m0:3 function:2 complete:1 form:2 m2:3 but:2 construction:3 line:4 pdes:7 truncation:3 ωx:4 whether:1 ut:2 ωt:7 us:14 below:1 ωj:1 simplifying:1 uj:1 problem:1 similar:1 professor:1 detailed:1 constant:3 choosing:2 defined:5 abstract:1 myt:2 single:1 check:2 constructed:5 functions:10 no:1 mathematica:1 when:2 nx:3 ny:16 other:2 branch:2 spatial:1 test:1 exp:6 time:1 problems:4 medina:1 a1:19 a2:17 linearization:1 structure:1 radha:2 independently:1 implies:1 longer:1 starting:2 pilar:1 nxy:3 depth:1 hirota:4 requires:3 4c:1 4a:1
|
solv-int9811012.txt |@word secondly:1 since:1 partial:2 consider:1 penrose:1 fa2:3 braam:7 bull:1 four:3 eds:3 scalar:3 commute:1 asian:1 grateful:1 hyperboloid:4 expressions:2 contributions:1 localized:1 row:1 whose:1 inverse:1 graph:1 tr:10 γj:1 finally:1 elliptic:4 under:2 visualizing:1 include:2 magnetic:2 p2:2 straightforward:1 induce:1 geometrical:1 faj:1 valued:1 fall:1 telling:1 nonlinearity:1 difference:6 matrices:5 1984b:2 condition:3 leads:1 mild:1 forth:1 notes:1 michael:3 solution:4 t1:2 large:1 discrete:18 convenience:1 vector:6 dealt:1 small:1 gauge:12 fµν:2 β2j:1 periodicity:1 sin2:1 consists:2 likely:2 dynamics:2 ode:1 theory:1 spectral:3 established:1 what:7 nonlinear:4 appear:1 euclidean:6 diag:1 section:1 unwound:1 version:4 expresses:1 t2:2 journal:1 satisfy:2 respectively:1 never:1 spacing:2 here:7 free:1 xν:1 alone:1 along:3 equations:23 change:1 obtained:1 remark:1 rdr:1 institute:1 study:2 studied:1 approaches:1 prior:1 simultaneous:1 usually:1 involves:2 quotient:1 appropriately:1 via:2 spatially:1 family:2 merely:1 replace:1 addressed:1 durham:2 use:1 handled:1 commun:3 remains:1 positive:8 contains:1 bundles:7 negative:1 ψj:2 sommerfield:1 therefore:1 reciprocity:3 taken:1 3le:1 stage:1 reflects:1 more:3 flat:2 duality:1 becomes:4 operators:3 stable:1 70th:1 curvature:9 2w2:5 virtue:1 known:1 ward:6 hold:1 me:1 springer:1 monopoles:26 equation:21 work:3 dx2:1 values:2 universe:1 following:1 example:6 numbers:1 f0:1 f1:2 f2:2 impose:1 ramifications:1 solved:2 referee:1 arise:1 sn2:1 cartan:1 sense:4 tan:2 simple:2 verlag:1 sir:2 rather:3 means:1 write:2 how:1 nontrivial:1 sec2:1 ordinary:1 palev:1 parameter:4 sin:2 simplicity:1 product:1 express:2 singular:1 may:3 derived:1 mapping:1 lump:2 fa:5 minitwistor:1 birthday:1 lax:5 choice:2 constants:2 2x2:1 higgs:3 sech:1 chern:1 lines:1 correspond:4 su:7 element:1 so:7 sn:3 sl:1 subsequently:1 order:1 gµν:1 closely:1 indeed:1 pointed:1 mainly:1 murray:4 interpreted:1 pm:1 signs:1 japan:1 its:5 roots:1 scale:1 derive:1 group:3 symmetry:1 chosen:1 manin:1 coordinates:7 actually:1 systems:5 derivative:1 defining:1 correspondence:4 non:3 good:1 motivated:2 material:1 cover:3 scaling:1 they:5 half:2 oxford:2 norbury:2 speculate:1 it2:2 it3:1 eigenvalue:1 hurtubise:2 γ2j:1 university:5 inequality:1 dφ:1 each:4 2n:1 2h:4 lorentzian:3 2k:1 homogeneous:2 arxiv:1 edinburgh:1 list:1 reduce:2 idea:1 related:5 t3:1 constitute:1 toda:6 investigated:1 static:1 obtains:1 1984a:2 measure:1 quantum:1 our:1 special:2 out:2 rp:3 matrix:7 space:42 furthermore:1 algebra:2 denotes:5 replacing:1 acting:1 geom:1 rational:2 lecture:1 induced:1 issue:1 twistors:1 math:6 linear:3 personal:1 variant:1 2h2:2 aω0:1 possibility:1 standard:2 admits:1 completely:2 dx:1 8r:1 quadric:1 definition:1 backwards:1 p2a:5 r3:2 geometry:2 hyperbolic:22 ds2:3 times:1 plane:1 signature:1 austin:7 βj:1 first:5 forwards:1 omitted:1 variables:1 geodesic:1 rank:1 lond:1 spinning:1 multiplying:1 another:1 reached:1 open:2 size:1 given:3 fk:2 publication:1 similarly:1 introduction:1 top:2 tata:1 system:11 least:1 their:4 brevity:1 draft:1 eqn:1 dt2:2 jarvis:2 gives:1 holomorphic:1 2ab:1 exactly:3 accurately:1 nahm:21 part:2 x2:2 x0:1 x1:1 than:3 coefficients:1 kind:1 determines:1 cyclic:1 sections:1 see:6 final:1 determined:1 were:3 dtp:1 minus:1 symmetries:1 rewrite:1 explicit:1 ann:1 corrigan:2 curves:2 say:1 emphasizing:1 conjugate:2 need:1 curved:2 null:2 adhm:2 complete:1 lie:2 dµ:3 zero:2 latter:1 mills:2 note:5 sciences:1 potential:1 take:2 timelike:4 jacobian:1 indexed:1 modulus:1 antihermitian:1 shall:5 most:1 cω0:1 eight:1 significant:1 pair:6 acknowledgements:1 stands:2 soliton:10 singer:4 parametrize:1 takes:1 consequences:1 clear:1 tβ:1 tγ:1 tα:3 nondegenerate:1 yang:2 overdetermined:1 physics:1 fact:2 quantity:2 show:1 discovered:1 relation:4 solutions:14 stepping:1 d2:1 parameters:3 conics:4 should:1 being:3 only:4 explicitly:1 geodesics:1 integrable:10 local:2 over:1 dn:4 do:1 his:1 dj:1 notation:2 get:2 simplest:3 overall:1 dc:1 aim:1 dϕ2:1 ones:1 words:3 dy:1 dv:2 dw:1 dt:4 du:3 dr:2 geometric:1 areas:1 evolution:2 continuum:4 covering:1 fields:3 differential:5 method:1 cf:2 double:1 fixed:1 riemannian:2 moduli:2 set:3 exists:1 notational:1 operates:1 namely:4 sec:2 w2:3 terms:5 limiting:1 goddard:3 techniques:1 visualize:1 doebner:1 ways:1 struction:1 currently:1 definite:3 sites:1 tend:1 symmetric:1 closed:1 between:5 invariant:3 subscript:1 conditions:2 notice:3 recently:2 twistor:3 hitchin:5 transpose:2 wj:1 vanishing:1 concentrate:1 jh:1 solv:1 article:1 inertia:1 both:1 cos:2 enables:1 many:2 taking:2 according:1 etc:1 connection:1 colloquium:1 huggett:1 expression:1 comes:1 grounds:1 ck:1 cj:2 relevant:2 cn:4 periodic:1 monad:1 period:1 cd:3 dimensional:11 concluding:1 anti:9 polynomial:1 prasad:1 points:1 considering:1 described:2 transformations:1 second:1 three:7 been:3 int:1 reduction:2 describes:2 hawking:2 likewise:1 pk:2 universal:2 define:2 describe:3 corresponding:6 quantities:4 essentially:1 covered:1 c2:1 c1:1 general:2 manifolds:1 case:14 p3:1 multi:2 p1:3 look:1 tanh:5 straight:1 bψ:1 single:2 value:1 will:4 dept:1 leaves:1 dad:1 cylinder:1 xµ:3 coupled:1 λaλ:1 metric:5 2t2:1 thus:1 instantons:2 surface:2 4h2:3 converts:1 dual:2 turns:1 2uv:1 make:1 atiyah:12 lett:2 poincar:3 princeton:1 complex:7 paj:1 several:1 subalgebra:1 disc:1 independent:2 used:1 infinity:3 singapore:1 parametrized:1 delicate:1 completeness:1 identity:2 off:1 well:1 consistency:1 five:3 con:1 self:1 dh1:1 usual:1 world:1 manifold:4 just:1 moments:1 generally:1 λa:1 drinfeld:1 questions:1 immediately:1 cp:5 nov:1 now:2 preprint:1 ads:4 yu:1 seems:2 except:1 transparent:1 lattice:15 interested:1 location:1 relevance:1 transformation:1 euler:2 real:6 eigenfunction:1 represents:1 read:1 spatial:1 possible:1 admitting:1 corresponds:1 sutcliffe:2 vζ:1 press:4 integer:6 desitter:11 follows:9 reduces:1 specific:1 bps:3 etry:1 works:1 mathematical:2 because:1 deal:1 polar:1 some:5 cs:1 examples:1 happens:3 provided:1 cψ:1 ellis:2 integration:1 equal:1 tends:1 proc:1 scientific:1 bc:2 equivalent:1 bh:9 bj:2 bt:3 step:1 although:1 simpler:1 about:2 anything:1 acd:1 freedom:2 covariant:2 a2:1 underway:1 propagate:1 introduced:1 consequently:1 automatically:1 seeing:1 soc:2 cambridge:1 h2:1 communication:1 into:1 integral:2 bjh:3 down:1 remarks:2 appropriate:1 right:1 references:1 determine:1 einstein:1 bombay:1 log:1 buchdahl:2 removing:1 there:1 question:1 transform:1 long:1 u2:2 pa:4 way:1 forward:1 bogomolny:3 was:3 function:1 dρ2:1 form:3 2hu:1 but:7 volume:1 construction:4 aµ:6 made:1 annihilate:1 consist:1 uv:1 maximum:1 us:4 assume:1 below:2 limit:8 uk:1 planes:2 fαβ:1 distribution:1 monopole:3 called:2 expect:1 constant:9 ad:1 defined:5 certain:3 abstract:1 aj:3 am:1 denote:2 intimately:1 conserved:5 dν:1 exist:1 dλ:1 dθ:1 defines:1 functions:9 2dv:1 determinacy:1 integrability:1 amounts:1 index:2 when:2 detail:2 reality:1 field:4 other:4 solitons:2 mathematics:2 acceptable:1 picture:1 star:1 hirota:2 important:1 velocity:1 variable:1 structure:1 algebraic:2 spacelike:2 bcd:1 factors:1 curve:3 time:14 backward:1 original:1
|
solv-int9811013.txt |@word consider:3 results:1 four:1 subclass:1 inverse:1 turkish:1 r10:2 wji:1 ankara:2 exits:1 hamiltonian:8 irreducible:2 δh1:2 δh0:2 rj:1 indices:1 anal:1 10d:1 second:2 bilkent:1 nonlinear:1 plays:1 hereditary:2 fuchssteiner:4 above:1 new:2 satisfy:1 degree:1 respectively:1 here:5 groups:1 equations:7 tian:2 sobolev:1 technical:2 study:1 studied:3 geng:1 formulated:1 classification:3 texts:1 pp:1 translational:1 total:1 use:1 takes:1 commun:1 contains:1 suppl:1 mckean:1 type:8 fokas:2 operators:8 2ud:4 known:1 cases:2 springer:1 ma:1 dodd:1 equation:1 work:3 det:1 2ux:3 following:2 nonsingular:1 example:2 council:1 give:1 sokolov:5 states:1 numbers:2 degenerate:4 verlag:1 boussinesq:3 r11:2 write:1 nontrivial:2 mat:1 singular:2 may:1 applications:1 levi:1 lax:1 faculty:2 constants:2 correspond:1 recursion:15 ito:1 hierarchy:2 over:1 mainly:1 london:1 preliminary:1 satisfies:1 urses:3 thank:1 fiz:1 interesting:1 systems:8 jacobi:1 olver:3 djk:1 non:2 pjk:1 propose:1 they:3 nov:1 now:1 easily:1 term:2 university:2 classified:1 2d:4 bihamiltonian:1 arxiv:1 sov:1 constitute:1 our:1 χij:3 out:1 shown:1 matrix:1 furthermore:1 rev:2 research:1 stud:1 u2x:1 math:8 linear:5 surveys:1 quite:1 admits:3 york:2 8v:1 8u:1 hence:2 bijk:1 first:3 symmetry:1 variables:1 ξji:1 given:5 adjoint:1 system:24 appl:1 convention:1 academy:1 udx:1 kupershmidt:1 part:3 jordan:1 authors:1 integrability:1 were:1 powers:1 symmetries:1 topics:1 seminar:1 lie:1 wilson:1 depending:1 latter:1 liu:2 shall:1 qxxx:2 reducible:1 class:1 considered:1 kj:1 physica:2 proceedings:1 principle:2 physics:1 laws:1 oevel:1 show:2 supported:1 find:1 based:1 parameters:1 rij:3 only:1 integrable:5 his:1 de:1 dx:3 du:1 ds:4 qx:1 differential:2 factorization:1 exists:1 edition:1 recently:3 qti:1 nondegenerate:1 functionals:1 its:2 written:1 terms:4 uux:1 originated:1 cijk:1 wu:1 jk:2 solv:1 tuba:1 both:2 admit:1 rosenau:1 otherwise:1 ci:1 point:1 moreover:1 16v:2 turkey:3 arts:1 transformations:1 skew:1 been:1 int:1 gao:2 systematic:1 derivative:3 present:1 case:2 will:2 behavior:1 aij:1 property:1 procedure:1 u2xx:1 coupled:2 vol:1 thus:1 uxx:1 middle:1 ik:1 vt:1 vx:3 uxxx:2 2uv:1 containing:1 anymore:1 identities:1 belong:1 several:1 flows:1 whole:1 well:1 analysis:1 academic:1 without:1 r01:2 r00:2 karasu:3 drinfeld:3 summed:1 adv:1 sciences:3 tubitak:1 lett:11 theorem:2 5d:1 east:1 bij:5 possible:1 admitting:4 press:1 using:1 qxj:2 qxk:2 δu:4 δv:4 korteweg:1 δh:4 qxx:1 essential:2 qxi:1 truncated:1 some:1 respect:1 kdv:9 extensively:1 comments:1 prog:2 prof:1 scientific:1 bi:5 constructive:1 fordy:3 91a:1 o:1 compatible:2 mixed:1 h0:1 h1:1 functional:2 pair:4 references:1 novosibirsk:1 einstein:1 operator:11 u4:1 there:1 u3:1 u2:2 start:1 conservation:1 form:3 2vd:2 but:1 repeated:1 russian:2 highest:1 rjk:1 adler:1 partially:1 ux:4 ut:1 6uux:1 up:1 backlund:1 ud:2 called:5 associated:1 ai:1 conserved:1 formulation:2 commuting:2 satsuma:2 functions:1 2dv:1 ref:1 graduate:1 valid:1 role:1 tij:1 department:2 mathematics:2 theor:3 sijk:3 includes:1 structure:2 qijk:1 vries:1 hirota:2 4d:2
|
solv-int9811014.txt |@word partial:4 consider:7 remarkable:1 similarity:6 results:6 leads:2 grateful:3 systematic:1 whose:1 preserves:1 inverse:3 albrecht:1 technique:3 answered:1 those:3 excluded:1 under:1 third:1 case:17 kent:2 straightforward:1 far:1 implicitly:1 rise:2 keeping:1 choice:1 difference:2 exact:1 deformations:1 condition:1 generalised:2 entire:1 school:1 immediately:3 presented:3 notes:2 solution:26 enon:2 large:1 solved:1 relation:2 force:1 consistent:1 painlev:47 involution:1 further:2 dynamics:1 10v:4 ode:6 10u:2 xψ:3 3x:1 appear:2 ct2:1 t2n:4 giving:3 d2:3 section:1 3v:7 3u:1 d3:1 current:1 poles:1 sur:4 above:7 sup:2 new:9 method:7 satisfy:1 led:1 degree:1 respectively:1 modify:3 here:8 les:4 address:2 consideration:1 equations:45 appears:3 change:2 ordinary:10 obtained:16 chaotic:1 institute:1 studied:1 allows:4 reason:1 commonly:2 periodic:1 action:1 linearised:1 suitable:1 changes:2 heiles:2 via:4 classification:2 extra:1 systems:1 isomonodromic:1 9x:1 emoire:1 9v:1 use:4 would:2 erentielles:4 remains:2 8v:4 contains:4 visit:1 negative:1 next:1 almost:1 f07:1 therefore:5 australian:1 type:4 today:1 more:2 chapter:1 elliptic:1 becomes:5 berlin:2 mansfield:1 particular:4 known:8 cases:2 hold:1 must:2 ramani:3 account:2 defines:1 equation:29 work:1 modified:3 london:1 flaschka:1 values:2 following:1 making:1 example:7 compare:1 2ln:9 give:10 preserving:2 discovery:1 involve:1 numbers:1 council:1 arise:1 transcendent:1 rescaling:1 conversely:1 verlag:2 information:4 provide:5 verify:1 six:3 algorithms:1 write:3 how:5 extended:2 fourth:3 instead:3 valuedness:1 parameter:8 obius:1 map:2 express:2 description:1 singular:3 may:3 singularities:1 movable:3 plane:1 lax:4 compatibility:2 constants:1 fordy:1 short:1 clarkson:4 imply:1 explicit:1 correspond:1 rather:1 so:8 order:19 holds:1 words:1 hierarchy:86 indeed:1 altogether:1 satisfied:1 course:1 paper:2 including:2 satisfies:12 its:5 before:2 derive:3 group:1 ln:40 solving:1 writing:3 lect:2 pac:1 copies:1 miura:1 derivative:3 main:2 defining:1 setting:2 overcome:2 them:3 return:1 pure:1 auto:10 acklund:68 they:4 half:4 nov:1 now:8 yu:1 day:1 easily:3 february:1 2w:1 university:4 2x:2 2y:6 2z:9 theory:2 xy:2 l2:1 l3:1 l0:1 each:8 found:5 2n:22 higher:8 referred:3 arxiv:1 another:1 lam:1 ed:2 revised:1 related:1 24v:5 our:21 mapping:3 extract:1 special:56 shown:5 gibbon:1 discrete:7 restricted:1 nuovo:1 since:9 rev:2 research:2 rational:8 get:1 math:18 shows:2 linear:2 sparked:1 given:8 possibility:1 standard:2 completely:2 york:3 members:5 beginning:5 generate:1 additional:1 pairs:3 derivation:6 could:1 turn:1 length:1 canterbury:3 invitation:1 crm:1 onto:1 first:14 degr:1 there:1 dont:4 symmetry:8 relate:1 variables:3 number:2 set:3 construct:1 directly:1 ses:1 xv:7 illustrate:1 xxxiv:1 little:3 checked:2 rewritten:1 similarly:1 introduction:1 carnevale:1 system:5 least:1 assumption:1 observations:1 airy:5 siam:1 relations:1 gives:14 newell:2 segur:5 x3:1 coefficients:4 albeit:1 unfortunately:1 namely:1 submitted:2 future:1 were:2 powers:2 symmetries:2 rewrite:2 modern:1 spectrum:1 uniforme:2 need:1 seen:2 any:8 solitons:1 mappings:1 zero:5 odd:4 answering:1 able:3 note:11 emphasis:1 take:5 finding:2 solve:1 begin:1 added:1 though:2 what:5 riccati:1 algebraic:1 nonlinear:5 successive:1 pair:3 iterate:1 acknowledgements:1 class:1 observation:1 nonlinearity:1 considered:1 clear:2 later:3 physica:1 proceedings:1 points:3 usual:1 vries:3 fact:5 quantity:1 show:3 reductions:2 supported:1 discovered:1 joshi:3 solutions:21 12v:7 substituting:2 trivial:2 find:4 principal:2 schwarzian:4 parameters:2 title:1 invertible:5 should:2 analytic:1 only:5 explicitly:1 transcendental:2 inherited:1 integrable:3 he:1 interested:2 do:8 ordre:5 dominant:2 means:2 de:3 cannot:4 dx:33 invariant:2 du:4 gen:2 differentiating:1 eme:1 evolution:4 differential:15 fixes:2 yield:1 mapped:1 through:2 fixed:1 musette:1 view:1 requirement:1 omission:1 modulo:5 constructing:1 reference:1 longmans:1 hicks:1 depends:1 result:8 eliminating:2 pvi:2 terms:10 techniques:1 practice:1 said:1 yet:1 written:7 difficulties:1 between:20 progress:1 approach:9 deformation:1 αn:80 notice:1 recently:1 extend:1 erieur:2 however:7 comm:1 key:1 solv:1 autonomous:1 wx:2 last:6 many:1 taking:1 equal:3 connection:4 erale:4 pde:1 whole:1 generalisation:2 co:1 extent:1 point:2 simple:1 2αn:5 mkdv:4 xi:1 sequences:3 polynomial:2 constant:4 actually:1 considering:4 transformations:24 second:17 addition:3 odes:16 been:5 int:5 reduction:4 much:2 interest:5 expected:2 pi:3 define:3 conte:2 stud:3 arises:1 corresponding:4 easy:3 andrew:2 locations:1 determination:1 6v:9 bull:1 6y:1 6z:1 present:1 applied:2 pacs:1 henceforth:1 value:7 choices:1 will:4 replaced:1 monodromy:2 revisited:1 property:7 procedure:4 lenard:1 century:2 vol:2 thus:6 non:2 uxx:2 according:1 ii:3 2ux:1 itself:4 vanish:1 hone:1 different:4 open:1 chazy:4 recursion:1 make:1 lett:4 same:3 member:10 complex:1 ince:1 modification:1 hierarchies:6 constructed:1 difficult:1 used:4 see:11 3y:6 i1:12 nj:1 possible:1 usually:2 v2:1 ablowitz:7 variety:2 well:4 analysis:3 concrete:1 without:1 gambier:4 very:1 left:1 unified:1 εv:5 manifold:3 just:3 being:2 linearisation:1 obtain:19 using:13 differentiation:1 alternative:6 scattering:1 singularity:1 fokas:1 family:3 conclusions:1 except:1 weiss:4 egrale:4 pickering:6 location:1 sydney:2 transformation:51 acta:3 australia:2 represents:1 iα:1 breaks:2 2v:27 plenum:1 test:1 integer:9 modifications:1 systematically:1 follows:3 reduces:1 specific:1 korteweg:3 integrals:33 become:1 therein:1 because:2 truncated:10 some:3 back:1 examples:3 choosing:1 diff:4 kdv:4 peter:1 nonzero:1 provided:4 est:3 resonances:3 shall:2 integration:3 ese:1 does:2 eliminate:2 provides:5 assuming:1 yields:2 algorithmic:1 tabor:2 equivalent:4 l1:2 expansion:11 step:2 although:2 substitution:1 relating:2 properties:2 p34:15 uxxxx:1 about:2 extension:1 most:1 brings:1 mean:1 mathematical:1 soc:1 cambridge:1 previously:1 into:5 bountis:1 integral:13 due:1 down:6 en:4 references:2 elementary:1 france:1 statistics:2 log:2 her:1 springer:2 sequence:7 question:5 transform:1 accordingly:1 appl:3 milne:2 way:3 series:1 was:9 function:6 carg:1 cosgrove:1 form:5 attempted:1 becoming:1 kudryashov:2 but:7 construction:2 elimination:5 removed:1 pdes:8 truncation:10 4v:7 made:4 whether:1 prevents:1 us:5 placed:1 problem:1 called:3 pii:83 associated:1 defined:3 certain:1 abstract:1 troisi:1 zeng:1 general:3 ap:2 single:1 formulation:3 simplest:1 adelaide:3 again:4 functions:4 completeness:1 cim:1 no:1 mathematica:1 when:3 green:1 application:2 other:3 role:1 branch:1 d2n:3 department:1 mathematics:3 happens:1 premier:1 critiques:2 problems:1 deriving:1 important:2 chris:1 independently:2 implies:1 4y:1 assume:1 physics:1 4u:1 together:2 equivalently:3 reprinted:1 time:3 dover:1 requires:1 having:1 once:2
|
solv-int9811015.txt |@word gu:1 partial:5 sch:18 remarkable:1 exponentiation:1 results:5 four:1 scalar:2 latter:1 comments:1 edu:1 sci:1 expressions:2 academic:1 consider:1 devoted:3 whose:1 certainly:1 inverse:3 const:2 subjected:1 equivalence:2 tr:3 acting:2 containing:2 vigier:1 finally:3 those:1 th:4 under:31 tf:1 tg:1 include:1 presentation:1 norm:1 ingredient:1 kσ:1 p2:12 g2:4 advantage:1 translations:2 springer:2 wave:6 ovsiannikov:1 every:2 fall:1 linearizability:1 exact:4 condition:4 treating:1 leads:1 annihilated:1 subsets:1 presented:1 t2:2 solution:5 large:2 solved:1 vector:23 conformally:1 math:12 recall:2 optics:1 specializes:1 ten:2 10b:1 dealing:1 consistent:1 10a:1 direct:2 literature:1 l3:8 second:11 quebec:1 further:6 analogue:1 linear:16 subscripts:1 nonlinear:16 appear:2 invertible:1 section:7 brief:1 shares:1 version:1 d0:2 above:6 new:4 boost:1 method:4 justification:1 explosion:1 eliminated:1 respectively:2 realizations:17 here:3 water:1 modular:3 them:1 galilean:1 groups:10 others:2 depend:4 112b:1 equations:76 appears:1 galilei:30 obtained:10 search:1 parameters:2 technical:1 study:5 studied:2 leaving:3 aδ0:1 usually:1 changes:1 zhdanov:1 iy:1 technique:1 useful:2 family:2 ix:1 9a:3 requiring:1 9c:1 9b:3 9d:1 modifying:2 logarithmic:1 generality:1 apply:2 derivatives:1 ψx:3 ψy:4 proceed:1 would:2 ψt:25 next:2 few:1 ψi:2 call:1 opposed:1 eckhaus:3 candidates:1 type:5 theoretical:1 reflects:1 more:3 patera:1 remark:1 odinger:45 kλ:1 particular:11 known:1 cases:3 r1:4 abundance:1 account:1 integrating:2 science:1 equation:44 work:1 modified:1 remain:1 infinitesimal:4 nine:4 following:3 example:2 performed:1 f2:5 f3:1 indicated:1 abelian:1 calculation:1 relativistic:1 preserving:5 ann:2 involve:1 numbers:1 sense:1 absolute:1 painlev:1 s3:4 s2:5 discussion:1 means:2 write:1 how:1 nontrivial:1 vital:1 significance:1 acta:1 ψij:2 parameter:3 priori:1 classify:3 classifying:2 product:1 mar:1 algebra:21 perrin:1 after:1 lengthy:2 collection:1 applications:3 levi:2 plane:1 faculty:1 representations:1 law:1 types:1 realized:5 natural:1 clarkson:1 whenever:2 author:1 explicit:1 correspond:1 element:1 rather:1 so:7 fundamental:6 sl:3 sc:1 definitions:2 sg:7 order:19 typical:1 interpretation:2 words:2 indeed:3 summarized:1 i22:1 paper:8 including:1 omitting:3 mentioned:2 satisfies:2 itu:1 its:2 boosts:1 solitary:1 group:42 thank:1 fit:1 chosen:1 interesting:1 solving:2 conjugation:1 actually:1 systems:1 jacobi:1 olver:3 bω2:1 setting:2 s1:2 prolongations:1 13b:1 13a:2 h1:6 return:1 obtaining:1 outlined:1 inductively:1 processes:1 kumei:1 functional:1 scaling:1 mention:4 hamilton:1 effects:1 they:7 rotation:3 now:2 realize:1 possess:1 2t:9 term:1 finite:1 invariants:22 university:2 classified:1 2x:3 2y:1 l4:8 l5:3 l2:12 ad4:1 reasonable:1 each:4 found:3 side:1 referred:1 homogeneous:4 rodriguez:1 arxiv:1 formulate:1 i8:2 reduce:1 related:1 prolonged:3 weinberg:2 quantum:7 eq:6 special:4 out:3 shown:3 sabatier:4 15a:1 αr:1 space:22 restricted:4 furthermore:1 since:3 denotes:2 re:1 contained:2 denoted:2 formula:1 get:1 ref:1 occurs:1 independence:1 semidirect:1 classification:5 fiber:4 theory:3 interactions:1 8b:2 8a:3 aω1:1 free:4 standard:5 admits:2 complicated:1 counterparts:1 besides:1 approach:2 subalgebras:2 i6:4 generate:2 15c:3 derivation:1 r2:3 r3:10 determining:1 impose:1 ad0:1 linearized:1 thing:1 navier:1 hence:4 generalizations:2 first:7 already:2 symmetry:24 bluman:1 variables:12 number:2 restrict:2 l37:1 multiplying:1 simplified:1 adopted:1 another:2 theorems:1 ψxy:2 precisely:1 several:1 xt:4 j9:2 given:4 necessarily:1 jet:3 their:4 introduction:1 unknown:2 system:6 construct:5 imposing:4 constants:2 calculations:1 realization:8 scheme:1 final:1 recovered:1 too:1 similitude:13 tool:1 immediate:1 calogero:1 ψx2:2 reflecting:3 l33:1 x2:4 translation:3 than:1 coefficients:1 diffusion:2 2f2:1 l47:1 showed:1 i32:1 require:1 cimento:1 integrability:3 winternitz:4 matter:1 express:3 classes:3 contrary:1 publ:1 were:2 symmetries:4 7b:1 7a:1 olmo:1 well:1 unchanged:1 turned:1 generalization:1 inequivalent:3 need:3 cumbersome:1 apparently:1 any:4 warsaw:1 lie:12 zero:1 depending:3 self:1 able:1 k3:1 instance:1 k1:2 negro:1 k7:4 take:1 forces:1 k4:2 finding:2 k9:1 k8:2 modulus:1 heisenberg:2 play:1 towards:2 led:1 though:1 most:4 involving:4 eight:1 but:4 significant:1 remarks:1 why:1 sub:1 sciarrino:1 observation:1 prolongation:3 clear:1 later:1 dimension:1 part:1 principle:7 kt:2 overdetermined:2 left:1 sum:1 fact:2 12a:2 12b:3 particularly:1 show:1 reductions:1 jµ:1 contemporary:1 gauge:1 solutions:8 decompositions:1 d4:2 d5:2 trivial:1 find:5 dilation:4 d1:1 knowledge:1 spite:1 dissipative:2 ngo:1 specified:1 should:2 only:5 generators:3 pursuing:1 lillo:1 integrable:1 local:7 do:4 nonlin:2 meanwhile:1 dependent:2 dg:5 routine:1 subfamilies:1 ones:1 reversal:2 homogeneity:6 gen:3 evolution:9 fields:14 differential:28 summary:1 rotationally:1 imposed:2 investigate:1 common:1 view:1 requirement:5 set:7 constructing:3 physically:3 j5:7 j6:2 j7:1 j1:3 j2:2 j3:4 see:3 full:1 result:1 terms:11 satisfying:2 commutation:5 doebner:3 review:1 µr:1 written:3 between:1 invariant:67 conditions:1 deformation:1 notice:1 recently:1 extend:1 importance:2 however:2 2αf:1 york:3 concentrate:1 jk:1 solv:2 article:2 remaining:1 raczka:1 l21:1 improved:1 goldin:2 always:2 many:2 conclusions:1 equal:1 called:4 propagation:1 ung:1 passing:1 finds:1 ansatz:1 comment:1 among:1 relevant:2 point:1 simple:1 corresponds:2 dimensional:24 simply:1 coordinates:3 associated:3 throughout:1 turkey:1 ensures:1 transformations:13 basis:4 addition:1 odes:1 been:5 expressed:2 defined:1 reduction:3 belongs:1 change:1 beams:1 ah:1 pj:4 algebras:9 linearizable:2 nuovo:1 generating:1 relations:6 corresponding:9 versa:1 both:1 iµ:1 great:1 observe:1 systematic:2 general:11 present:5 case:9 p1:12 laser:1 stochastic:1 might:1 choices:1 will:13 euclidean:2 diverse:1 replaced:1 property:5 conformal:8 leaves:1 procedure:1 nonrelativistic:2 13c:2 coupled:1 vi:7 ir:2 thus:1 surprisingly:1 ii:1 characterize:2 ik:2 ij:1 il:1 different:2 l53:1 sch2:1 sch1:1 perform:1 make:2 belong:1 same:3 poincar:1 figuring:1 complex:8 emphasize:2 modification:2 constructed:4 subalgebra:2 higher:2 i9:1 independent:5 used:2 cubic:4 i1:10 i3:4 i2:5 i5:2 i4:3 i7:1 hand:3 parametrized:1 action:6 admitting:1 l1:14 infinite:3 ψyy:1 invariance:11 identity:1 recent:2 schr:45 center:1 acknowledgement:1 k22:1 spacetime:1 no:4 numerous:1 analysis:1 obviously:1 barut:1 de:1 without:1 solve:2 ψxx:4 organization:1 grounds:1 stating:1 subgroup:2 proposed:6 less:2 being:3 when:5 obtain:13 rest:1 reviewed:1 identify:1 turbulence:1 polish:1 alternative:1 functionally:1 adding:1 like:2 diffeomorphisms:5 generator:4 k2:1 conclude:1 seems:1 yt:4 add:3 other:9 transformed:2 lett:1 easy:1 theorem:2 del:1 4f2:1 plasma:1 transformation:1 k6:2 real:8 tests:1 marco:1 k5:2 spatial:2 possible:7 spanned:1 objective:1 five:1 know:2 vacuum:1 press:2 using:6 j4:4 occurring:1 modifications:1 necessary:1 semi:1 particle:3 systematically:1 follows:3 reduces:2 specific:1 yields:2 arbitrary:20 reduced:1 mathematical:1 right:1 old:1 namely:7 some:5 repeat:1 b1:26 b2:20 k92:1 extended:11 proofs:1 fushchych:1 generates:1 nonzero:1 proceeding:1 dimensions:5 shall:1 quintic:4 subclass:2 decomposition:1 provides:1 steps:1 propagating:1 refer:1 pr:8 11a:1 obey:1 power:1 11b:1 equivalent:3 2c:1 bj:4 pressure:1 step:1 k62:1 properties:3 stokes:1 about:1 central:1 carried:1 extension:3 completing:1 quasilinear:1 discussed:1 generated:1 o:3 essential:2 15b:1 introduced:3 consequently:1 15d:3 considerations:2 conserving:1 cambridge:2 rectify:1 h2:4 into:5 rectification:1 rotations:1 isomorphic:3 three:5 phase:3 references:1 operator:1 reducing:1 additional:1 eleven:1 there:3 class:11 start:2 restricts:1 appl:1 way:2 was:5 function:21 transformable:1 arise:1 complete:3 form:16 attempted:1 conjugacy:1 amongst:1 heat:1 construction:3 pdes:1 j10:2 he:1 nonlinearity:3 versions:1 minkowski:1 smooth:1 up:2 us:9 v1:2 simplifying:2 problem:2 similar:1 laplace:1 jσ:1 mechanics:5 constant:2 ag:1 ln:2 int:2 certain:3 abstract:1 describe:1 linearity:1 nattermann:1 denote:2 single:2 ar:2 exist:1 families:1 plan:1 commuting:1 physical:5 functions:6 istanbul:2 variety:4 amounts:1 mathematica:1 generally:1 field:8 valid:1 role:1 details:1 papers:2 department:1 mathematics:1 nice:1 elements:2 star:1 superposition:5 separate:1 models:1 mechanical:1 problems:2 includes:3 deriving:1 reiφ:1 important:2 a4:7 variable:4 generalized:1 especially:1 needed:1 careful:1 implies:2 longer:2 vice:1 i11:2 i10:3 original:2 time:10 4a:1 having:1 once:1
|
solv-int9811016.txt |@word logarithms:1 ams:1 consider:7 remarkable:1 rev:1 integration:4 m1x:2 types:2 partial:1 expressions:1 weierstrass:1 terms:3 schiff:4 superspace:1 violation:1 finally:1 th:1 under:4 presentation:1 norm:4 mpg:1 straightforward:4 zhang:1 very:1 rise:6 straße:1 wave:2 explanation:1 manin:3 deformations:1 p4:3 hamiltonian:16 integrating:2 δh2:8 δh1:6 generalises:2 manifestly:1 anal:1 12c1:1 consistent:1 translating:1 painlev:14 value:1 further:10 odd:7 ode:1 khesin:3 theory:1 bilinear:3 intersection:3 nonlinear:1 dφd:1 giving:2 d2:5 section:10 3p:8 expressed:2 d3:3 version:1 poles:7 3m:1 new:5 consisting:1 shocks:1 pioneering:1 patt:1 respectively:2 inviscid:1 component:4 here:7 water:5 believed:4 objects:1 galilean:3 groups:1 irrespective:1 alone:1 consideration:1 strong:1 equations:21 change:1 obtained:5 study:1 changed:1 allows:1 p2:27 resulting:2 loop:1 action:1 hospitality:2 conveniently:1 peakon:2 involves:1 uuxxx:9 diffeomorphisms:1 9n:1 discontinuous:1 mech:1 rep:1 viz:1 apply:2 planck:2 virasoro:4 derivatives:1 ψx:2 takes:7 would:2 commun:1 remains:3 contains:1 visit:2 negative:1 substitutions:1 comparing:3 call:1 therefore:1 associated:4 type:11 tell:1 more:5 introducing:2 israel:2 multiplying:2 anticommuting:1 becomes:2 curvature:1 holm:13 particular:3 known:2 fermionic:19 ramani:1 springer:2 valued:5 origins:1 c42:1 φdφ:1 science:2 equation:47 work:1 regularity:1 mt:6 pressing:1 values:4 den:2 following:3 example:2 proof:1 references:1 kadomtsev:1 5c1:1 give:5 expanding:1 monge:1 performed:1 arise:5 rescaling:3 completes:1 evidently:2 verlag:2 vanish:1 rather:1 s2:12 occur:1 nontrivial:2 2c1:1 dg:1 instead:2 hi:2 parameter:12 lam:1 product:4 ft:1 frobenius:1 algebra:17 replacing:1 max:2 after:1 singularities:2 movable:4 explored:1 lax:1 waves:1 verified:1 choice:6 constants:4 9p:1 natural:1 third:1 explicit:2 diffeomorphism:2 ηit:1 so:5 deconstruction:6 order:5 uvx:2 hierarchy:1 indeed:3 choose:1 paper:3 2v:5 y1:11 y0:11 satisfies:1 integrands:1 its:4 derive:1 group:18 sξ:1 singular:4 interesting:4 exhibits:1 writing:8 absence:1 systems:26 inconsistencies:1 derivative:1 main:1 might:1 supersymmetry:7 non:1 h1:4 combination:1 number:1 mention:1 13p:1 they:5 devchand:3 nov:1 now:3 yu:2 discuss:1 above:2 mystery:1 term:2 2p:11 university:2 level:1 via:2 γ2s:1 l2:5 bonn:1 accounts:1 mean:1 subsystem:1 differential:1 doing:1 series:10 solution:13 extended:1 sectional:1 substantially:1 our:2 extract:1 ψxx:1 rp:1 hyman:1 since:4 lagrangian:1 content:3 fx:6 investigation:1 geom:1 theoretically:1 4pp:1 formula:1 induced:2 integrated:2 math:7 c32:1 linear:4 interchange:1 discontinuity:1 φdm:1 possibility:1 standard:2 admits:1 3p3:2 hep:1 ovsienko:2 geometry:3 just:2 motion:2 turn:1 4p2:2 incorporated:1 carnevale:1 first:8 ud2:1 already:1 features:1 symmetry:1 u1:9 variables:2 symbolic:2 geodesic:23 hitherto:1 exact:1 2p2:1 simplified:2 specifically:1 another:2 precisely:2 open:2 maple:2 passes:2 given:8 similarly:2 introduction:1 leading:1 hydrodynamics:2 2fx:1 system:32 needed:1 zeros:4 vxx:1 calculations:2 gives:6 udv:1 u0x:3 relationship:2 tool:1 shallow:4 kupershmidt:2 part:1 too:1 norms:1 x3:1 than:2 vxxx:1 peaked:2 determines:1 unfortunately:1 fuchs:1 double:4 integrability:11 preparation:1 succinctly:1 determined:5 integer:3 displays:1 exhibit:1 fashion:2 half:2 substantial:1 conjugate:1 need:3 seem:1 recover:1 orders:1 solitons:1 lie:3 fxx:2 zero:10 depending:1 convenient:1 latter:6 able:1 note:4 instance:1 deconstructing:1 potential:1 take:3 mis:1 many:1 ξxx:9 even:3 sol:1 shall:4 consistency:3 what:1 metrics:1 most:2 uξ:1 germany:2 amongst:1 preliminary:1 pair:1 acknowledgements:1 why:1 involving:1 laurent:2 especially:1 considered:3 curvatures:1 regularisations:1 fx3:1 bracket:2 generalising:1 mechanical:1 usual:1 vries:4 fact:1 2m0:2 2m1:1 show:1 reductions:2 dy0:1 dy1:1 x2:5 solutions:15 d6:1 substituting:1 trivial:2 find:3 d1:4 q1:10 q0:12 q3:2 q2:10 q4:2 parameters:7 topological:1 should:2 only:5 explicitly:1 generators:3 coefficients:2 factor:1 integrable:20 circle:1 hope:1 centrally:1 do:5 dm:1 handle:1 ϕx:4 viewpoint:1 ϕt:1 de:5 fluid:2 methods:2 ones:1 dz:1 dx:10 despite:1 dv:1 during:2 dt:2 du:1 prime:1 evolution:1 exhibiting:1 bar:2 fields:7 arxiv:1 expansions:2 yield:1 investigate:4 michor:1 qi:8 coefficient:1 2p3:1 set:1 modulo:2 exists:1 gottfried:1 see:6 computer:2 geometrically:2 result:1 eliminating:2 recently:2 3c1:1 points:3 satisfying:1 singularity:1 naturwissenschaften:2 written:4 classes:6 between:2 αi:2 invariant:6 geometric:3 approach:1 adv:1 triples:1 uux:2 restricting:1 weak:3 however:1 interfere:1 implementing:1 vd2:1 ud:2 solv:3 thank:1 suggested:1 both:11 generator:2 powers:1 taking:9 admit:1 wtc:6 context:1 quite:1 expression:1 bott:4 generalisation:1 ch:11 conclude:1 appeared:1 leipzig:2 superfield:4 chandrashekar:1 dimensional:4 pole:2 simply:1 coordinates:4 lagrange:2 diff:1 peakons:1 throughout:1 camassa:13 kp:4 considering:1 mathieu:4 described:1 transformations:3 second:6 basis:3 addition:1 z0:11 due:1 been:6 defined:3 reduction:6 describes:2 logarithmic:1 interest:1 ph:1 algebras:2 define:2 c22:1 arises:3 supersymmetric:16 deeper:1 rescalings:3 gan:1 lengthy:1 understand:1 m1t:1 func:1 c2:17 c1:15 evidence:2 former:1 present:3 case:5 p3:8 p0:1 p1:4 look:3 unlike:1 shkoller:1 appearance:1 examine:1 arnold:3 choices:4 will:2 u1x:1 near:9 suppose:1 promising:1 aid:1 property:7 procedure:1 studied:2 rescaled:1 metric:10 thus:8 surprisingly:1 uxx:16 encountered:1 2ux:6 examined:1 il:1 vx:3 uxxx:12 superconformal:10 hone:1 φq:1 different:2 vy1:1 φt:2 suggests:1 perform:1 check:2 parts:2 φd:7 arguments:1 widely:1 physica:1 finite:2 φn:2 higher:1 independent:2 supercharge:1 literature:1 again:1 upon:2 effect:1 flows:5 hand:1 purpose:1 changing:2 2u1:1 task:1 petviashvili:1 well:3 analysis:4 burgers:1 solve:1 sets:1 coordinate:2 model:1 arising:4 dimension:1 left:2 unified:1 nonanalytic:1 manifold:3 graded:1 proposed:1 being:1 when:4 linearisation:1 grammaticos:1 obtain:6 underlying:1 identify:2 thanks:1 questions:1 immediately:2 yet:1 previous:1 blow:1 biu:1 preprint:1 family:6 candidate:2 infinitely:1 ϑu:1 except:1 weiss:1 quadratures:2 simple:7 other:3 lett:3 remaining:2 euler:5 τu:1 manton:2 checking:3 possible:4 test:10 know:1 using:6 variants:1 unique:1 necessary:2 like:1 differentiations:1 follows:4 reduces:2 δu:4 specific:1 δm:10 yields:8 mpi:1 δh:3 arbitrary:8 depend:1 mathematical:1 right:1 often:1 namely:2 tells:1 some:7 identified:1 b0:6 b1:3 choosing:1 respect:5 kdv:17 nonzero:3 manipulator:2 jeremy:1 dimensions:1 demonstrates:1 investigations:1 superfields:1 does:1 eliminate:1 provides:1 assuming:1 korteweg:4 intersections:1 proc:1 presented:1 misiolek:2 tabor:1 ξt:10 equivalent:1 pp:4 expansion:1 11p:1 although:1 substitution:2 super:2 properties:2 simpler:1 pt:1 extension:6 pu:4 discussed:1 o:2 dually:1 regular:2 extensions:7 insufficient:1 introduced:1 denote:2 automatically:2 homogeneous:1 outlook:1 h2:3 superderivative:1 within:1 functional:4 ηi:11 three:4 m0t:1 ηt:3 bihamiltonian:7 raises:1 determine:1 operator:2 nsr:2 bosonic:2 m0x:1 ηx:1 institut:2 classical:2 assumed:1 there:4 question:2 u0:10 u3:1 u2:3 dispersion:1 appl:2 inner:4 way:2 m1:7 sections:2 m0:7 function:1 complete:1 form:24 compressible:1 phenomena:1 but:5 construction:1 low:1 ramat:1 2vx:1 he:1 made:1 applying:1 ux:25 whether:2 ut:14 uv:1 up:3 us:2 ur:3 regularising:1 below:1 limit:2 verification:1 demonstrate:1 problem:1 dudv:1 similar:3 called:2 mechanics:1 bearing:1 ac:1 ab:3 constant:5 int:3 flow:20 abstract:1 contribute:2 general:7 ap:1 single:3 periods:1 bountis:1 formulation:1 corresponding:1 commuting:1 simplest:2 grassmann:11 functions:12 no:6 mathematik:3 generally:1 detail:2 field:3 setting:5 spatial:1 department:2 mathematics:2 conclusion:1 ξx:24 15p:1 may:5 ilan:2 class:7 radul:3 describe:1 ξu:2 inherently:1 includes:1 ξi:5 important:1 variable:1 describing:1 sides:1 structure:11 15n:1 implies:1 dφ:5 4p:3 dot:1 time:1 having:5 once:1
|
solv-int9812001.txt |@word φ1j:1 φ1k:1 consider:24 lack:3 invent:1 extensively:1 leads:1 eds:1 proposition:1 generalize:1 kowalewski:8 row:3 devoted:1 whose:2 inverse:7 depend:4 tu:2 father:1 γk:2 γj:11 uniqueness:3 petersburg:2 elliptic:10 under:1 breach:1 td:2 circumstances:1 γg:2 p2:7 belonging:1 r12:22 orthogonal:3 very:1 pages:1 rise:3 intriguing:1 mph:1 reinterpret:1 minded:1 entries:3 matrices:39 deformations:2 condition:1 groups:1 four:1 dubrovin:1 riemann:2 hamiltonian:20 rmatrix:2 solution:6 t0:4 solved:1 vector:1 fortiori:1 div:3 zn:1 mn:1 zk:1 det:17 c0:1 faddeev:1 brill:5 integrability:2 heine:1 substitute:1 canonical:28 spectral:8 nonlinear:2 appear:2 brackets:2 section:1 celebrated:2 expressed:1 uniform:6 henceforth:3 below:1 above:3 new:5 method:4 contrast:2 body:1 completion:1 led:1 degree:3 respectively:3 here:20 tangent:2 cos2:1 separation:7 q12:13 standard:9 equations:6 implicit:1 change:23 obtained:2 great:1 divisor:2 algebra:9 institute:1 larger:1 allows:2 tolstoy:1 loop:4 poisson:4 published:1 action:1 proof:3 changes:1 york:1 heiles:5 φkj:2 formulated:1 useful:2 family:5 apply:1 use:5 takes:2 would:1 prove:2 distinct:1 positive:1 h0:24 give:2 φgn:1 next:1 linear:12 therefore:3 type:3 possible:1 tk:3 separated:1 formally:1 duality:6 started:1 initial:6 holt:7 odinger:1 validity:1 berlin:1 particular:3 known:4 cases:1 must:2 ramani:1 springer:2 moser:1 ma:1 permits:2 recall:8 equation:31 work:2 oscillator:2 reads:4 reviews:1 values:1 following:18 rij:6 modifies:1 root:2 example:9 deg:1 wojciechowski:1 do:1 generically:1 involve:1 sphere:2 minimum:1 metamorphosis:3 dxj:4 degenerate:2 evidently:2 calculated:1 yang:3 rather:1 s2:3 s1:7 get:3 unordered:2 df:1 nontrivial:1 criterion:2 r21:9 pure:1 dwj:2 dwk:4 reestablish:1 parameter:1 classify:1 buchstaber:1 r2n:1 product:4 blocks:4 description:1 singular:1 may:23 after:7 singularities:1 movable:2 connects:1 tsiganov:6 plane:3 lax:40 representations:8 fj:3 constants:1 2x2:1 physical:6 dynamical:6 third:5 henon:5 explicit:1 element:3 sj:2 so:11 fundamental:2 sl:11 definitions:1 first:10 order:4 restriction:2 unsolved:1 s3:7 hierarchy:1 essence:1 choose:1 fξ:2 course:3 paper:3 london:1 existence:1 satisfies:2 y2:9 jacobians:1 before:1 group:1 interesting:1 fix:2 solving:1 coordinates:13 degrees:4 systems:61 jacobi:10 mail:1 main:1 defining:1 deformation:2 correspondence:4 non:18 within:2 obtaining:1 introduce:12 number:1 framework:1 hamilton:12 they:2 identically:1 front:1 singularity:4 now:4 discuss:2 comptes:1 inversion:1 gets:10 name:1 goldstein:1 ft:2 university:1 level:1 2x:1 identified:2 2e:1 2f:1 2g:5 l0:24 each:3 found:1 2n:4 baxter:2 differential:1 ek:1 map:19 journ:1 reduce:2 idea:1 related:8 φg1:1 toda:2 extended:1 entering:2 quantum:2 our:3 mapping:1 extract:1 special:2 ru:1 rv:1 rp:2 matrix:62 space:14 restricted:1 rep:1 since:3 lagrangian:2 denotes:1 mα:2 rational:3 denoted:1 rn:1 math:10 common:7 theory:5 surveys:1 quite:1 admits:1 nth:2 completely:4 base:1 complicated:4 term:2 put:3 van:2 e1:3 finite:1 e2:4 definition:4 pairs:3 qj:28 applications:1 geometry:1 omit:1 motion:16 turn:3 abuse:1 gordon:2 hence:2 βn:4 βj:1 βk:1 xj:10 already:1 xn:3 relate:1 variables:18 geodesic:3 twisted:7 restrict:4 xy:5 relations:4 another:4 ring:1 given:15 cartesian:6 suitable:2 rewritten:1 introduction:2 unknown:3 top:4 yj2:1 system:49 construct:5 appl:1 zeros:2 superintegrable:1 calculations:1 takhtajan:1 hyperelliptic:8 gives:1 holomorphic:6 e0:1 part:1 x2:25 natural:9 x1:5 than:2 coefficients:4 dtk:1 effective:1 edition:1 enabled:1 painlev:6 determined:4 were:1 russia:1 w2:1 derivative:1 rewrite:1 half:1 curves:13 kepler:7 stolin:1 veronese:2 st:52 any:9 solitons:1 lie:2 zero:3 depending:4 note:5 instance:5 potential:8 take:1 jacobian:2 coincide:1 lectures:1 begin:1 multiple:1 shall:11 algebraic:8 connected:3 but:1 automorphism:3 representation:8 phase:3 extremely:1 φk:1 enveloping:1 soliton:2 constructed:7 considered:8 torus:3 coincides:4 physica:1 αy:1 points:5 exp:1 mechanical:2 physics:3 fact:1 presentation:1 supported:1 discovered:1 spaces:1 solutions:4 tacitly:1 find:1 q1:67 q0:2 q2:57 resemblance:1 q4:1 parameters:1 adler:2 analytic:1 only:13 explicitly:1 generators:1 x4:1 ambiguity:3 equipped:1 parabolic:8 integrable:23 enolskii:1 hamiltonians:14 local:3 γn:7 dn:2 abelian:1 dl:1 notation:1 admissible:1 dependent:1 dym:1 combinations:1 dt:11 ds:1 sta:1 shr:1 reading:1 δwk:1 arxiv:1 expansions:2 investigate:1 noncanonical:1 drinfeld:3 qk:10 fixed:2 qm:1 dpj:1 qn:13 btt:1 set:10 δjk:1 differentials:9 j0:7 bears:1 connections:1 λk:2 depends:2 p21:4 projections:2 p22:4 terms:2 curvilinear:2 cofactor:1 satisfying:1 tensor:1 nondegenerate:1 preimage:3 λn:3 symmetric:10 f21:2 classes:1 various:1 closed:8 between:5 αk:8 αj:1 approach:2 αn:2 preserve:1 attention:3 recently:1 nature:1 initially:1 transpose:1 complement:1 ωn:2 weak:2 however:3 p2j:4 comm:1 russ:1 solv:2 outer:3 amer:1 p2y:12 p2x:8 p2z:2 both:5 ett:1 many:1 conclusions:1 according:4 distinguished:1 ackel:51 dl0:1 symplectic:2 ws:1 holonomic:1 expression:2 cj:1 q13:1 point:15 simple:4 harmonic:2 poly:1 2nd:1 dimensional:11 polynomial:8 associated:23 separable:2 sine:1 transformations:14 second:20 basis:8 pz:1 px:31 py:28 three:2 been:1 z1:1 int:2 belongs:3 z2:4 expected:1 pk:4 algebras:4 pn:4 ann:1 define:1 surjective:1 addison:1 generating:3 corresponding:31 determination:1 bolza:3 denote:2 spin:1 present:1 case:12 twist:2 p0:2 p1:10 look:1 unlike:1 auxiliary:1 solid:1 s4:6 arnold:1 choices:1 will:1 near:4 suppose:2 rendus:1 spbu:1 property:6 procedure:1 rename:1 noether:6 vectors:1 almost:1 twists:1 thus:2 surface:3 equal:11 ik:4 itself:1 vt:8 dual:22 qj2:2 rfbr:1 cjk:2 different:9 grant:1 generic:2 same:5 complex:2 arguments:1 propose:3 hierarchies:2 several:1 consequence:1 difficult:1 independent:6 used:3 horozov:1 see:4 cubic:1 i1:3 permutation:1 differing:1 hand:1 usually:1 potentials:12 infinite:3 expand:1 lower:2 genus:6 kleinian:2 band:1 whole:2 well:3 analysis:3 obviously:2 thought:1 concrete:1 without:2 coordinate:21 entry:4 model:1 cj1:3 parametric:2 dimension:1 usual:2 uniquely:1 manifold:1 proposed:4 less:1 being:2 newton:2 grammaticos:1 obtain:3 underlying:3 λg:2 transforms:2 immediately:3 facts:1 λj:3 momenta:3 nov:1 functionally:1 k2:2 regarded:1 quadratures:1 lattice:2 add:3 tuples:1 transformed:1 lett:1 easy:2 theorem:1 transformation:21 dqj:2 skj:13 real:2 acta:1 read:1 2v:10 integer:1 hereafter:1 necessary:2 bracket:2 follows:5 diffeomorphic:1 exhausted:1 yields:3 either:3 integrals:8 arbitrary:2 works:2 stationary:1 reduced:4 mathematical:3 because:1 neumann:1 classical:4 sequence:2 sobczyk:1 some:5 2y:2 s1j:4 q22:11 q23:1 examples:4 respect:3 kdv:1 ourselves:1 proceeding:1 lead:1 integration:4 does:4 δk:3 presented:1 λi:3 obey:2 q2g:3 notations:1 expansion:2 wesley:1 step:1 qng:2 although:1 injective:1 submanifold:2 about:2 puts:1 column:1 freedom:5 commun:1 discussed:3 o:4 practical:1 mutually:1 ξk:1 obeys:1 leykin:1 introduced:2 moerbeke:2 block:3 computational:1 h2:2 into:6 h1:7 integral:4 appropriate:2 references:3 determine:3 operator:1 factor:1 abel:19 methods:2 rows:1 span:3 additional:5 her:3 there:1 u1:2 transform:2 u2:2 quadratic:2 was:5 a2:2 function:35 complete:4 form:17 regard:1 ht:4 volume:1 pj:5 construction:1 rauch:1 laurent:2 divisors:2 partially:2 x2k:1 ux:1 consist:1 cik:1 us:25 4v:1 liouville:2 un:1 limit:1 uj:9 ud:5 problem:20 more:5 called:9 mechanics:2 zeroes:2 taylor:1 constant:6 defined:3 universal:1 describe:2 general:5 dξ:1 single:2 associates:1 exist:3 dλ:4 bountis:1 field:1 khoroshkin:1 defines:4 functions:17 nk:1 detail:5 application:2 other:5 branch:1 papers:1 department:1 mathematics:1 polar:7 briefly:3 elements:1 class:1 problems:3 a0:3 important:1 anal:1 studied:1 variable:9 generalized:1 structure:2 coupling:3 using:12 assume:2 requires:1 curve:25 rule:3 time:26 starting:1 once:1
|
solv-int9812002.txt |@word represent:2 partial:1 consider:3 chain:6 funct:1 leads:1 proposition:2 consists:1 expressions:1 inverse:2 depend:3 vs:1 nonlocal:1 those:1 under:6 applied:1 g2:1 g1:1 very:1 urel:3 choice:1 2rv:1 2ru:1 condition:19 forth:1 sklyanin:1 large:1 discrete:4 commute:1 au4:2 dealt:1 application:1 periodicity:2 consistent:17 direct:1 integrability:5 pass:1 dynamics:1 substitute:1 index:1 what:1 nonlinear:2 letts:3 sum:1 expressed:1 version:1 above:5 lifshitz:2 expresses:1 consisting:2 lifshits:3 satisfy:4 here:5 dimensionality:1 represented:2 const:3 along:1 sine:1 equations:13 change:1 obtained:2 remark:2 studied:3 allows:1 trial:8 qzz:2 useful:1 projection:1 vil:1 derivatives:5 use:2 takes:1 commun:1 next:1 taken:3 type:2 more:3 uxx:4 particular:1 known:4 cases:3 iii:1 equation:13 obstacle:1 following:8 making:1 dec:1 example:2 beautiful:1 nearest:1 give:1 effectively:2 stereographic:1 degenerate:1 end:1 fn:3 rather:1 utilize:1 answer:1 instead:1 priori:1 mat:1 algebra:2 may:1 singularities:1 plane:1 data:1 constants:1 sy:2 dynamical:5 effective:1 computations:1 explicit:1 sv:1 su:1 so:5 definitions:1 order:5 davey:1 perelomov:1 serving:2 interpretation:1 produces:1 essence:1 pointed:1 interpreted:1 paper:1 through:1 during:1 mentioned:2 still:1 its:3 chosen:1 interesting:2 affine:2 forms:1 systems:2 derivative:1 main:2 might:1 setting:1 aeq:3 them:1 introduce:2 landau:5 cutting:1 they:3 half:3 now:4 2v:1 several:1 2q:1 classified:1 2d:4 sufficiently:1 2g:1 qx:22 found:5 2h:2 constraints:5 mikhailov:1 differential:5 another:2 series:1 reduce:2 related:1 toda:15 literature:1 combining:1 our:1 eq:16 special:1 out:1 try:1 shown:1 rx:1 ry:1 denotes:1 similarly:1 u2x:1 symme:1 turning:1 theory:1 standard:2 admits:1 difficulty:1 completely:1 put:1 log:3 impose:1 excluding:1 counterpart:1 turn:1 gordon:1 consequence:2 first:1 initial:3 symmetry:24 variables:20 powerful:1 number:1 u0:2 instances:1 directly:2 xs:2 given:2 checked:2 rewritten:1 hyperbolic:3 introduction:1 unknown:1 system:18 their:4 c2n:1 vxy:4 vxx:4 statement:2 commutativity:1 tool:1 continuous:1 imposing:4 undoubtedly:1 than:2 coefficients:1 kind:4 classes:1 vx2:1 hz:1 symmetries:11 rewrite:2 corrigan:2 generalization:1 vn2:2 border:1 any:2 lie:1 convenient:1 instance:1 take:1 qyy:3 olshanetsky:1 algebraic:1 vnt:1 connected:3 preliminary:1 pair:1 approved:1 vnx:1 yamilov:1 qt2:1 consequences:2 clear:3 coincides:1 points:2 fact:1 phenomenon:1 show:1 reductions:1 supported:1 bring:1 solutions:1 analogue:1 find:3 decade:1 based:1 should:2 only:6 vxxx:1 integrable:19 local:5 between:1 famous:2 ones:2 dx:1 new:7 lattices:4 du:1 gen:1 closure:4 qt:2 qy:10 numerous:1 arxiv:1 method:4 imposed:1 qz:6 fixed:1 view:1 qtt:3 set:5 analy:1 physically:1 notice:2 see:4 result:1 recently:2 subject:1 um:1 urses:2 symmetric:1 written:1 smallest:1 simplest:1 invariant:2 boundary:39 approach:3 ends:1 terms:4 uux:1 qt1:1 however:1 concentrate:1 hypothesis:1 solv:1 uτ:1 both:2 last:1 unt:1 unx:1 etc:1 connection:1 passing:1 con:1 among:2 shabat:2 solving:1 cn:5 point:2 simple:1 polynomial:2 associated:7 math:3 described:1 addition:1 skew:1 three:1 been:3 int:2 reduction:1 cauchy:1 basic:1 algebras:1 choose:1 zamolodchikov:1 corresponding:1 quantities:1 c2:3 c1:3 present:1 case:1 multi:1 p1:5 value:3 choices:3 will:3 property:3 avx:1 non:7 vn:1 iv:1 ii:1 reads:2 examined:1 vt:3 turns:2 vx:9 vy:4 uxxx:1 rfbr:1 different:1 grant:1 admit:1 same:3 finite:5 higher:9 independent:2 used:1 vvx:1 flows:1 purpose:1 infinite:10 lower:1 off:1 reflection:2 well:2 analysis:3 obviously:1 without:1 solve:1 consistency:1 claims:1 model:5 dimension:1 rietdijk:1 ae:2 less:3 transforms:1 years:1 scattering:2 vτ:1 localities:4 except:1 lattice:18 other:4 transformation:2 generalized:1 read:1 possible:1 five:1 using:1 like:1 appearing:1 cu2:2 semi:4 follows:1 remind:1 yields:1 either:1 arbitrary:6 become:1 qxx:6 qxy:4 reduced:4 2qt:2 because:2 old:1 classical:1 some:3 back:1 2qx:2 growth:1 examples:1 b2:14 kdv:1 ourselves:1 vt1:1 dimensions:7 integration:1 does:1 chains:2 refer:1 equivalent:1 2c:12 bj:8 constraint:13 novikov:1 discussed:2 dependence:1 compatible:2 introduced:2 dorey:1 conserving:1 bu3:1 into:4 formulae:1 references:1 additional:2 there:1 question:2 transform:1 u2:1 ut1:1 ghoshal:1 was:4 function:4 form:15 2qz:1 aqx:2 but:3 hn:5 line:2 highest:1 adler:1 illustrative:1 info:1 tarasov:1 uy:2 ux:9 ut:5 uv:1 up:1 us:10 krichever:1 un:11 problem:6 similar:3 called:5 b1:20 constant:3 defined:4 certain:1 abstract:1 av:1 commuting:1 sasaki:1 again:2 extract:2 when:4 field:2 conditions:17 why:1 problems:2 a1:2 class:1 important:1 qτ:4 gets:2 structure:1 ago:1 ditions:1 4v:1 interval:1 itself:1 time:2 appl:1 original:1
|
solv-int9812003.txt |@word gu:1 consider:6 chain:1 funct:1 12b:1 mines:1 four:2 proposition:4 computation:1 edu:1 go:1 expressions:2 gl:13 gj:1 devoted:1 whose:1 inverse:8 ver:1 breather:1 γq:1 tr:24 γj:2 finally:1 those:1 under:3 include:1 p2:1 straightforward:1 orthogonal:1 springer:1 results:4 ishikawa:1 2rx:1 matrices:16 2rq:1 leads:4 school:1 34a:1 34b:1 hamiltonian:6 positions:1 solution:12 solved:7 vector:3 ε2m:6 anal:1 noted:3 solutions:13 upper:4 wronskian:1 2k1:4 zj:1 zk:11 coefficient:1 direct:2 zero:2 zy:1 involution:1 further:5 situated:1 substitute:3 subscripts:1 will:2 what:3 nonlinear:3 const:1 appear:1 diag:1 section:3 expressed:11 3t:3 version:6 concisely:1 above:7 3b:1 3a:1 method:13 satisfy:7 degree:1 respectively:6 component:7 here:9 reported:1 γx:2 concluding:2 depend:2 appropriate:1 marchenko:5 equations:46 change:1 19b:1 obtained:2 remark:2 arrive:1 parameters:2 c2n:4 studied:7 coifman:1 products:1 poisson:5 permutation:1 hospitality:1 changes:1 composed:1 useful:2 summations:1 6a:1 replace:3 decrease:1 sgn:1 rkl:2 apply:1 total:1 unit:4 ψx:4 asymptotic:3 would:1 prove:6 positive:1 jpn:6 6b:1 ψt:1 next:1 noting:1 call:4 therefore:2 expanding:1 associated:1 type:1 vj:1 2y0:3 more:4 introducing:1 advance:1 becomes:2 odinger:1 curvature:1 iηj:2 berlin:1 appendix:7 normalized:1 known:2 33d:1 hold:1 33a:1 33c:1 33b:1 account:2 ma:1 jpsj:1 tokyo:3 science:1 equation:68 work:2 det:1 modified:8 values:1 mr:1 following:17 im:2 dec:1 example:3 proof:6 conference:1 f1:2 f2:1 impose:1 38c:1 give:2 calculation:3 december:1 beals:1 indicates:1 14b:1 numbers:1 14a:1 tions:1 axis:4 counterpart:3 s3:4 s2:24 s1:32 get:18 pure:3 significance:1 instead:2 parameter:2 e2i:2 simplicity:1 alternative:2 express:1 u22:3 information:1 ζi:1 ζj:5 after:2 ζl:3 ζn:1 plane:7 ζt:1 δj:2 summarize:1 law:2 fl:5 compatibility:1 constants:2 stress:1 outline:1 sech:2 explicit:3 korepin:1 element:1 bunkyo:1 so:1 sn:2 fundamental:1 decreasing:2 representation:4 operate:2 order:3 holds:2 ηj:1 hierarchy:2 indeed:1 entries:1 mainly:1 satisfied:1 interpreted:2 paper:5 through:1 reconstruct:1 existence:1 satisfies:4 its:3 diagonalized:1 derive:1 rapidly:3 37a:1 37c:1 37b:1 37d:1 writing:1 forms:3 condition:6 ozer:1 mail:1 main:1 defining:1 yi:2 yk:2 yj:9 entire:1 propose:1 introduce:4 bound:1 they:1 half:7 bogoliubov:1 takayuki:1 discuss:1 procs:1 densities:4 easily:1 inversion:1 2q:1 2r:1 s11:1 university:4 shiroishi:1 2x:4 utilized:1 fs:1 sufficiently:1 xy:1 each:4 2m:72 2n:11 traces:1 2i:8 2j:4 2k:2 square:8 ei:18 directly:2 ek:40 ej:17 there:2 reduce:1 idea:1 applicable:4 ξj:2 used:2 yield:1 combining:1 quantum:1 our:2 eq:59 special:2 rt:2 shown:6 matrix:78 discrete:1 vj2:5 since:1 rx:2 denotes:2 wide:1 dsf:2 formula:4 induction:1 math:3 shows:3 ζk:1 linear:2 symbolic:1 interactions:1 free:1 standard:1 assures:2 gardner:1 members:1 put:1 approach:1 inductive:1 log:6 definition:1 pairs:1 poles:8 ds2n:4 transition:2 ds2:14 ds3:2 ds1:16 motion:1 thing:1 u21:3 ism:15 hence:1 lax:9 xij:1 βj:2 first:5 xk:3 konno:1 already:2 symmetry:1 qkl:1 miura:1 variables:4 cj:40 number:6 4i1:1 restrict:1 xx:2 multiplying:1 done:2 construct:3 another:2 open:1 zi:2 given:22 fk:1 similarly:2 introduction:1 data:9 eqs:13 system:10 relations:13 parallel:1 their:1 assumption:1 normalization:1 1i:39 siam:1 scheme:1 structures:1 gives:2 discussion:1 recursively:1 17b:2 17a:2 optical:1 authors:5 focusing:1 x3:6 x0:11 than:4 coefficients:3 modes:1 18b:1 18c:2 18a:2 18f:2 18d:2 18e:1 approximations:1 integrability:3 classes:1 µ2m:5 enables:1 sty:1 published:1 behaviors:1 2δij:1 generality:1 rewrite:1 w0:2 generalization:4 z0:11 conjugate:1 need:1 seem:1 any:3 solitons:4 elsewhere:1 convenient:1 self:1 εq:2 isolated:2 note:1 yajima:2 k1:14 internal:1 εi:2 take:2 εj:5 xi:11 appreciates:1 spectral:3 begin:1 added:1 philadelphia:1 correlation:1 systems:2 riccati:1 algebraic:1 regular:3 connected:2 significant:1 qxxx:3 pair:6 coded:1 class:1 soliton:19 pohlmeyer:2 physica:1 ckj:1 proceedings:1 bracket:5 ku:1 physics:2 fact:3 laws:7 12a:1 nls:18 show:7 v12:2 v11:2 dependences:3 relation:8 akns:1 keywords:1 substituting:6 find:2 boundaries:1 oikawa:2 duncan:1 state:1 should:8 analytic:3 only:2 explicitly:2 subsection:4 integrable:3 circle:2 he:1 local:2 columns:2 boulder:1 hereman:2 his:1 notation:2 means:4 dependent:7 de:1 dz:1 dx:11 new:4 determines:1 dr:4 ds:4 gel:5 qq:1 evolution:1 qr:9 qt:3 qx:5 transposition:1 arxiv:1 expansions:1 µ2j:1 cf:1 iqt:2 38a:2 38b:1 set:12 38d:2 physically:1 δjk:1 see:3 result:2 y0:9 discussions:1 terms:2 contour:2 sincere:1 cofactor:1 instance:2 fand:5 kl:2 irt:1 liouville:4 symmetric:4 written:1 determined:1 succeeding:1 closed:1 between:3 c2j:4 limit:1 boundary:4 αj:1 conditions:8 discovery:1 choose:1 recently:1 shabat:1 anti:1 wk:2 were:1 jp:1 however:2 manakov:1 jm:1 jn:2 solv:2 jetp:1 recall:1 received:1 last:1 kruskal:1 many:2 taking:3 36b:2 according:1 36a:2 0b:1 etc:1 connection:1 passing:2 expression:2 quaternions:2 ck:4 among:3 solving:1 cn:1 cl:3 simple:6 2i2:1 16a:1 16b:1 2i1:1 mkdv:39 simply:1 applicability:1 path:1 respect:4 v2m:8 levitan:5 second:1 addition:2 19a:1 arbitrary:1 informed:1 due:3 been:9 defined:9 reduction:6 19c:2 u11:3 pk:4 u12:3 pn:1 pl:1 define:5 v22:1 v21:1 6c:1 partly:1 both:1 quantities:3 xxx:3 miki:1 48b:1 ordering:1 systematic:1 c2:4 c1:11 present:2 case:7 k2:11 multi:7 p1:1 exponential:1 solvable:1 value:12 employ:3 cast:4 while:1 suppose:1 behavior:1 slk:2 procedure:1 vectors:1 coupled:14 vi:16 refs:1 vk:7 thus:6 vm:1 ij:1 rij:1 vx:1 ic:2 uxxx:1 cjj:1 cjk:12 different:3 fibers:1 perform:2 recursion:3 make:2 determinant:1 same:2 complex:3 φe:3 modification:1 proved:4 constructed:2 independent:3 extended:1 http:2 i1:2 i0:4 i2:2 functions:9 v0:14 v1:1 iv1:4 potentials:6 infinite:6 changing:1 ablowitz:2 expand:2 lower:3 schr:1 reflection:2 acknowledgement:1 analysis:3 without:2 solve:6 i2m:10 components:1 lim:8 model:4 eilbeck:1 comment:1 λp:1 monet:1 λv:1 proposed:1 less:1 being:1 residue:5 obtain:14 valuable:1 thanks:1 using:9 hongo:1 λj:4 λi:1 scattering:20 λm:1 bullough:1 density:1 zakharov:1 remember:1 jost:6 lett:1 theorem:4 5d:2 5a:2 5c:1 5b:1 real:16 iδ:1 iζ:4 21b:1 21a:1 press:2 integer:1 part:1 helpful:1 loss:1 like:2 semi:3 deta:19 follows:7 δl:2 transform:2 korteweg:1 either:1 integrals:1 hirota:8 become:1 qxx:3 reduced:1 www:4 because:8 2qr:1 neumann:4 deal:1 2iζ:5 some:4 2qx:1 s1n:1 home:1 kdv:7 icj:1 scale:1 lead:1 extensively:1 comments:1 ykl:1 does:4 provides:1 assuming:2 prog:3 iξx:7 considering:2 biology:1 11a:1 ba:2 11b:1 equivalent:1 2z0:1 use:2 expansion:3 bt:1 imaginary:3 fordy:4 clarkson:1 about:1 extension:4 constraint:3 column:1 freedom:1 completing:1 commun:1 discussed:1 dependence:5 o:64 δij:1 15b:1 2x0:7 soc:6 cambridge:4 statements:1 colorado:1 into:11 successive:1 integral:2 22b:2 22a:2 ut:2 nothing:2 hermitian:1 right:1 sov:1 qrx:3 s2n:20 rows:2 classical:1 assumed:4 initial:13 u1:1 u0:1 4i2:1 start:1 conservation:9 way:1 ed:2 δlk:2 was:2 sanuki:1 function:6 complete:3 form:4 restrictions:1 hw:1 but:4 equa:1 dξe:2 larger:1 russian:1 segur:1 true:2 faster:1 made:1 ux:1 evident:1 whether:2 cij:1 up:1 us:3 um:1 below:1 ui:5 uk:12 uj:11 eiξx:5 problem:18 ψe:4 similar:1 called:2 ac:2 ab:1 constant:3 qij:2 int:2 describe:1 generating:1 48a:1 general:3 dξ:4 conserved:8 proves:2 exist:1 formulation:5 typeset:1 identities:1 check:2 physical:1 satsuma:1 qγ:6 equivalently:1 mathematica:1 generally:1 pfaffian:1 invalid:1 graduate:1 field:1 definitions:1 other:3 remarks:2 papers:1 department:2 mathematics:1 theor:3 izergin:1 elements:2 exp:7 symbol:1 4i:3 problems:1 includes:3 15a:1 commutator:2 wadati:6 important:1 sides:1 structure:2 rq:3 auxiliary:1 algorithm:1 assume:7 vries:2 interval:2 4r:1 4q:1 rxx:2 sasa:3 time:15 appl:1 applied:1 quantity:1 original:1 tsuchida:2
|
solv-int9812004.txt |@word represent:1 sci:2 consider:3 similarity:1 vasiliev:2 results:1 roy:1 scalar:1 commute:1 depend:1 calculate:1 paris:2 noncompact:1 subtleties:1 p2:1 wave:18 putting:2 jack:4 condition:2 level:1 irreducible:1 solution:1 discrete:1 vector:1 b286:1 gauge:1 degeneracy:2 zn:1 imply:2 pass:1 further:1 hansson:2 while:2 expressed:2 brink:4 version:1 nonexceptional:1 new:1 degree:3 respectively:1 here:2 lodz:2 sogo:1 appears:2 z2:2 obtained:2 trans:1 dfλ:1 studied:1 products:1 action:9 fourier:1 gambardella:1 uniquely:1 unitary:1 takes:1 ψp:1 hilbert:2 few:1 nucl:1 bases:1 therefore:2 type:1 theoretical:1 operators:2 equipped:1 normalized:1 varying:1 known:2 cases:1 ii:2 ma:1 recall:1 equation:3 following:3 dec:1 example:2 wojciechowski:1 compare:1 kosi:1 calculation:1 states:2 axis:1 motion:2 end:1 b401:1 rather:1 holds:1 write:1 classifying:1 product:2 mat:2 algebra:4 may:1 after:1 representations:1 choice:2 dynamical:1 sectors:1 correspond:1 element:1 dilatation:3 so:2 sl:14 representation:10 order:3 typical:1 kbn:1 insight:2 course:1 paper:1 london:1 existence:1 its:2 lb:1 majewski:1 energies:1 interesting:1 coordinates:7 actually:1 degrees:1 a95:1 them:1 gauging:2 introduce:1 landau:1 now:3 easily:2 term:2 university:1 hamiltonian:3 identified:1 inherent:1 2n:4 side:2 2k:1 homogeneous:2 weight:1 edinburgh:1 series:4 energy:4 related:3 obtains:1 quantum:4 our:3 eq:8 p03b:1 space:4 since:1 rational:1 get:2 ref:1 math:8 hcm:3 theory:2 panigrahi:1 diagonal:1 york:1 put:2 e0:2 e2:1 marchioro:1 r2:3 counterpart:1 introduction:1 neglect:1 first:5 xj:10 xi:19 xn:1 symmetry:1 laguerre:4 variables:4 number:2 angular:1 given:6 ian:1 rewritten:1 forrester:1 tor:1 eqs:4 system:1 construct:1 their:1 normalization:1 gives:1 ryzhik:1 2am:5 part:4 x2:1 ϕnk:4 second:3 contrary:1 lowest:1 rewrite:2 spectrum:2 any:3 lbn:3 angle:2 latter:1 take:1 jacobian:1 lassalle:3 continuous:3 rhs:1 most:1 regular:1 superintegrable:2 gradshteyn:1 nothing:1 coincides:1 exp:6 physics:1 fact:3 sector:1 superintegrability:1 show:2 supported:1 purely:1 relation:1 solutions:1 d2:3 find:2 ground:3 x1:1 state:3 monomial:1 only:2 explicitly:1 generators:4 factor:3 moser:4 do:2 fλ:5 means:1 dependent:1 4ωr:1 cannot:1 dz:9 closely:1 combinations:1 du:1 dr:3 reveal:1 covering:1 arxiv:1 cf:1 common:1 ignored:1 set:2 modulo:1 exists:1 j2:9 j3:1 relative:5 depends:3 sec:1 result:3 stanley:1 eigenfunctions:2 symmetric:3 written:2 invariant:1 conditions:1 terms:5 extend:1 p2i:3 however:1 comm:1 solv:1 group:1 amer:1 jb:1 both:2 x2i:4 according:2 whole:1 comes:1 relevant:3 conclude:1 simple:1 harmonic:2 translationally:1 simply:1 nishino:1 spans:1 polynomial:9 nr2:1 16r:1 pr:1 basis:10 due:4 been:2 int:1 much:2 basic:1 pk:12 pi:2 define:2 corresponding:1 concerning:1 c1:1 present:1 case:2 exponential:1 nski:1 lαn:2 property:1 drr:2 jpn:3 obeying:1 reads:3 ij:1 cond:2 different:1 classified:1 grant:1 gets:1 λfλ:1 difficult:1 independent:1 see:2 counterparts:1 hand:3 identity:1 eigenvectors:1 lower:1 center:3 poland:1 well:2 analysis:1 obviously:1 academic:1 without:1 sets:1 coordinate:1 model:8 calogero:26 left:1 spherical:2 being:2 obtain:1 gonera:2 polish:1 scattering:1 adv:1 tables:1 preprint:2 generator:1 lett:4 easy:1 transformation:3 real:1 eigenfunction:1 read:2 spanned:3 corresponds:1 press:1 using:2 formal:1 insert:1 identifying:1 follows:2 reduces:1 specific:2 integrals:5 tower:1 reduced:1 mathematical:1 right:2 old:1 2iλ:3 classical:1 some:1 slanka:1 neglecting:1 diagonalizing:5 provided:1 describing:1 provides:1 proc:1 mellin:1 properties:3 dunkl:2 ol:10 dzd:1 extension:1 freedom:3 dependence:1 mukunda:1 soc:5 warsaw:1 kuznetsov:1 into:3 acad:2 references:1 operator:2 a69:1 statistics:1 span:1 there:2 transform:1 way:1 was:1 function:6 complete:1 form:2 analyse:1 but:1 hi:2 gain:2 pwn:1 implies:2 considerable:1 he:1 multiplicity:1 ωr:4 up:1 us:4 historically:1 ul:1 ωn:1 dv:1 called:1 mechanics:1 constant:1 defined:3 abstract:1 describe:1 globally:1 formalism:1 commuting:2 proceeds:1 constructed:1 again:3 functions:14 fixing:1 other:2 department:1 out:3 nu:2 nv:1 expressible:1 models:1 polynomials:8 wadati:3 pomorska:1 lifschitz:1 structure:9 4z:2 baker:1 d22:1 4n:1 mass:3 time:1
|
solv-int9812005.txt |@word kbn:1 consider:4 proposed:1 similarity:2 supported:1 results:1 gonera:2 purely:1 relevant:2 transforms:1 alternative:2 still:1 q1:2 inverse:1 based:2 cm:1 majewski:1 panigrahi:1 show:3 coordinates:1 actually:1 forms:1 finally:2 explicitly:4 transformed:1 tk:1 easy:2 ti:2 moser:3 nucl:1 transformation:13 real:1 do:1 get:2 read:1 sufficient:1 corresponds:1 define:3 p1:2 know:1 they:2 now:1 transparent:1 it0:1 easily:2 term:4 gets:2 2q:2 particle:1 presented:2 should:1 university:1 arxiv:1 t2:5 t3:5 inequivalence:1 t1:4 ωq:2 paper:1 arbitrary:1 qi:28 qj:4 out:1 side:1 nishino:1 set:4 constructing:1 classical:4 doing:1 cond:2 some:2 inverted:7 relative:1 second:1 frequency:1 sec:1 t0:2 quantum:3 dynamics:1 eq:4 canonical:11 nonzero:1 shown:2 commutation:1 2e:2 particles:1 written:1 puting:1 rational:2 hep:1 ref:1 math:1 hcm:7 gives:1 recently:1 implying:1 q2i:2 equivalent:3 p2i:3 given:2 free:1 iǫijk:1 lodz:2 job:1 q2:2 ωqi:3 here:1 solv:1 preprint:3 relating:1 takes:1 obtained:2 both:3 cos:1 interaction:1 last:1 discussed:1 ignoring:1 counterpart:1 p2:4 poisson:1 nski:1 makes:1 other:1 first:2 equivalence:2 family:1 conclude:1 into:3 harmonic:6 three:1 put:1 symmetry:1 square:1 references:1 construct:1 sgn:5 reducing:1 pi2:2 defined:1 slanka:2 described:3 transformations:7 start:1 introduction:1 eqs:2 negative:3 been:1 next:1 their:1 however:1 describes:1 therefore:2 tj:1 qi2:2 really:3 theoretical:1 more:1 th:1 form:3 concerning:1 but:1 fixed:1 particular:1 known:2 hc:6 sign:1 iii:2 former:1 present:1 center:1 case:6 pi:10 ma:2 whether:1 oscillator:2 verifies:1 us:2 ul:1 brzezi:1 converts:1 dec:1 obtains:1 unitary:1 reduces:1 int:1 coincides:1 abstract:1 b324:1 proven:1 ii:2 separating:1 reads:1 right:1 2t0:1 formulation:1 rid:1 hamiltonian:3 check:3 constructed:2 again:1 different:4 ing:1 mappings:2 grant:1 perform:1 polychronakos:1 calogero:15 holds:1 composing:1 detail:2 same:1 rules:1 noninteracting:1 role:1 take:2 department:1 mass:1 p03b:1 parameter:1 composition:1 independent:2 mat:2 algebra:2 models:2 oscillators:3 time:3 mapping:1 hand:2 less:1 wadati:1 levels:1 successive:1 variable:1 changing:1 pomorska:1 recent:1 dynamical:3 poland:1 well:1 dilatation:1 secs:3 bracket:1 so:1 sl:3 sin:1 model:14 otherwise:1 physics:1 order:2 fact:1 posses:1
|
solv-int9812006.txt |@word proposition:6 nψ:2 partial:12 consider:12 secondly:1 excellent:1 trisecant:1 results:2 leads:20 eds:1 commute:1 edu:2 consists:2 customary:3 expressions:2 rigidity:1 whose:3 c0:1 depend:1 combinatorial:1 graph:2 subjected:4 tr:4 young:2 tn:7 finally:5 cartier:1 tj:2 those:1 under:3 phil:1 analogous:1 mehta:4 proj:1 applied:3 witten:1 fay:6 string:3 orthogonal:5 very:1 homogeneous:1 conditions:3 3s3:1 wave:14 corollary:8 p1:1 every:2 lecture:3 li:1 difference:1 matrices:16 deformations:1 condition:5 partitions:1 entire:1 school:1 tokyo:1 riemann:5 level:5 bn:3 induction:5 notes:2 rosenzweig:2 t2:3 solution:13 uu:1 t1:21 deals:1 discrete:1 vector:4 phase:1 louvain:3 ml:2 small:2 eigenvalues:3 shows:3 originally:1 solutions:1 zm:7 zn:15 wronskian:1 alluded:1 occurrence:1 zj:36 zk:37 dealing:2 zf:1 estimates:1 direct:1 sign:2 painlev:13 djα:2 zz:1 follow:1 growing:1 further:1 defines:2 estimated:1 odd:8 linear:6 spectral:3 established:2 what:1 nonlinear:1 appear:3 invertible:1 sum:5 while:3 expressed:5 cell:2 asv:2 version:3 poles:1 above:11 method:1 new:6 row:1 equivalent:1 pioneering:1 xy:1 degree:1 even:9 spacing:4 equals:1 desired:1 inverse:1 them:1 ωk1:1 groups:1 represented:3 ratio:1 along:1 sine:4 equations:34 appears:3 z2:13 obtained:5 akz:2 remark:1 property:6 parameters:2 shift:4 akp:7 pi:13 akk:1 prior:1 aki:1 products:1 poisson:1 ak1:2 usually:2 hospitality:1 deg:2 makes:1 zj0:29 sci:1 appropriately:1 schur:2 limy:3 useful:2 extra:1 belongs:1 explained:2 plenum:1 replace:1 logarithmic:1 aa2:1 api:1 wk:9 apply:3 tools:1 virasoro:17 derivatives:4 use:2 graphs:2 projector:2 usa:2 prove:7 probabilities:2 positive:2 give:1 kα:7 next:10 vol:1 mori:3 m1:2 therefore:11 m2:2 taken:1 alvarez:1 associated:3 schulman:1 type:2 theoretical:1 diagrams:1 more:7 zeroes:1 introducing:1 israel:1 formally:1 4ar:1 becomes:1 operators:26 ti:43 corrected:1 validity:1 jk1:7 t3:3 s3:3 virtue:1 particular:3 known:4 central:2 cases:1 iii:1 graphical:1 must:2 springer:2 zi2:2 impenetrable:1 zi1:4 ed:4 science:2 equation:34 work:4 det:56 cak:1 unknowns:1 infinitesimal:3 values:1 widths:1 following:25 mckean:1 specifies:1 dec:1 example:2 proof:48 tau:1 conf:1 figure:2 stated:3 akℓ:1 expanding:4 permutations:1 lψ:1 bessis:1 high:1 dm:3 sense:1 yα:3 appearance:1 dzn:2 conversely:1 µj:2 simple:2 dk:2 needs:2 end:1 pure:1 darboux:2 ideas:1 s1:7 holds:5 feature:2 recovers:1 write:1 maps:1 edge:2 pair:1 get:4 answer:1 instead:2 mccoy:1 parameter:1 ensemble:2 sato:6 product:1 proc:2 algebra:5 replacing:1 after:1 derived:2 dx2:3 bkk:4 ζp:48 applications:2 ω2j:2 plane:6 bkp:5 value:2 fg:4 date:2 ties:2 law:1 data:1 constants:2 proceeds:2 physical:1 remember:2 third:1 whenever:2 izergin:1 spectra:3 explicit:3 yielding:2 ential:1 quadrant:2 brandeis:6 si:1 integrability:1 so:6 sect:1 correlation:2 representation:2 order:8 typical:1 origin:1 s0:4 wigner:4 ϕk:4 schwartz:1 undoing:1 hierarchy:18 indeed:7 over:2 move:1 satisfied:3 interpreted:1 zℓ:8 paper:4 including:1 enumeration:1 statistical:6 left:3 y1:47 japan:1 satisfies:33 y2:14 excitations:1 its:10 roots:3 before:1 aj:7 s2:9 gaum:1 geometric:1 symmetry:1 la:1 ln:3 jim:5 a21:1 lk:4 actually:3 peng:1 complex:2 systems:10 lp:2 mail:1 main:4 might:1 into:5 serie:1 yi:36 j2k:3 non:9 yj:3 contention:1 yn:17 ji1:5 elementary:1 jα:2 scaling:2 2p:1 vect:1 billiard:1 they:5 singularity:1 now:9 yu:5 t21:1 wp:1 pz:8 deift:2 february:55 several:1 equality:4 2r:12 always:4 university:8 hamiltonian:1 2y:3 2z:2 sin:7 orthonormal:1 sufficiently:1 exponential:1 diagram:1 each:9 qkℓ:5 found:2 universit:1 circular:1 2i:8 tiℓ:1 constraints:3 heavy:1 lie:1 lectures:1 differential:31 weight:28 evolve:1 subset:5 commuting:2 physica:2 applicable:1 kℓ:6 isospectral:1 toda:5 investigated:1 expect:1 measure:2 quantum:5 our:1 ev:8 event:1 special:3 out:4 conjectures:1 large:1 ultimately:1 converted:1 jimbo:5 matrix:71 3rd:1 space:5 since:8 rev:1 chaos:2 denotes:2 lacki:1 re:10 acting:3 geom:2 formula:13 rn:1 suffices:3 ri:2 announced:1 unifying:1 foundation:3 provide:1 theory:11 associate:2 singularities:1 aω1:3 mψ:1 free:1 standard:1 indices:1 completely:2 aˆx:8 term:2 span:6 estimate:1 publ:1 log:19 definition:1 interaction:1 derivation:1 ω2i:2 argument:4 aj1:7 aj2:1 omit:1 levi:1 times:2 γq:1 introduction:1 ω2k:10 proportionality:1 δij:3 hence:2 lax:1 generalizations:1 first:23 xj:1 initial:3 probability:5 striking:2 πn:3 variables:5 pa:11 ez:2 geodesic:1 xd:3 xz:8 multiplying:2 done:1 fast:1 another:3 a2i:8 blows:1 transcendent:1 zi:35 defined:9 ixz:3 given:19 zψ:2 moduli:1 similarly:1 ordering:2 leading:5 adjoint:3 behaves:3 vandermonde:2 system:4 relations:5 their:4 quadratic:2 identity:17 statement:5 1f:1 1i:1 airy:4 yℓ:10 foundations:1 gives:2 holomorphic:2 a31:1 fraction:1 relationship:1 cyy:2 continuous:2 kosmann:1 morozov:1 ix:6 assumption:2 part:10 because:4 consult:1 number:1 spacings:4 qj1:3 2az:1 than:1 coefficients:4 zγ:5 grassmann:1 showed:1 cyclic:1 was:1 second:8 aak:1 winternitz:1 computations:1 future:2 yi0:23 ktk:2 contribution:1 declare:1 sophia:1 result:1 eai:2 symmetries:7 footnote:2 acknowledged:3 ann:1 spectrum:4 curves:1 korepin:1 atomic:2 ω1k:8 zu:3 disjoint:2 tells:1 viewed:2 sk:3 zm2:2 mij:2 zero:1 depending:5 describe:1 lim:8 latter:1 1d:1 gravity:3 inv:1 note:16 instance:3 k1:11 potential:2 analogy:1 jacobian:2 xi:2 ixy:2 coincide:1 techniques:1 cl:1 bilinear:10 play:2 exactly:2 gα:4 shall:2 twodimensional:1 denominator:2 satisfy:7 simplify:1 involving:10 connected:1 plan:1 nothing:1 babelon:1 tracy:4 class:1 inequalities:1 soliton:9 constructed:1 takes:2 orlov:1 exn:1 average:1 dissertation:1 kn:16 km:2 mod:1 kr:2 proceedings:2 points:4 ckp:9 exp:1 kt:3 combinations:1 kz:2 kx:9 typically:2 section:8 fact:4 precise:4 noumi:1 dickey:1 leibniz:1 definite:1 random:75 computes:2 ending:7 purely:1 miwa:5 relation:17 xτ:1 grassmannian:1 interpretation:2 fear:1 tend:2 d2:3 find:5 fifth:1 principal:3 q1:2 indicator:1 removed:1 based:3 ensembles:6 dividing:2 aω:27 aψ:4 iti:4 written:2 lemma:28 only:12 explicitly:1 generators:2 zβ:3 factor:3 integrable:11 circle:2 ser:1 do:1 his:1 fnrs:1 notation:2 means:2 dependent:1 de:3 ki:7 ones:1 dz:24 zuber:1 dx:16 dy:7 dv:4 hermitian:1 du:11 ds:3 differentiating:2 interchanging:1 ˆk:1 determinants:7 widom:4 nicely:1 fields:3 λu:5 arxiv:1 baz:1 βl:1 yield:4 αl:1 aspects:1 2πi:1 investigate:1 underlying:2 leur:1 qk:12 fixed:4 valid:1 view:4 kernel:31 requirement:1 set:6 computed:3 exists:4 pick:1 jτ:2 national:2 differentials:1 j0:21 j1:10 j2:1 observed:2 differentiation:1 see:10 w2:1 w1:1 vertices:1 close:1 dµ:1 contour:1 jy:4 satisfying:11 commutation:3 αw:1 nuclear:3 away:2 qk1:5 ωk:1 jkℓ:6 symmetric:1 state:2 µn:2 µi:1 s21:1 µk:6 between:5 αi:4 invariant:1 boundary:5 approach:4 email:1 side:6 meromorphic:1 adv:1 ends:6 terms:41 iterated:1 rims:1 wn:4 resonance:1 a41:1 combining:3 however:1 bak:1 kp:28 gratefully:3 jn:3 harvard:1 hypothesis:1 ji:13 jj:6 jk:5 solv:1 bose:1 iki:1 iπν:2 come:2 problem:3 both:4 σi:1 uf:1 last:6 2n:7 many:1 taking:2 density:1 vanishing:1 laplace:1 δz:9 connection:2 vℓ:5 figures:1 context:3 comm:2 neuve:1 gr:5 expression:10 finds:6 experimental:1 sake:1 ck:4 cj:1 ci:3 relevant:1 spanc:2 point:5 appeared:1 poissonian:1 asymptotically:1 ce:1 2nd:1 dimensional:6 cz:2 simply:1 algebraic:1 consideration:1 table:1 zeta:1 ucl:1 diff:1 picking:2 simpler:1 math:17 considering:1 kernels:10 most:2 commutative:8 aˆ:2 union:3 ti2:1 moerbeke:68 varieties:1 ai1:1 due:6 been:3 z1:41 int:2 reduction:3 much:1 asymptotics:3 goes:1 basic:1 pj:5 pk:13 algebras:2 pn:7 universal:1 pl:1 define:12 cambr:1 determinant:20 rather:1 corresponding:6 itzykson:1 sufficient:1 residue:2 commun:6 cos:2 else:1 bulk:1 6r:1 observe:3 derivative:1 c2:1 worked:1 denote:1 spin:1 kashiwara:2 present:1 reverse:1 case:6 extracted:1 replaces:1 zm1:2 look:1 being:2 bω2:3 ij:2 bω:28 evaluated:1 ωkn:1 will:5 near:6 replaced:7 behavior:1 lect:1 situation:2 revisited:2 endpoints:1 iℓ:2 eax:3 dλ:2 exponent:1 shiota:10 iz:3 jℓ:12 coupled:2 chaotic:2 ne:1 thus:15 yk:29 jk2:1 according:8 ii:9 need:3 ik:2 itself:3 im:7 dual:1 maximal:3 wkp:12 qj2:3 vanish:1 ie:12 underlining:1 different:1 develop:1 grant:3 identities:4 problems:2 same:9 any:3 shifts:1 unity:1 parts:1 wℓ:23 colloquium:1 proved:1 finite:7 composition:1 generated:2 higher:1 independent:3 a2r:5 used:5 singapore:1 i1:9 i0:14 i2:7 upon:19 flows:3 hand:8 action:1 levels:4 introduce:2 decouple:2 infinite:8 robust:1 a2k:1 concluding:1 pde:7 normalization:1 numbered:1 lower:16 fourier:2 knj:1 proceed:2 possibly:1 edition:1 λk1:1 min:1 well:2 physics:2 obviously:1 off:2 continous:1 comes:1 components:1 exponentials:1 claims:1 model:1 arising:1 stating:1 usual:1 ny:1 world:3 manifold:3 dzm:2 just:1 increasingly:1 when:10 obtain:1 uℓ:7 reviewed:2 press:3 λa:1 intervals:2 properties:2 transforms:3 questions:1 immediately:1 λk:11 λi:1 scattering:1 λn:1 ucker:1 letting:2 intersection:1 preprint:2 cm:6 k2:4 gαi:8 conclude:1 boston:1 lattice:3 other:3 nato:1 lett:2 y3:1 theorem:47 relevance:1 formal:2 iτ:1 divided:1 march:1 around:3 eigenvalue:4 big:2 showing:2 sums:3 comparing:2 matters:2 background:1 belgium:1 using:27 ams:1 unique:2 moreover:2 prominent:2 meaning:1 appearing:4 like:3 semi:2 merely:1 bpi:1 follows:17 reduces:1 slavnov:1 characterization:1 translates:1 δn:1 δm:2 yields:2 δk:1 integrals:3 characterizes:1 transformation:1 stationary:1 waltham:2 mathematical:1 kac:1 sketch:1 right:4 zim:4 neumann:1 namely:3 formulas:1 successfully:1 some:17 back:2 japanese:1 understood:1 λk0:1 acad:2 examples:3 respect:3 λkt:1 kdv:10 establishing:5 provided:2 xp:1 excitation:1 lead:5 normal:2 zσi:3 dz1:5 partials:3 does:1 eliminate:1 expressing:1 assuming:2 l2:3 confusion:1 schwarzbach:1 bessel:5 tk:5 porter:2 jν:6 process:1 ajℓ:4 ba:2 energy:2 kyoto:3 journal:2 arbitrary:3 oscillating:2 pp:1 expansion:3 bk:8 symp:1 shifting:6 although:1 putting:1 hilbert:2 asymptotic:2 rare:1 extension:2 constraint:3 dzi:2 dzk:3 theorems:3 numerator:1 dependence:1 o:28 reduced:4 distinct:5 aℓ:7 a2:2 repulsion:2 fredholm:19 dzx:1 book:1 automatically:1 mlk:1 vi:1 duke:2 soc:1 cambridge:1 letters:1 christoffel:1 inclusion:1 previously:1 dyson:3 integral:6 functional:1 three:2 multiply:1 appropriate:5 square:1 references:1 operator:34 ai2:2 often:1 van:69 classical:2 ψk:2 support:2 there:4 transform:2 sarnak:2 u2:2 ordered:10 borel:2 way:4 series:1 generalizing:1 sections:3 sinai:1 combined:1 function:54 form:8 szeg:1 regard:2 but:6 hk:1 yz:1 construction:1 hn:1 bψ:1 highest:1 true:2 adler:68 ωy:12 pull:1 ωz:28 compute:8 uz:1 orthonormality:1 cij:2 ωu:1 up:6 us:2 relabeling:1 below:3 dms:2 limit:7 uk:7 3t3:1 ωa:2 distribution:6 ωb:2 similar:4 called:1 b1:2 mechanics:3 ac:1 taylor:2 constant:9 links:1 classic:1 ai:40 certain:2 ak:16 pseudodifferential:2 generating:3 general:4 eu:1 scientific:3 ar:1 rule:2 aw:2 transcendents:1 ax:2 1k1:1 az:14 distributions:5 simplest:1 surmise:1 again:1 functions:21 completeness:1 hermitean:1 coefficient:1 no:4 gomez:1 whereas:3 generally:2 vanishes:1 rewriting:1 field:2 setting:13 role:2 details:1 bℓ:5 department:3 mathematics:4 you:1 really:1 naive:1 arithmetic:1 briefly:1 may:1 generates:1 zhou:2 expressible:1 models:3 gas:1 symbol:3 vertex:35 shown:2 polynomials:7 a1:23 a3:7 important:2 variable:1 bn1:1 gap:1 jkm:1 sides:1 contributes:1 interval:2 function3:1 implies:3 monic:2 assume:3 exz:14 factors:1 pseudo:3 ti1:1 together:2 mass:2 time:3 n0:1 appl:2 nuclei:1 requires:1 original:1 once:4
|
solv-int9812007.txt |@word represent:3 logarithms:5 partial:1 consider:1 alg:2 global:4 desirable:1 computation:5 reasoning:1 whose:2 paris:4 discard:1 containing:2 does:4 th:1 stable:1 aux:1 pickering:2 divergent:1 applied:1 minist:1 very:1 erale:3 bulletin:1 keeping:1 every:3 condition:2 school:2 implying:1 notes:2 solution:29 correct:1 detected:1 indices:21 infinities:1 neighborhood:2 occurrence:1 direct:1 sign:1 painlev:17 j23:1 dynamics:1 ode:4 fonction:1 canonical:2 index:5 nonlinear:8 appear:1 giving:1 annali:1 section:6 selected:1 near:4 3u:2 find:1 succeeds:1 version:3 en:3 sur:7 establishes:1 3c:2 expresses:1 increasing:1 method:27 coefficient:1 full:3 led:1 degree:1 excludes:1 here:1 behaviour:1 following:3 les:4 tangent:1 others:1 equations:13 appears:1 logarithmic:3 conte:6 remark:3 difficulty:3 technical:1 study:4 allows:3 later:1 periodic:1 usually:1 resonance:1 settled:2 useful:1 family:13 aimed:1 apply:2 emoire:1 establish:2 derivatives:1 feb:1 handled:2 would:2 prove:2 remains:1 positive:2 negative:8 france:2 linear:9 call:2 therefore:3 8u:1 type:2 theoretical:1 more:2 lowering:3 acceptable:1 under:3 limitation:2 tested:1 berlin:1 warm:1 basically:1 particular:11 known:4 must:2 logarithm:3 none:1 valued:8 word:1 extension:1 recall:1 equation:45 des:7 ere:1 values:1 canonically:1 dec:1 root:2 example:8 proof:4 f1:4 f2:2 cosmological:2 give:1 process:1 generically:1 dxn:1 assumptions:2 information:3 darboux:2 travel:1 meanwhile:1 feature:3 pura:1 fourth:1 answer:1 acta:2 ordinary:3 parameter:5 map:2 fr:1 singular:5 may:4 after:2 singularities:5 movable:22 applications:1 recognizes:1 law:1 gauthier:1 fordy:2 short:1 third:1 whenever:1 maybe:1 classe:1 chazy:4 complexity:2 cannot:2 so:4 fundamental:1 sc:2 representation:2 order:26 help:1 indeed:3 ordre:2 mainly:1 undetected:1 stability:4 already:1 existence:8 poincar:5 its:6 meromorphy:1 thank:1 la:5 susceptible:1 plethora:1 exhibits:1 absence:3 copies:1 derivative:6 main:1 easier:1 them:1 cea:1 they:4 identically:1 singularity:4 now:2 valuedness:1 possess:1 2u:2 term:5 ethodes:1 name:1 explains:1 university:1 level:1 each:3 found:6 soc:1 homogeneous:1 domain:2 arxiv:1 simplicity:1 series:21 hypergeometric:2 reduce:1 applicata:1 inhomogeneous:2 yvette:1 happen:2 extract:1 special:1 etat:1 shown:2 matrix:1 since:6 induces:1 chaos:1 similarly:1 contained:1 daniel:1 denoted:1 lecture:1 ref:2 occurs:1 math:3 theory:1 divergence:1 free:1 quite:1 admits:2 small:2 detecting:1 beginning:1 carg:2 forbids:1 log:5 definition:1 retained:1 created:1 starts:1 needing:2 linearized:9 u20:4 due:1 leading:4 consequence:2 nouvelles:1 exhibited:1 first:8 degr:3 there:14 dont:3 perturb:1 number:5 linking:1 n23:2 simplified:1 given:4 perturbation:11 service:1 their:3 unknown:2 least:1 needed:1 echet:1 perturbations:5 holomorphic:2 e0:3 way:3 zeroth:4 immediate:1 part:3 x2:3 x0:28 than:4 coefficients:2 distance:1 fuchs:13 sections:1 require:1 second:10 matter:1 doubly:1 powers:1 perturbative:12 exhibit:1 generality:1 unchanged:1 premier:1 multivalued:1 seen:2 null:1 orders:1 contents:1 generic:1 zero:5 depending:1 εu:1 lim:1 responsible:1 able:1 isolated:2 note:1 sciences:1 εn:6 take:2 jacobian:1 solve:1 unperturbed:1 multiple:2 rhs:5 algebraic:7 satisfying:2 successive:1 why:2 branching:1 laurent:9 χp:2 considered:1 sometimes:1 physica:1 counted:1 countable:1 eriv:1 points:12 principle:1 physics:1 sum:4 fact:1 precise:1 12c:3 phenomenon:1 nρ:1 terminate:2 multicomponent:1 purely:1 solutions:9 july:1 principal:2 based:1 parameters:3 situations:1 explain:1 should:4 erentielles:5 only:9 x4:1 integrate:1 various:1 local:2 3n:1 dn:1 do:3 intractable:1 above:1 notation:1 get:1 de:7 overall:1 ones:1 integrable:1 dx:3 compute:1 du:8 imin:2 mixmaster:1 approach:2 differential:11 expansions:11 acknowledgments:1 common:5 fixed:1 musette:2 crm:1 set:2 computed:1 exists:7 detection:2 depends:2 computer:2 radius:1 result:3 close:2 page:1 eres:1 fails:5 detect:2 nature:1 enough:3 smallest:2 bureau:7 closed:3 simplest:3 conditions:10 checks:1 meromorphic:2 terms:2 extend:2 missing:3 initially:1 confusion:1 however:1 solv:3 s98:1 both:1 recherche:1 last:1 met:1 many:2 infinitely:1 according:2 chosen:1 expression:2 finds:3 arbitrarily:1 relevant:1 co:2 conclude:3 reasons:2 corresponds:2 pole:6 simply:1 constant:1 diff:5 pp:2 addition:1 locally:1 odes:2 been:1 int:6 cauchy:1 basic:2 define:1 obtained:1 direction:1 rather:1 families:4 xxv:1 quantities:1 understand:2 6u:1 systematic:1 bull:1 gˆateaux:1 efficients:2 general:19 present:2 case:4 exception:1 replaces:1 resummation:1 value:2 will:4 while:3 situation:1 di:1 property:5 noncritical:1 loop:1 uniforme:1 ix:2 seven:2 century:1 refs:1 thus:3 non:1 equal:2 ii:7 ebriques:2 different:3 combination:1 imax:2 author:1 perform:4 algorithmically:2 same:6 any:2 complex:1 widely:1 units:1 finite:4 higher:3 independent:2 imply:2 see:2 bonus:1 hand:1 v1:1 v2:1 afraid:1 uses:1 purpose:1 necessity:1 hospitality:1 infinite:3 2u3:1 2u0:2 identity:1 lower:1 makes:1 well:1 without:5 gambier:6 greatest:1 model:2 arising:1 possesses:2 usual:2 λv:1 just:4 less:2 physique:1 partielles:1 obtain:1 questions:1 previous:2 villars:1 fuchsian:13 point:9 had:1 except:2 egrale:3 valid:1 lett:2 easy:3 theorem:14 violations:1 transformation:2 useless:1 represents:1 checking:1 possible:2 possibly:1 using:1 unique:1 formal:4 loss:1 necessary:5 like:7 performing:1 unnecessary:1 ees:1 steps:1 either:2 arbitrary:12 reduced:1 names:1 mathematical:1 because:4 methods:12 namely:1 sequence:3 some:6 springer:1 q20:1 acad:2 examples:4 moreover:1 est:3 kowalevski:6 resonances:2 avoid:2 cχ:2 integration:2 ese:3 critical:9 provides:2 yields:1 refer:1 algorithmic:3 power:2 june:1 equivalent:3 confluent:1 expansion:6 constructive:2 although:1 refers:1 properties:1 analysing:1 about:1 proven:1 most:1 coexist:1 theorems:3 generated:1 o:1 essential:4 regular:2 plus:2 insufficient:2 introduced:1 converging:1 perturbed:2 letters:2 ecanique:2 presence:3 previously:1 into:2 three:2 unstable:1 references:1 elementary:1 neumann:1 additional:1 support:2 initial:1 u0:22 u3:1 pages:1 gif:1 accordingly:1 describes:1 terminates:2 ed:3 was:1 bianchi:2 function:1 complete:1 form:6 but:3 failure:2 cedex:1 matematica:1 convergence:2 highest:2 made:1 applying:1 builds:2 uu:1 multiplicity:1 us:4 below:1 multivaluedness:4 boldface:1 uj:2 called:2 detailed:1 taylor:2 associated:2 defined:3 abstract:1 describe:2 textbook:1 denote:1 globally:1 fixes:4 single:14 arises:1 exist:5 corresponding:1 again:1 puzzling:1 integrability:1 no:11 when:4 detail:1 application:1 build:2 other:3 details:1 branch:3 test:8 conclusion:2 condens:1 critiques:4 problems:2 miscellaneous:2 eleste:2 meaning:2 important:2 building:3 auxiliary:1 algorithm:2 practically:3 4u:3 saclay:1 χj:2 impossibility:1 volumes:1 time:2 requires:2 original:3 once:1
|
solv-int9812008.txt |@word secondly:1 partial:9 consider:5 remarkable:1 represent:2 eaires:1 global:2 results:6 ry:2 leads:2 eds:1 scalar:17 proposition:1 computation:1 resisted:1 whose:4 inverse:2 depend:3 paris:5 technique:1 presents:1 list:1 finally:3 present:3 th:3 under:4 aux:1 include:3 worth:1 summarizes:1 case:11 updated:2 advantage:1 very:1 erale:4 choice:2 homography:1 difference:2 exact:2 entire:7 school:2 level:7 irreducible:1 tanh:6 july:1 solution:13 correct:3 involution:2 indices:5 optics:1 originally:1 akns:6 intermittency:2 consistent:1 hetero:1 painlev:24 insertion:1 pass:1 chen:1 dynamics:1 konstant:1 d4:1 substitute:1 canonical:3 spectral:1 established:2 what:1 nonlinear:12 appear:1 ere:1 section:8 bc:2 calcul:1 d3:1 current:1 version:5 en:4 sur:6 above:4 sup:1 new:5 d1:2 ever:1 method:23 3e:1 satisfy:3 med:1 full:2 integrated:1 degree:6 never:1 component:3 gabay:1 here:4 met:1 les:4 sinh:2 address:1 represented:1 consideration:1 sine:3 equations:45 appears:1 logarithmic:2 deduced:1 conte:12 derivable:1 conviction:1 difficulty:1 study:1 allows:1 later:1 base:1 resulting:7 usually:2 hospitality:1 had:1 suitable:2 y13:1 y12:2 via:3 followed:1 classification:4 explained:1 systems:2 plenum:1 replace:1 linearization:2 rψ:1 derivatives:4 ψx:7 feb:1 handled:1 would:3 prove:2 distinct:1 give:1 ψt:2 next:2 call:1 therefore:4 taken:1 associated:1 stage:3 type:2 until:1 more:3 introducing:1 equivalence:2 initiated:1 definition:4 successful:3 solitons:1 operators:3 berlin:2 warm:1 particular:3 known:2 projective:1 iii:2 must:9 sample:1 springer:2 word:2 recall:1 equation:27 des:3 det:1 modified:1 unknowns:2 obvious:1 following:4 fulfill:1 dec:1 ay1:2 example:3 proof:1 f1:2 f2:2 challenging:1 links:1 dxx:1 process:3 g5:4 high:1 indicates:1 chelsea:1 assumptions:1 numbers:1 bekki:1 verlag:1 information:1 respective:1 boussinesq:5 minist:1 darboux:14 travel:1 six:1 feature:1 formations:1 csx:2 fourth:4 acta:2 ordinary:1 parameter:2 express:1 blocks:1 singular:9 may:4 after:1 singularities:8 movable:7 axx:1 3y1:1 plane:2 lax:40 ff:1 waves:3 end:1 summarize:1 gauthier:1 fordy:1 sx:1 physical:1 dynamical:1 third:12 sech:2 author:1 explicit:3 correspond:1 st:2 sk:3 rather:2 so:8 martina:2 sc:3 representation:1 4st:1 order:41 c2:1 restriction:2 help:2 hierarchy:1 developed:1 over:1 ordre:4 satisfied:5 transcendents:1 2sx:1 y1:24 existence:3 satisfies:6 y2:17 its:16 before:1 solitary:2 ginzburg:2 derive:1 group:2 thank:1 la:1 τf:4 interesting:1 fix:1 decreases:1 absence:1 complex:4 choose:3 inconsistencies:1 derivative:2 main:1 defining:2 correspondence:1 them:4 good:2 cea:1 bxx:1 auto:5 acklund:14 levi:1 landau:2 yx:1 they:3 identically:1 singularity:4 now:4 yt:1 possess:1 easily:1 term:2 finite:5 2p:2 name:3 preferable:1 university:1 presented:1 2y:1 2z:4 2q:7 applied:2 iff:2 l2:7 each:8 found:5 higher:6 side:2 mean:1 differential:11 ek:2 ej:9 ed:2 elementary:2 yvette:1 eu:5 our:2 operation:1 beyond:1 eq:3 special:2 out:1 etat:1 shown:3 precisely:1 matrix:2 admissible:1 gradient:3 kotera:3 since:10 rev:2 chaos:1 daniel:1 stud:1 reader:1 formula:2 sme:3 ref:5 occurs:1 math:11 provide:2 turning:1 linear:10 kaup:10 little:1 ascending:1 admits:1 small:1 reason:3 necessarily:2 york:3 e5:1 e4:2 e1:3 e0:1 e3:2 e2:4 incorporates:1 pairs:8 derivation:3 applications:3 determining:6 could:3 wrong:2 linearizing:2 conducted:1 place:2 gordon:3 xii:1 consequence:1 shadwick:1 g25:6 frequent:1 first:8 cy2:3 cy1:1 lunds:1 features:1 miura:1 variables:2 powerful:1 number:5 rank:1 xe:1 restrict:1 xx:3 done:1 relations:2 another:3 robust:1 modulo:1 ψxx:6 fj:2 given:4 birational:1 reference:2 service:1 similarly:1 unknown:3 carnevale:1 system:11 unspecified:1 their:8 assumption:6 too:1 statement:2 2ac:1 proving:1 kupershmidt:7 part:3 x2:8 x0:4 x1:4 than:8 coefficients:6 linking:1 relative:1 kind:1 expansions:1 ew:1 fuchs:1 see:2 winternitz:1 classes:4 historical:1 were:1 nozaki:1 truncating:1 enumerated:1 linearizable:4 premier:1 argument:2 say:1 uniforme:1 7q:1 seem:1 linked:2 contents:1 zero:2 depending:2 convenient:1 lin:1 physique:1 ideas:4 uuxx:1 ode:6 instance:2 potential:1 build:1 sufficiency:1 gambier:8 unconstrained:1 salle:1 even:1 opposite:8 who:2 sequence:1 3y:4 newell:1 riccati:11 most:7 errors:3 formulae:2 pair:31 why:3 inconsistency:2 laurent:1 nonlinearity:1 considered:1 clear:1 sometimes:1 repeated:1 physica:1 kr:1 points:3 physics:2 χj:1 exx:1 reserve:1 nls:2 currently:1 show:1 dy1:4 fifty:1 purely:1 attempts:1 relation:1 solutions:6 d6:1 rogers:1 analogue:1 d5:1 d2:1 find:5 fifth:1 principal:1 completion:1 schwarzian:1 2bx:1 situations:1 state:2 should:3 monomial:1 only:24 experiment:1 intrinsically:1 integrable:5 local:1 λy:1 columns:1 dn:2 do:4 his:2 handle:2 ϕx:3 notation:1 means:4 df:3 ϕt:2 de:2 bear:2 βc:1 famous:1 cannot:1 nearly:1 dx:1 ϕj:1 dt:9 du:5 evolution:1 aex:1 transposition:2 arxiv:1 fixes:2 remove:1 acknowledgments:1 sum:1 twice:1 common:2 fixed:1 musette:11 crm:1 coefficient:3 set:2 art:1 computed:1 exists:3 edited:2 2c:1 observed:1 depends:4 result:3 eliminating:2 inequivalent:2 best:2 surfaces:2 eres:1 still:2 hybrid:1 please:1 eorie:2 written:1 future:1 various:1 closed:1 between:22 invariant:9 subscript:1 conditions:5 ends:1 recently:1 hecke:1 nature:1 erieur:1 matveev:1 villars:1 vanishing:4 wtc:7 solv:3 s98:1 come:1 both:1 pempinelli:2 desired:1 many:2 taking:1 equal:1 against:1 chosen:1 une:1 context:1 distinction:2 pde:24 expression:5 finds:1 comes:2 otherwise:2 among:2 relevant:3 reasons:2 5q:2 sawada:3 tabor:1 16c:1 dimensional:6 mkdv:2 cx:7 simply:1 applicability:1 polynomial:5 constant:12 diff:3 considers:1 conserves:1 pp:7 described:1 transformations:8 second:26 infinit:1 three:11 been:5 int:5 reduction:1 much:1 dont:2 asymptotics:1 interest:2 4q3:1 trunc:1 pn:1 define:1 obtained:7 generating:1 families:11 truncations:4 pickering:3 representative:1 6y:1 general:7 those:4 p2:3 p1:5 p6:5 p5:1 might:1 resummation:2 bψ:1 single:2 choices:3 will:4 while:1 proves:1 replaced:3 applies:1 stopping:1 revisited:1 property:9 leaves:1 procedure:3 due:1 uxt:2 cons:1 century:1 vol:2 refs:1 thus:4 non:1 uxx:2 encountered:1 ii:3 characterize:1 reads:1 ϕxx:1 avd:1 vanish:1 capture:1 different:2 pseudopotential:2 generic:1 identities:1 lett:5 same:5 any:6 member:1 parts:2 degr:1 widely:1 sinegordon:1 several:2 cs:1 four:3 status:1 independent:1 used:2 solved:1 singapore:2 grundland:1 compared:1 infinite:1 frequently:2 ablowitz:1 implement:1 identity:2 recent:1 numbered:1 nevertheless:2 reprinted:2 well:5 analysis:12 thought:1 academic:2 without:1 solve:3 components:2 sets:2 firstly:1 entry:2 usual:2 4q2:2 manifold:7 just:2 being:1 able:2 resp:4 obtain:3 etriques:1 thanks:1 world:2 scattering:11 yet:1 boiti:2 spatiotemporal:2 family:16 hint:1 seems:2 lhs:2 weiss:6 egrale:2 cxx:6 belongs:1 treatment:1 easy:2 kuramoto:1 transformation:22 take:1 identical:3 involutions:2 showing:1 2ex:1 inconsistent:1 increases:1 quest:1 five:1 pages:1 press:1 imposed:2 unique:2 αf:1 apart:1 necessary:1 like:2 success:2 follows:3 steps:1 homographic:2 arbitrary:5 become:2 mathematical:1 because:2 often:2 namely:3 truncated:3 3bx:1 some:9 truncates:1 understood:1 acad:2 examples:2 table:2 kdv:3 guess:1 nonzero:1 sivashinsky:1 est:2 proceeding:1 erentielles:3 lead:1 esimal:1 avoid:1 cχ:1 injects:1 classical:1 everything:1 ese:2 critical:2 exposition:1 eliminate:2 provides:1 3q:1 ct:1 critiques:2 either:1 bd:1 linearizations:1 algorithmic:2 scientific:2 intimate:1 june:1 equivalent:7 l1:8 use:2 expansion:1 bt:26 uneasy:1 step:15 corp:1 although:2 substitution:2 bx:2 properties:1 earlier:1 eψ:1 uxxxx:1 om:1 2cx:1 extension:1 constraint:1 2i:1 le:1 regular:1 nothing:2 theory:1 eica:5 discard:1 introduced:1 consequently:1 dψx:1 gibbons:1 integration:1 generalized:1 contains:1 publishing:1 orders:2 into:3 successive:1 odes:5 variable:8 appropriate:2 right:1 references:2 qψ:1 operator:2 proportional:1 france:1 van:1 log:16 support:2 there:8 u1:1 transform:1 class:1 gif:1 appl:1 way:3 series:6 var:1 function:6 building:1 carg:1 complete:1 form:7 but:2 failure:1 cedex:1 link:8 elimination:8 segur:1 pdes:14 truncation:30 made:5 applying:1 ux:8 ut:8 inside:1 up:1 us:7 kk:3 below:1 uj:2 problem:7 similar:1 called:2 ex:1 detailed:1 ac:2 ab:1 proved:1 ad:1 patterns:2 defined:3 abstract:1 linearity:1 denote:1 chap:1 warning:1 exist:3 eom:1 sxx:1 ax:2 formalism:1 prevail:1 check:1 defines:1 satsuma:1 functions:9 broer:2 integrability:4 no:2 amounts:1 nb:1 when:9 2dx:1 field:5 other:1 details:2 spatial:1 test:2 conclusion:2 generates:2 truncate:2 condens:1 symbol:2 hirota:1 problems:6 ultimately:1 deriving:1 commutator:2 tackle:1 describing:2 structure:1 nonintegrable:3 searches:1 implies:2 4y:1 assume:2 values:2 required:1 holes:1 saclay:1 together:1 notion:1 fact:2 time:1 requires:1 original:2
|
solv-int9812009.txt |@word consider:6 chain:1 varying:2 four:1 proposition:3 gk:28 whose:6 inverse:1 paris:2 subjected:1 technique:1 tr:12 finally:4 elliptic:1 under:3 conjecture:1 provides:1 g0:2 dokl:1 geometrical:1 δµi:3 δgk:8 δµb:2 difference:1 matrices:10 condition:1 dim:1 riemann:6 hamiltonian:3 sklyanin:2 math:2 universal:1 small:3 eigenvalues:1 setup:1 direct:2 surrounding:2 second:3 canonical:3 spectral:11 index:1 diag:1 section:2 near:1 expressed:3 sheeted:3 poles:19 above:16 new:1 nnk:1 contributes:1 method:3 led:2 even:1 component:1 here:4 met:1 ansatz:1 groups:1 quite:1 equations:4 appears:3 interpret:1 δλi:6 obtained:2 remark:3 divisor:4 study:1 vectors:3 allows:1 procedure:1 action:15 symmetrical:1 involves:1 quotient:3 uniquely:1 identification:1 family:1 requiring:1 replace:2 talon:3 use:1 takes:1 prove:1 remains:1 suppl:1 universally:1 explicitly:1 call:1 therefore:2 type:2 theoretical:2 more:2 zeroes:2 multiplying:1 duality:1 billey:1 phong:2 particular:3 known:2 parameterize:1 keeping:2 valued:1 canceled:1 recall:2 equation:10 work:1 det:1 theories:1 values:1 stabilizer:1 freedom:2 dec:1 proof:2 wedge:3 calculation:1 december:1 smirnov:1 generically:1 reconstructed:1 sphere:3 νg:1 assumptions:1 recognized:1 νi:7 µj:3 normalize:1 rather:1 get:8 occur:1 write:2 located:2 varies:1 parameter:6 simplicity:1 product:4 description:1 algebra:2 may:1 algebro:4 orbits:1 residues:8 constraint:1 lax:10 coming:3 fi:13 choice:1 data:2 natural:6 dynamical:17 third:1 chern:1 lines:2 correspond:1 element:1 generic:2 so:7 allow:1 jussieu:1 order:7 indeed:2 over:1 choose:2 paper:1 jnk:1 its:8 before:1 group:6 thank:1 singular:3 ln:3 interesting:1 fix:1 solving:1 lk:13 coordinates:11 forms:1 degrees:2 systems:5 non:7 good:1 propose:1 introduce:2 they:4 half:1 now:3 kirillov:3 eigenvalue:1 term:9 characterizes:1 2g:2 l0:7 each:3 universit:1 constraints:1 differential:2 resλ:4 doing:1 related:2 moser:1 toda:1 used:2 interplay:2 entering:1 our:2 eq:8 out:1 living:1 shown:1 matrix:17 space:15 since:16 cancels:1 boˆıte:1 contained:1 geom:1 rational:3 formula:3 rj:7 shows:3 fiber:4 linear:1 diagonal:14 standard:1 analytical:1 approaches:3 base:3 generate:1 definition:2 pairs:2 qj:1 geometry:1 impose:1 keep:1 motion:1 ordering:2 int:2 place:1 hence:12 first:8 xk:5 xl:1 variables:12 powerful:1 number:5 nested:1 improvements:1 precisely:1 separation:1 given:4 sheet:1 introduction:1 system:6 their:1 normalization:3 gives:2 progr:1 exactly:5 contribute:3 part:9 differentiate:2 branches:1 coefficients:10 double:1 depends:3 project:1 powers:1 etage:1 curves:1 yielding:4 need:1 seen:4 any:1 viewed:1 lie:4 angle:2 zero:1 depending:2 calogero:4 able:1 note:6 k2:8 k1:8 take:4 jacobian:2 acquires:1 circles:2 residue:6 cnrs:2 trace:1 though:1 who:1 algebraic:1 regular:19 sponsored:1 sheets:2 phase:10 acknowledgements:1 class:1 branching:2 considered:1 clear:1 1er:1 sum:3 fact:2 show:4 gauge:1 solutions:2 find:1 parameters:5 specified:1 enough:1 quotiented:1 should:1 avan:1 analytic:2 only:4 difficulties:1 generators:2 factor:1 integrable:5 circle:1 hamiltonians:1 local:4 jac:2 columns:1 abelian:1 dl:4 dk:6 notation:1 means:2 express:3 δl0:1 altogether:2 covering:6 babelon:3 approach:2 arxiv:1 fixes:1 qi:5 fixed:3 view:1 meromorphic:2 moduli:1 set:1 fibered:1 resb:8 namely:4 result:2 δλk:1 discussions:1 terms:7 dµ:5 points:19 bernard:1 ways:1 µq:1 written:2 µn:2 µi:13 correctly:1 between:2 invariant:2 geometric:3 conditions:1 µb:4 preserve:1 notice:1 various:1 recently:1 extend:1 subject:1 veselov:2 however:4 vanishing:4 solv:2 amer:1 problem:1 σj:1 last:2 many:1 taking:1 equal:3 chosen:1 tour:1 symplectic:13 contribution:4 genus:5 whole:2 ck:2 reconsidered:1 point:11 simple:4 vicinity:1 lpthe:1 pole:8 conjugation:1 associated:1 diff:1 kp:1 described:1 transformations:1 basis:2 locally:2 three:1 been:3 strategy:1 defined:4 reduction:2 pk:4 algebras:1 abstract:1 define:3 determinant:1 describe:2 corresponding:1 commutes:1 hurwitz:1 observe:1 lives:1 generalization:1 c1:1 denote:1 spin:4 case:3 look:1 value:1 will:2 rationally:2 while:1 situation:1 loop:1 δfi:3 vi:1 surface:2 characterize:1 dual:1 ie:1 2g0:1 different:2 perform:1 connection:1 same:4 antisymmetry:2 complex:1 gets:2 independent:6 extended:1 see:2 parametrizes:1 analyticity:1 identity:1 eigenvectors:3 expression:1 analysis:1 model:3 dimension:6 left:3 proposed:1 moments:1 obtain:1 λb:1 identify:1 immediately:1 λk:25 λi:10 previous:1 k3:7 like:1 character:1 add:1 lett:1 momentum:2 around:4 decomposed:1 using:4 occurring:1 theor:1 necessary:1 l0n:3 follows:2 specific:2 δl:11 δf:4 conclusion:1 reduced:3 specifies:1 because:5 methods:1 some:3 trends:1 moreover:2 proper:1 provided:1 umr:2 does:4 expressing:1 assuming:1 equivalent:1 expansion:2 bundle:4 properties:1 most:1 column:1 novikov:2 o:10 act:1 2iπ:2 soc:1 h1:1 due:5 pair:3 references:1 determine:1 sov:1 isospectral:1 next:1 log:4 there:3 question:1 ψi:1 analyze:1 was:1 naturally:1 function:5 complete:1 form:17 soliton:1 simplifications:1 regard:1 but:1 cedex:1 properly:1 hn:4 line:2 highest:1 count:1 made:1 compute:6 places:1 characteristic:1 up:1 us:7 par:1 krichever:5 ln0:1 integrating:1 coadjoint:8 called:1 eigenvector:6 obtains:1 separated:1 constant:5 computing:1 ai:3 ak:17 aj:1 general:4 transl:1 single:1 dλ:32 supersymmetric:1 physical:1 again:2 functions:2 nk:14 completeness:1 no:4 when:1 vanishes:6 application:1 bracket:2 role:1 details:1 branch:9 pi:8 nice:2 polar:3 elements:2 models:1 polynomials:1 a1:1 commutator:1 important:3 structure:5 rq:2 implies:2 auxiliary:1 assume:2 curve:15 orbit:9 bethe:1 time:1
|
solv-int9812010.txt |@word scl:1 concept:1 homomorphism:1 consider:3 global:2 splitting:1 unchanged:1 gx:2 four:5 eds:2 proposition:7 computation:3 consists:2 partial:4 expressions:3 analiz:1 preserves:1 const:1 aug:1 ty:2 equivalence:3 send:1 γt:2 tl:1 aut:1 stable:1 rham:1 breach:1 te:2 tc:1 p2:3 string:1 straightforward:1 pages:1 choice:2 valued:8 entries:1 manageable:1 matrices:9 condition:4 look:1 notes:3 t2:2 applicable:1 vector:16 53c42:1 slu:1 relation:5 anal:1 der:5 still:1 grateful:1 lecture:1 sin2:6 b22:36 zero:18 incidentally:1 spect:1 theory:7 spectral:3 what:1 nonlinear:4 g22:1 incompatible:2 tchebycheff:6 expressed:2 version:1 above:6 3b:2 3a:2 consisting:1 satisfy:2 conf:3 respectively:2 never:1 component:4 here:5 fiberwise:1 tangent:2 aid:1 represented:1 consideration:1 along:2 equations:22 obtained:4 michal:2 arrive:1 wesley:1 institute:1 vectors:2 leaving:1 action:8 suitable:1 quotient:1 uniquely:1 formulated:2 projection:2 classification:3 explained:1 teorii:1 nonlocal:1 1st:1 apply:1 should:1 derivatives:2 use:2 would:2 cohomological:1 distinct:1 contains:1 bundles:2 finally:1 sports:1 wood:2 melko:1 taken:2 conservation:1 exhaustive:1 more:1 flat:2 formally:2 expose:1 under:2 curvature:22 berlin:1 chast:1 particular:2 known:1 cases:5 must:2 springer:1 isomorphism:1 recall:3 equation:6 work:1 γf:2 unknowns:3 itself:1 determining:1 following:4 dec:1 example:5 triple:3 give:3 relativistic:1 arise:1 ann:1 dependence:1 yθ:4 assumptions:2 cartan:2 sense:4 needs:1 ib:5 end:4 notation:2 rather:1 acts:2 maps:3 adjacent:2 answer:1 acta:1 parameter:11 sin:40 gordon:1 fr:2 algebra:11 bkl:1 fy:1 immersed:2 after:1 derived:1 mapping:4 bkj:1 diagram:1 applications:4 74b:1 plane:2 representations:5 horizontal:3 geometrical:2 constants:3 diagonal:5 natural:2 computations:1 onto:1 grant:4 element:3 diffeomorphism:1 so:3 fundamental:2 representation:15 martini:1 g11:1 holds:1 dx:11 over:2 nonparametric:2 paper:1 y1:32 existence:1 satisfies:1 y2:21 its:3 equiv:1 lf:6 style:1 group:6 thank:1 fiz:1 fix:2 solving:1 coordinates:11 actually:1 forms:2 systems:8 mail:2 main:2 might:1 variables:1 yi:1 non:5 acklund:2 they:2 now:5 represents:1 term:1 netherlands:1 stated:1 goldstein:1 always:1 university:4 identified:1 2f:4 each:2 found:2 economy:1 mean:2 domain:1 differential:17 ed:1 related:2 combining:1 our:5 calling:1 eq:5 special:1 category:1 ru:1 matrix:5 rr:1 space:2 since:2 unknown:1 denotes:1 2b12:4 contained:1 geom:3 formula:3 get:1 math:2 sbs:1 fiber:3 linear:23 codazzi:6 differ:3 dx2:6 reason:1 included:1 york:1 members:2 nition:1 βt:1 definition:6 pairs:1 derivation:3 ministry:1 geometry:7 phrases:1 harlow:1 levi:1 turn:1 derivations:1 1x:2 βh:1 first:2 xi:2 fx:11 symmetry:1 possessing:1 geodesic:4 xx:1 xy:1 approximately:1 another:3 results:1 ring:1 electronic:1 given:5 derives:1 rewritten:1 jet:1 similarly:1 introduction:1 leading:1 adjoint:1 system:4 least:1 their:4 appl:3 lifting:1 structures:3 tuple:2 moscow:3 helpful:1 jordan:2 authors:1 x2:10 x1:18 coefficients:1 determines:4 sections:1 second:4 project:1 determined:7 vinogradov:2 russia:1 pre:1 symmetries:1 pro:1 endomorphism:1 say:2 variable:1 flatness:1 any:13 alence:1 lie:11 homological:1 self:1 agency:1 bobenko:3 instance:1 ideal:1 internal:1 take:3 typeset:1 opava:4 new:3 subject:1 fpf:1 though:1 algebraic:1 said:4 but:1 automorphism:1 pair:1 acknowledgements:1 why:1 αt:1 soliton:4 prolongation:1 curvatures:2 dimension:1 bracket:2 physics:1 section:3 lying:3 laws:1 supported:2 spaces:1 gauge:9 trivial:6 q1:4 q3:3 based:1 explain:1 outside:1 jection:1 only:4 explicitly:1 aϕ:5 removable:2 integrable:16 constant:4 local:2 correspondence:1 dh:3 means:2 czechoslovakia:1 de:1 nijenhuis:2 cannot:3 words:3 dy:17 during:2 geometric:1 simplest:1 covering:30 fields:4 arxiv:1 remove:1 method:2 aspects:1 whether:2 isothermic:1 kernel:2 krasil:5 set:1 exists:5 imposing:2 module:9 connections:1 namely:1 computer:1 result:1 terms:3 weingarten:5 y3:4 concern:1 surfaces:15 youth:1 satisfying:5 tensor:1 y4:3 written:1 classes:4 closed:2 between:3 αh:1 αk:1 before:1 approach:1 available:1 cλ1:5 august:1 vertical:5 attention:1 however:1 wu:1 answers:1 key:1 jets:1 problem:2 both:1 cos:8 many:1 0x:2 demanded:2 connection:7 pde:1 point:2 address:2 cf:4 cd:15 dimensional:3 solv:1 conjugation:3 βt2:1 respect:4 diff:1 pr:1 longman:1 mainardi:6 described:1 commutative:3 basis:1 wien:1 locally:4 sl2:9 int:1 belongs:1 iy1:5 iy2:3 adb:1 algebras:2 universal:1 define:1 addison:1 corresponding:5 remark:3 2g12:1 finished:1 c3:5 c2:5 c1:6 manifolds:2 case:13 p3:3 p1:4 splits:1 invariants:2 defining:1 nski:3 barbashov:1 will:3 euclidean:1 while:1 harmonic:3 sli:3 intas:1 eif:16 situation:1 property:1 procedure:1 iy:2 ix:2 endowed:4 metric:2 thus:5 surface:2 sas:1 vs:1 dual:2 vx:10 vy:2 vanish:1 municipal:1 rfbr:1 author:4 recursion:1 make:1 belong:2 same:3 vieweg:2 complex:2 proved:1 finite:2 subalgebra:1 sterling:1 independent:1 used:2 http:1 see:7 sym:4 parametrized:5 usually:1 nesterenko:1 braunschweig:2 infinite:2 identity:2 recent:1 shortly:1 nevertheless:1 well:3 elem:1 analysis:2 obviously:3 without:2 solve:1 components:1 coordinate:1 parametric:2 possesses:1 criticism:1 manifold:4 λt:1 being:3 obtain:6 questions:1 immediately:1 facts:1 yet:1 previous:1 submodule:2 preprint:1 family:3 gmc:6 cl:2 setting:1 transformed:1 lett:2 ada:1 b12:60 transformation:3 generalized:1 real:4 bil:1 bij:3 bik:1 depends:1 easily:2 brno:2 sums:1 possible:1 admitting:1 corresponds:1 possibly:1 five:1 apt:1 using:2 accepted:1 κt:1 projects:2 formal:2 insert:1 like:1 cz:1 dept:1 automorphisms:1 yields:1 either:1 arbitrary:9 immersions:1 works:1 reduced:3 depend:6 therein:1 twelve:1 www:1 old:1 methods:2 classical:1 czech:3 fordy:2 some:4 understood:2 trends:1 b1:3 zcr:13 b3:2 happens:1 provided:1 total:2 describing:1 shall:1 per:1 does:2 exposition:1 proc:3 esi:3 ferapontov:1 equivalent:7 cλ:5 b212:6 cθ:1 olicher:2 transformations:3 trivialization:2 constraint:2 silesian:2 discussed:1 a3:2 o:95 covariant:1 a2:2 introduced:1 consequently:1 other:2 morphism:1 subbundle:1 into:4 negative:1 lies:1 appropriate:1 extending:1 references:2 been:1 einstein:1 operator:2 additional:1 there:7 question:1 transform:1 class:6 joseph:1 way:3 was:3 gij:1 naturally:1 function:3 xy1:1 form:18 denoting:1 gauss:10 construction:2 russian:2 removed:2 true:1 partially:1 extend:1 october:1 wise:4 tθ:2 cie:3 default:1 characteristic:6 smooth:5 below:1 coverings:7 ix2:2 distribution:7 ix1:2 similar:1 called:5 ac:1 associated:1 b2:2 computing:1 defined:1 coincides:1 abstract:1 yadra:1 denote:6 ap:1 together:1 ax:1 education:1 check:1 fill:1 again:1 functions:10 masaryk:1 prilozh:1 integrability:2 no:3 na:1 when:1 field:9 book:1 republic:2 details:2 normal:2 b11:51 mathematics:2 operators:1 may:4 problems:1 bundle:23 stay:1 a1:3 commutator:2 generated:1 tribution:1 allowing:1 linearization:2 replacement:1 structure:12 auxiliary:1 assume:5 dτ:4 shchik:5 equivalently:1 35q53:1 lychagin:1 svx:1 dϕ:1
|
solv-int9812011.txt |@word similarity:60 dynamic:1 four:14 consists:2 replacements:2 calculate:4 paris:5 29b:1 29a:1 γn:6 nσn:2 under:9 hermann:1 aux:1 alternating:3 conjecture:2 rise:1 ǫa:1 every:1 ǫg:1 school:2 ref:1 solution:11 convenience:1 vector:9 indices:4 upr:1 consistent:1 nonautonomous:8 direct:6 second:10 rigorous:1 expressions:8 even:15 established:4 selected:1 above:5 new:12 increasing:1 consisting:7 coefficient:1 27a:1 deemed:1 27c:1 simultaneously:1 here:13 drei:1 asymmetry:1 represented:2 obtained:19 study:10 completely:1 symmetrical:1 changes:1 equivalence:1 projection:1 classification:1 9a:1 9b:1 plenum:1 highly:3 cons:2 total:1 univ:3 linearly:2 derivatives:3 would:2 substitutions:2 noting:4 call:1 therefore:4 m2:3 heralded:1 type:15 coupled:4 curvature:1 warn:1 berlin:1 hold:2 must:11 ii:13 springer:3 mn:6 mk:6 theories:1 mq:11 mr:1 example:4 indicated:5 give:5 preserving:3 involve:2 indicates:1 want:1 type1:1 absolute:1 provide:2 feature:1 very:4 nontrivial:2 adjacent:1 ordinary:16 description:5 earlier:3 diagram:2 lax:22 constants:1 effective:3 enter:2 order:21 operations:3 interpretation:2 over:3 punkten:1 satisfied:7 deducted:1 japan:4 before:5 fit:2 37a:1 fix:1 37b:1 writing:2 fig:1 treating:1 them:5 combination:3 amenable:1 they:11 singularity:10 represents:2 component:2 each:14 side:5 t2:1 semiclassical:1 used:12 combining:2 extract:1 contend:1 jimbo:5 restricted:2 rx:3 ry:2 aji:1 ajj:1 newly:1 independence:1 39c:2 39b:1 39a:2 linear:27 associate:1 free:8 standard:2 admits:1 publ:1 incorporates:1 starts:1 xux:1 mvn:1 already:10 features:1 miura:13 restrict:1 ℓj:1 another:4 tλj:1 illustrate:1 similarly:4 eqs:8 needed:1 master:1 too:1 centered:1 tool:1 17b:1 17a:1 piii:5 iteration:2 zero:6 interrelated:1 extracting:1 rewrite:1 modern:1 mind:1 spectrum:1 analysis:3 seen:4 seem:1 magnus:1 convenient:2 latter:8 responsible:1 amusing:1 schlesinger:22 shall:7 object:2 birkh:1 riccati:2 involving:5 assessed:2 φk:19 inconsistency:1 don:1 calculated:3 vertices:3 points:12 principle:5 vries:2 notion:1 saying:2 probl:1 sakai:2 reductions:6 random:1 implying:1 gauge:16 solutions:17 subtle:1 analogue:10 d2:3 specify:1 rich:3 pursuing:1 hamiltonians:1 rectangle:1 sur:5 do:5 dk:9 de:5 dw:3 dt:2 du:4 dp:1 nν:17 ponents:1 quintessential:1 38a:2 38b:3 38c:2 reference:1 27b:1 observed:1 depends:3 w3:2 result:3 w1:3 w0:3 subject:1 xvx:1 µz:1 µv:1 µr:3 symmetric:7 simplest:2 approach:8 discovery:1 terms:63 extend:3 nature:1 wn:2 however:14 nǫ:2 extent:1 analytique:1 com:1 2nm:2 2na:1 16a:1 16b:1 interrelations:1 polynomial:1 diff:4 2nq:1 2np:2 basis:2 three:7 been:16 much:3 9jt:1 interest:3 basic:8 graphical:1 families:3 25b:2 quantities:3 concerning:1 25a:2 confinement:9 2n1:3 applied:3 exception:1 remaining:4 employ:1 symbolically:1 aii:2 aij:1 property:13 elaborate:1 procedure:2 a21:8 a22:8 a23:8 a24:8 iv:2 obeying:3 flaschka:1 im:1 uxxx:1 containing:2 perform:1 make:6 linked:1 complex:4 hierarchies:1 several:2 couple:2 independent:9 counterparts:1 hand:16 auser:1 braunschweig:1 a2n:1 zweiter:1 left:5 unified:1 just:5 solvability:1 identify:1 transforms:2 tilde:1 scattering:1 yet:3 previous:9 adding:1 enters:3 regarded:1 ele:1 transformed:1 easy:1 apart:1 5a:2 5b:2 explained:1 possible:5 possibly:3 indicative:1 background:1 unique:1 disadvantage:1 appearing:1 permuting:2 performing:1 specific:2 steps:3 polytechnique:1 arbitrary:9 evolutions:2 right:9 deal:1 truncates:1 confusing:1 proceeding:1 bottom:1 unavoidable:1 korteweg:2 algorithmic:1 mσn:3 kruskal:2 predicting:1 losing:1 properties:5 proceed:2 o:16 plus:1 continous:1 slightly:7 considerations:1 mbn:4 transcendents:9 differentialgleichungen:1 22b:2 22a:2 down:2 lies:1 acad:1 often:1 unambiguous:1 ψk:11 combinatorics:1 initial:16 transform:1 seiler:1 way:19 was:32 m0:1 interrelation:1 form:72 forming:1 differences:1 denoting:5 remarking:1 encoded:1 stand:1 true:2 versions:2 attached:1 stages:1 ln:6 abstract:2 proven:2 exist:8 dλ:2 accounting:1 check:1 constructed:1 nk:4 integrability:10 no:4 wesentlich:1 na:4 whereas:5 generally:1 setting:1 role:6 np:9 picture:1 models:3 preceding:1 15a:2 15b:2 ξn:9 hietarinta:2 variable:29 parities:1 longer:1 assume:4 together:26 time:5 n0:3 n1:11 n2:17 backward:1 n4:13 remarkable:2 global:1 focus:1 leads:12 supplement:1 computation:1 primes:1 interlaced:1 inverse:4 depend:1 recurrence:1 finally:7 analogous:1 string:2 orthogonal:4 erale:3 seemingly:1 geometrical:1 entries:6 exact:2 notations:3 υn:11 presented:7 turns:2 discrete:147 permutability:2 der:1 upper:1 work:1 occurrence:1 dealing:1 sign:1 substitute:1 spectral:5 adds:1 stands:4 43b:3 favour:1 43a:2 reminiscent:1 goes:3 papageorgiou:4 along:4 appears:1 change:3 shift:17 studied:2 simultaneous:1 linearised:1 studies:2 useful:1 extra:1 merely:1 isomonodromic:16 additive:1 prove:1 perk:1 france:3 selfdual:1 live:2 memory:1 scope:2 associated:22 introducing:7 duality:5 vieweg:1 appendix:2 virtue:1 cases:4 insights:3 valued:1 originally:3 values:14 hope:2 following:51 making:3 arrive:3 hiroshima:2 claim:1 figure:4 expanding:1 permutations:1 bessis:1 14b:2 performed:1 14a:2 conversely:1 verlag:5 s0:3 s4:1 write:6 criterion:1 pure:1 ensure:1 parameter:30 obius:1 map:6 product:3 may:10 needs:4 levi:1 date:2 representations:1 data:6 compatibility:7 stress:1 natural:4 outline:1 whenever:1 sp:2 explicit:12 yielding:1 so:10 sn:3 sc:4 definitions:3 ghn:1 typical:1 indeed:1 pointed:2 soc:3 years:4 course:2 statistical:1 omitting:1 argued:2 cole:3 irene:1 τn:51 derive:30 group:7 τk:2 how:6 interesting:5 sα:28 forms:16 window:1 offers:1 constitutes:1 main:4 decades:2 correspondence:1 non:6 thereby:1 acklund:22 introduce:12 scaling:5 ls2:1 identically:1 arriving:2 now:23 discuss:3 possess:1 term:7 name:1 january:1 establishing:1 possibilities:1 form2:1 stockholm:1 entirely:1 en:3 arbitrariness:1 hypergeometric:1 ec:1 mapping:1 eq:25 es:2 emerges:2 ultimately:2 space:2 furthermore:3 contained:2 investigation:1 rational:2 formula:2 correct:1 bleher:1 after:5 theory:16 singularities:7 quite:2 complicated:2 derivation:9 impose:3 turn:6 place:3 view:12 first:15 origin:2 degr:1 xn:180 symmetry:12 omitted:1 variables:45 xx:1 directly:7 comprises:1 open:2 singling:1 xt:1 1p:1 given:43 checked:2 associ:1 1a:3 1c:4 1b:5 brevity:1 convention:2 structures:1 speaking:1 gives:3 asymmetric:5 continuous:38 discretised:1 appearence:1 than:4 coefficients:6 relative:1 skdv:5 third:3 require:2 future:2 were:7 ann:1 premier:1 argument:1 any:6 offering:1 note:3 potential:9 take:5 objective:1 cnrs:1 clearer:1 algebraic:7 formulae:4 multiply:1 especially:1 surprising:1 considered:7 later:4 ohta:4 quantity:5 precise:3 festschrift:1 show:13 discovered:1 joshi:1 corner:2 ratio:4 gauges:1 written:3 analytic:8 only:13 going:2 thompson:1 identification:2 2mq:1 ladik:1 get:4 aim:1 conjunction:4 gen:1 quispel:4 gel:1 regarding:1 yield:2 21b:6 musette:3 reveals:1 imposing:2 connections:2 namely:34 cim:1 eliminating:5 surfaces:2 eigenfunctions:1 ways:4 review:5 sites:6 label:3 behind:2 plaquettes:1 between:20 αn:1 multiplied:1 notice:2 concentrate:1 analyzed:1 x2n:7 σn:27 resides:1 reinterpreted:1 many:5 pertain:1 according:4 propagation:1 tour:1 sβ:2 comes:2 mkdv:17 qs0:3 moreover:1 fruitful:1 considering:1 computing:1 workshop:1 combined:2 differently:2 wants:1 direction:12 qsq:1 6t:2 careful:1 spirit:3 those:4 case:15 u1k:6 kimura:1 developing:2 periwal:1 engineering:1 intimately:1 cast:2 ongoing:1 situation:6 conformal:2 eventually:1 uxx:1 nomenclature:1 different:16 verified:2 etc:2 renormalize:1 same:22 x2:1 shifts:15 extended:1 ux2:1 trivially:3 arose:1 invariance:2 ablowitz:7 expression:5 without:5 components:5 ujk:1 model:2 gdp:24 being:1 when:2 ch:1 pσn:2 differentiation:1 ps0:5 multidimensional:1 seems:5 interested:1 treatment:1 aspects:6 around:4 easily:10 repetitions:1 early:1 test:1 grid:1 21a:5 using:27 psp:2 vertically:1 identifying:1 reduces:3 exploit:1 either:7 characterizes:1 multiplicative:2 pinkall:1 reduced:2 exposed:1 deduce:3 2ξn:6 specified:1 provided:4 xn2:1 dimensions:1 2xn:2 footing:4 extensively:1 provides:2 refer:1 power:2 sixth:2 equivalent:3 notable:1 notably:3 ragnisco:1 explicitely:1 exciting:1 2n:6 comparison:2 ok:1 oj:2 y2n:1 meaning:1 obeys:3 act:2 mixed:1 cambridge:1 ηm:4 qrt:1 determine:1 elementary:2 coalescences:1 log:7 assumed:1 strictly:2 there:16 start:9 series:1 survives:1 complete:3 elimination:2 trying:1 applying:2 embedded:1 obtains:2 ad:2 ai:1 certain:1 ak:2 describe:3 general:24 examine:1 postulating:1 aw:1 formulation:3 az:1 fill:1 again:6 mathematik:1 field:1 valid:1 shimomura:1 mathematics:1 oneself:1 separate:2 vertex:2 a1:15 a3:14 important:3 a4:14 recognise:1 building:1 n3:14 rxn:30 tricks:1 curve:1 hirota:9 starting:12 original:3 represent:1 consider:7 commute:1 montr:1 follow:7 alt:2 referring:3 tu:2 former:1 th:1 ti:7 tc:2 degeneration:2 ofthe:1 straightforward:6 far:5 translations:3 difference:48 deformations:1 condition:9 generalised:2 accompanying:1 list:2 t3:1 t1:1 large:2 anal:1 a125:1 programme:2 appearance:1 past:1 painlev:101 perspective:1 further:7 reine:1 canonical:3 bilinear:40 what:16 nonlinear:33 section:34 version:3 gi:1 fractional:1 method:3 revealing:1 edited:1 full:2 modify:1 behaviour:3 leeds:2 irrespective:1 directions:13 equations:214 conte:4 search:1 tµ:2 allows:5 minsk:1 permutation:3 action:2 chain:1 via:16 family:14 vii:2 establish:7 select:1 takes:3 nijhoff:13 contains:3 summarised:1 comparing:3 ψn:23 a56:1 more:11 linden:1 degeneracies:1 fokas:9 operators:1 basically:2 particular:10 known:10 ramani:14 keeping:1 equation:150 des:1 det:4 dec:1 compare:1 challenging:1 rodriguez:1 numbers:1 sense:7 transcendent:1 ryn:5 respective:2 awkward:1 rather:6 maps:1 acta:3 algebra:1 angew:1 derived:14 ζm:1 ζn:27 plane:3 faculty:1 develop:2 choice:8 concentrating:1 fn:11 short:3 asymptotics:1 interpolates:1 discretisation:1 playing:1 help:2 reservoir:1 hierarchy:2 developed:6 oblique:1 paper:12 through:9 existence:3 its:32 d34:1 unity:1 d30:1 actually:7 resort:1 systems:29 might:3 deformation:20 good:1 return:1 yn:48 universality:2 49a:1 49b:2 obeyed:2 framework:3 oxford:1 formulating:1 2t:2 2u:2 2w:2 2p:13 2q:2 fully:5 level:14 loosely:1 iff:2 2a:3 2b:3 2m:3 universit:2 characterized:1 referred:3 transcribe:1 formulate:4 contiguous:1 reduce:2 idea:1 investigated:2 yoshida:1 expect:2 quantum:5 operation:1 beyond:3 really:1 solved:1 nuovo:1 since:14 denotes:3 dominated:1 issue:5 reformulated:1 found:11 reason:1 members:1 put:1 asi:1 generate:1 definition:5 pairs:8 bring:1 omit:1 a223:1 consequence:4 exhibited:1 dont:3 relate:1 number:5 done:1 least:1 maple:1 story:1 introduction:2 leading:14 construct:4 assumption:3 vxx:2 statement:1 dt2:1 scheme:21 recovered:1 shifted:10 elaboration:1 saint:1 newell:1 immediate:1 part:2 translation:1 believe:2 vxxx:1 determines:1 fuchs:2 determined:1 risks:1 motivation:1 comput:1 etage:1 7a:4 outstanding:1 uniforme:2 lie:1 lim:2 self:13 k2:17 interconnection:1 finding:1 analogs:1 play:4 added:1 most:6 appear:1 soliton:3 tν:6 tλ:16 kj:1 clear:8 coincides:3 kn:25 physica:6 segur:2 physics:3 phenomenon:3 relation:14 carefully:1 find:6 parameters:46 subsection:17 transcendental:5 factor:10 integrable:26 circle:2 notation:2 specialisations:1 express:6 famous:1 3b:3 combinations:1 during:2 resolve:1 continuum:4 arxiv:1 investigate:2 isothermic:1 crm:1 fledged:1 set:11 ser:1 achieved:1 unpublished:1 see:3 individual:1 bare:1 pvi:37 close:1 contour:1 analog:1 pvn:8 fand:1 eorie:1 classes:1 various:20 conditions:2 recently:3 analogues:8 2σn:2 solv:1 31b:1 31a:2 both:21 last:5 reverse:1 connection:10 les:4 context:3 whole:1 point:32 simple:2 corresponds:6 dimensional:11 incompatibilities:1 simply:3 throughout:1 7b:4 pp:1 described:1 transformations:32 py:1 due:1 iupui:1 reduction:20 coarse:1 nato:1 pi:2 pn:8 lett:16 generating:1 kajiwara:1 determination:2 p2:9 ǫb:1 intriguing:1 p1:1 unify:1 look:2 ǫh:1 while:3 replaced:2 ǫu:1 identical:3 unitary:2 century:2 von:1 reads:2 itself:4 ωn1:1 wherein:1 grand:2 products:2 conflict:1 higher:2 development:1 literature:2 syn:4 flows:2 purpose:1 necessity:1 recent:4 lower:2 posedness:1 paramters:1 obviously:6 stellen:1 concrete:2 gambier:1 consistency:9 entry:1 applicandae:1 uℓ:4 shape:1 immediately:4 λk:1 λj:3 alternative:2 cut:1 conclusions:1 alternate:3 exclusively:1 egrale:3 source:1 solvable:1 transformation:17 evaluate:1 characterise:1 bit:1 formal:3 semi:1 systematically:2 follows:6 collect:1 yields:1 exploiting:2 mathematical:1 pertaining:1 methods:1 absolutely:2 mathematicae:1 some:18 back:1 understood:2 towards:2 examples:5 pτ:4 redefining:1 30a:3 30b:1 ourselves:4 describing:2 though:1 integration:4 behave:1 eliminate:4 tends:1 proc:1 bc:1 bn:19 step:7 relating:2 subtract:1 integers:2 constraint:44 pν:41 remains:2 regular:2 consequently:1 into:9 within:8 integral:1 isomorphic:1 appropriate:6 zuber:1 primarily:2 nsp:1 mkn:2 question:3 u0:5 long:1 forward:1 sections:4 gauss:1 link:1 russian:1 themselves:3 raising:1 ux:3 ut:1 up:2 us:22 ur:1 un:29 uk:41 sum:4 autonomous:4 similar:22 called:1 uber:2 constant:5 defined:9 cover:1 inferred:1 single:7 endlichen:1 formalism:6 subcases:1 satsuma:4 amounts:4 fixing:1 nan:9 rewriting:1 application:1 priori:1 department:2 deviate:1 elements:2 calculating:1 critiques:2 problems:19 polynomials:3 expressing:2 replace:2 generated:2 allowing:1 vectors:3 linearization:4 sides:3 structure:20 ago:1 independently:1 implies:1 age:1 equivalently:4 requires:1 having:3 once:3 qvn:8 partial:15 results:6 eds:5 proposition:2 go:1 gn:11 issues:1 disposal:1 uniqueness:1 include:3 interchange:1 g3:5 g2:7 g1:4 kck:1 wave:1 putting:1 matrices:12 entire:4 notes:1 deals:1 trz:1 noted:3 configurations:3 zn:49 zx:6 concludes:1 zt:2 dynamics:2 odd:8 ode:5 index:5 plays:1 expressed:6 3t:5 schwarzian:7 consistently:1 3c:1 expresses:1 3a:3 prefactor:1 body:1 led:3 ibid:2 respectively:11 pushing:1 erieur:1 identifications:6 objects:14 z4:1 abbreviating:1 extreme:1 remark:8 involved:1 resulting:4 opinion:1 implement:1 makes:3 sup:1 involves:2 composed:1 formulated:2 integrations:4 private:1 addressed:1 apply:2 tools:2 use:19 asymptotic:2 commun:5 recalling:1 next:17 few:2 exhaustive:1 formally:3 ecole:1 becomes:2 feuilletages:1 occurred:1 pfn:4 carrying:2 central:2 iii:1 account:2 riemannhilbert:1 ρk:6 obvious:2 capel:5 control:1 calculation:5 effectively:3 np2:1 six:1 dependent:3 pair:8 instead:5 valuedness:2 establishment:2 greatly:1 exemplify:1 singular:2 demonstrating:2 clarkson:1 lines:1 correspond:1 redundant:1 element:4 allow:2 jussieu:1 subsequently:1 evolutionary:1 holomorphicity:1 insight:1 interpreted:6 whilst:2 localised:1 including:2 lattices:2 horizontally:1 le:2 la:1 chosen:2 lk:9 lect:1 choose:4 derivative:3 a97:1 defining:1 auto:10 mention:5 asymmetrical:1 day:1 university:4 identified:6 references:1 isomonodromy:2 constraints:21 bw2:1 related:11 constitute:1 operator:1 measure:1 separating:2 our:6 programmes:1 special:15 out:9 matrix:29 rev:5 stud:1 lecture:1 suffices:1 math:23 8b:1 8a:1 diagonal:2 xzx:1 approaches:1 york:1 8t:1 u0k:11 geometry:1 could:2 iwasaki:1 counterpart:11 derivations:1 hence:1 retain:1 distinguish:1 lagging:1 homogene:1 precisely:5 deceptive:1 revealed:1 adjoint:1 system:47 relations:43 their:19 intermediate:1 zxx:2 adopts:1 reversed:2 exactly:6 reflecting:1 manipulation:1 branches:1 dynamical:1 richer:1 roberts:1 zx2:1 ber:1 providing:2 distinguished:1 ueno:1 symmetries:4 kitaev:1 need:17 constrained:3 clearly:4 viewed:2 mappings:4 studying:1 able:1 gravity:4 mechanism:1 instance:1 klasse:1 detector:1 techniques:1 mit:2 lectures:2 2mv0:1 who:1 eight:2 representation:6 class:5 32b:4 32a:4 stronger:1 χn:3 superscript:1 fact:39 gain:1 12a:4 12b:4 purely:3 miwa:8 subtracting:1 q2:3 based:3 jap:1 should:1 erentielles:4 hopf:3 achieve:1 ordre:4 means:5 ones:5 words:1 dpv:3 evolution:16 coalescence:1 differential:28 fixes:1 comprising:1 ascertain:1 cℓ:7 fixed:6 dpi:2 qn:3 requirement:2 constructing:1 exists:1 differs:1 bobenko:3 still:2 rims:1 tend:1 state:1 unravel:1 closed:13 invariant:3 boundary:6 vorlesungen:1 key:3 dependance:1 configuration:2 dorfman:1 limits:11 taking:11 equal:5 kagamiyama:1 qfn:4 2zn:2 otherwise:2 ck:8 relevant:7 cn:14 conclude:2 ordnung:2 cf:30 cz:1 respect:9 cw:1 addition:6 treat:1 define:3 determinant:1 arises:1 corresponding:12 sufficient:2 angles:1 bull:1 c0:1 present:11 novel:1 harder:1 value:21 will:53 monodromy:26 vi:3 refs:1 thus:34 site:1 vn:194 vp:24 vq:5 examined:1 vt:2 dual:7 vx:2 sits:1 higashi:1 35b:1 35a:1 cross:5 enumeration:1 highlighted:1 palaiseau:1 finite:4 φn:13 infinity:2 effect:1 v0:20 v1:1 v2:1 v3:1 infinite:25 nonetheless:1 well:38 thought:1 patterns:1 sets:1 arising:1 usual:2 26b:2 26a:2 increasingly:1 grammaticos:13 obtain:42 manifestation:1 underlying:3 adv:1 preprint:3 b278:1 lattice:139 add:3 combine:1 attractive:1 resolved:1 vα:22 vβ:11 know:3 resolves:1 press:8 nvn:1 insert:1 necessary:3 like:4 28a:2 alternatively:1 28c:1 28b:3 δn:2 δm:2 δk:1 δi:1 become:3 works:2 replacement:2 parity:1 because:4 classical:1 okamoto:2 choosing:1 proper:3 kdv:32 2qm:1 happens:1 est:3 lead:4 demonstrates:1 breakthroughs:1 manipulations:2 does:2 chains:1 11a:1 obey:2 11b:1 expansion:2 although:4 pv:14 p34:3 stage:1 gained:1 actual:1 freedom:1 dependence:16 compatible:10 a2:16 introduced:6 equally:2 own:6 previously:1 singul:1 eine:1 isospectral:1 van:1 additional:6 painleve:1 appl:4 naturally:4 function:12 eal:1 but:15 construction:5 hn:24 goals:1 count:1 made:2 mτn:2 evident:1 whether:3 lineare:1 below:3 convince:1 limit:16 demonstrate:2 problem:24 display:1 mechanics:1 pii:10 int:4 inv:1 linearity:1 denote:2 interchanged:3 relates:1 functions:20 compared:1 ingredients:2 other:14 details:5 itzykson:1 theor:1 zhou:1 shown:9 qτ:1 inspiration:2 coupling:1 u1:1 cpt:1 factors:2 understand:1 augmented:1 4b:4 4a:5
|
solv-int9812012.txt |@word limited:1 partial:1 consider:3 amplifier:1 results:1 perturbations:2 localized:11 inverse:2 deterministic:3 gbit:1 stable:6 very:1 geometrical:1 lyapunov:2 putting:1 fractal:5 hamiltonian:1 transmission:9 solution:18 large:1 small:1 hasegawa:2 zh:1 pulse:3 cosh:1 rate:6 estimated:1 linear:1 aim:1 nonlinear:11 appear:1 while:1 subspaces:1 3b:1 3a:1 hb1:1 method:5 satisfy:2 fiz:1 eksp:1 here:3 packing:1 separation:1 represented:1 consideration:2 equations:1 change:2 obtained:2 property:1 makes:1 useful:1 austria:1 total:2 use:1 discus:1 would:1 positive:1 therefore:1 until:1 diagrams:1 becomes:1 envelope:1 odinger:6 tested:1 carrying:1 known:2 must:1 science:1 equation:19 work:1 values:2 following:3 dec:1 example:1 figure:3 neglected:1 high:1 numbers:1 information:2 recursive:1 discussion:1 exceptional:2 adjacent:1 answer:1 may:1 faculty:1 effective:1 light:2 st:1 abdullaev:1 fan:1 operate:1 order:1 pulsed:1 choose:1 stability:6 pulses:3 y0:3 its:2 group:5 thank:1 ln:1 solving:1 lj:1 actually:2 forms:4 systems:1 τs:1 affected:1 greater:1 propose:1 fig:8 they:1 oxford:1 february:1 university:1 2y:1 wong:1 2a:1 2b:1 each:1 2j:3 mean:2 differential:1 series:2 energy:2 society:1 frequency:1 expect:2 sectional:1 our:2 special:1 space:3 rev:1 chaos:3 increase:3 contained:1 fiber:11 theory:1 interactions:1 completely:1 hc1:14 hence:1 teor:1 number:2 philadelphia:1 construct:2 q02:1 open:2 kodama:1 publication:1 service:1 system:3 least:1 1a:3 1b:1 too:1 statement:1 siam:1 calculations:1 tashkent:1 part:1 authors:1 coefficients:1 submitted:1 determined:1 amplitude:2 enables:2 symmetries:1 55µm:1 argument:1 unlikely:1 lim:3 able:1 take:2 analogy:1 finding:1 destroy:1 electric:1 counterbalance:1 phase:2 soliton:8 nonlinearity:1 considered:1 calculated:1 physica:1 optical:13 principle:1 velocity:1 physics:1 fact:1 text:2 supported:1 relation:5 solutions:14 d2:1 find:2 q0:3 q2:1 based:1 parameters:1 explain:1 outside:1 only:4 going:1 integrable:1 get:3 uncountable:3 vries:1 new:7 produced:1 shr:1 arxiv:1 yield:3 tappert:1 coefficient:2 close:1 exponent:2 speed:1 definite:1 enough:1 various:1 between:2 c2j:5 approach:1 available:2 shabat:1 solv:1 holds:1 both:1 many:2 according:1 propagation:1 experimental:2 ck:1 cj:2 cn:1 ca:1 applicability:1 destroyed:1 described:2 transformations:3 describes:2 asymptotics:1 pm:1 relations:4 corresponding:1 quantities:2 sufficient:1 subspace:3 fund:1 c3:1 c2:2 c1:25 c5:1 case:1 gnt:5 plain:1 originate:1 value:2 will:7 near:2 ultra:1 equal:1 different:4 recursion:1 make:1 cross:1 same:2 complex:1 finite:1 higher:1 effect:1 haus:1 infinite:1 robust:1 ablowitz:1 schr:5 well:1 analysis:1 without:2 coeficients:1 proposed:2 shape:1 world:1 alternative:1 scattering:2 yet:1 zakharov:1 absorption:1 photons:1 improvement:1 source:1 attractive:1 input:2 transformation:1 momentum:1 real:3 usable:1 possible:2 press:1 using:3 mod:1 loss:1 like:1 specific:1 communications:8 yields:2 arbitrary:1 multiplicative:2 ha1:2 stationary:6 classical:1 phenomena:1 b1:1 kdv:1 dc1:1 does:2 unstable:1 core:1 noise:2 power:3 equivalent:1 clarendon:1 although:1 properties:2 about:1 carrier:1 significant:2 incoherence:1 into:1 h1:4 numerically:1 sol:1 pair:1 references:1 operator:1 theoretically:1 area:1 there:2 question:1 transform:1 dispersion:2 width:2 appl:1 was:1 function:2 complete:1 form:4 energies:1 convergence:1 hc:2 segur:1 whether:1 us:2 verification:1 problem:1 define:1 int:1 certain:1 abstract:1 covers:1 general:1 conserved:2 enable:1 exist:1 wavelength:1 when:1 field:1 republic:2 solitons:5 department:1 conclusion:1 superposition:1 important:1 peak:1 starting:1 dτ:2 resolution:1 lett:1
|
solv-int9812013.txt |@word since:4 partial:2 consider:2 similarity:1 global:1 trigonometric:1 four:6 montr:3 3a0:1 2r2:1 localized:2 inverse:2 const:1 byrd:1 supported:1 finally:2 those:3 elliptic:12 stable:3 tg:1 maryland:2 include:1 worth:1 kπ:2 r12:13 provides:3 translations:2 wave:13 putting:3 scholarship:1 exact:1 condition:6 groups:3 leads:3 δt:1 presented:2 solution:22 cascading:10 occurs:1 large:1 shows:1 optics:1 ville:1 specially:1 sin2:1 pulse:1 sign:2 painlev:7 traveling:1 equal:1 further:2 theory:1 what:1 nonlinear:3 rate:1 dr1:1 section:9 expressed:2 poles:2 2r1:1 scientists:1 new:2 consisting:2 satisfy:4 degree:1 respectively:2 sinh:3 along:1 quite:1 equations:35 obtained:9 involved:3 study:2 studied:2 3f:1 periodic:11 characterizing:2 decouple:2 studies:1 departement:1 vp1:1 family:3 h3c:1 requiring:1 replace:1 eiφk:1 apply:1 rω:9 use:2 would:1 commun:2 distinct:2 positive:2 negative:1 periodically:1 going:1 call:1 m2:5 survive:1 type:3 theoretical:1 more:1 excluded:1 eiφ1:2 operators:1 under:4 odinger:2 derivation:1 normalized:3 particular:2 known:3 cases:9 friedmann:1 iii:1 must:5 ramani:1 springer:2 valued:1 locked:6 science:1 equation:15 ferro:1 values:10 publications:1 following:4 dec:1 root:4 buryak:4 f1:36 f2:27 f3:29 wang:1 give:1 share:1 kivshar:5 indicates:1 sn2:2 council:1 allowed:1 r24:1 r23:2 r22:4 r21:1 needs:2 rather:2 six:1 berlin:1 occur:2 write:1 fourth:1 opt:7 ordinary:7 parameter:4 e2i:1 singular:11 may:4 earlier:1 singularities:4 movable:3 fa:5 succ:1 produce:1 waves:12 fi:5 compatibility:1 constants:15 times:1 imply:1 explicit:6 element:1 cannot:1 so:3 allow:2 acknowledges:1 order:5 restriction:2 indeed:1 assanto:1 mainly:1 stability:1 course:1 paper:1 through:2 signs:1 differs:1 existence:2 satisfies:1 its:2 roots:12 solitary:16 group:7 thank:1 chosen:2 6c0:1 absence:1 systems:3 substituing:1 olver:1 travelling:1 defining:1 them:4 good:1 return:1 entire:1 obtaining:1 material:1 introduce:1 mention:2 effects:2 they:6 now:2 yu:5 discuss:2 possess:2 2t:1 ebec:1 term:1 several:1 2p:1 2r:4 fully:2 university:1 establishing:1 possibilities:1 2a:2 each:1 found:1 universit:1 higher:2 side:1 constraints:2 differential:9 ei:2 directly:1 journ:3 reduce:4 quantum:2 2b0:17 eq:46 special:6 out:2 canada:3 shown:2 rr:1 space:1 algebra:3 rev:5 investigate:1 research:3 similarly:3 investigation:1 get:1 integrated:1 math:2 rk:2 sinh2:1 fiber:1 linear:1 dilatations:1 free:2 standard:1 completely:1 proportionality:1 york:1 put:2 finite:6 r1:51 r2:69 r3:1 impose:3 fb:4 nonnegative:1 turn:2 hence:1 βi:1 first:4 rand:1 features:1 symmetry:9 variables:1 reaches:1 philadelphia:1 simplified:1 2a3:1 2a0:12 given:2 rewritten:1 needed:1 introduction:2 leading:1 system:10 relations:3 sech2:1 their:9 smoothen:1 siam:1 behaved:2 final:1 recovered:1 exploring:1 a30:1 4b0:1 rejected:1 transverse:1 optical:2 manifestation:1 cosh:1 representing:2 than:4 coefficients:4 distance:1 double:2 require:4 second:7 limiting:4 winternitz:7 determined:3 amplitude:2 were:1 exhibit:1 raman:1 symmetries:2 san:1 rewrite:1 editors:1 need:1 any:1 viewed:1 lie:6 zero:2 depending:3 partly:1 self:3 note:1 instance:2 reals:1 trillo:1 unless:1 fundamental:6 shall:3 simplify:1 propagate:1 drummond:2 significant:1 phase:8 analytically:1 chap:1 soliton:2 kf:1 nonlinearity:1 considered:1 sf:1 segur:2 exp:1 overdetermined:2 oscillates:2 2m1:1 particularly:1 show:2 authors:1 notations:1 relation:2 solutions:61 substituting:1 careful:1 find:5 d0:25 cr2:1 parameters:3 should:3 only:6 explicitly:2 factor:1 integrable:8 ematiques:1 do:7 his:1 iωt:1 torner:3 de:2 beam:1 ones:4 invariant:4 du:1 qu:1 arxiv:1 2b3:2 applications:1 method:1 imposed:1 qc:1 analytical:2 including:1 fixed:1 crm:1 ignored:1 requirement:1 set:1 hagan:1 exists:2 achieved:1 national:1 summed:1 maximum:1 namely:10 βa2:1 eliminating:1 discussions:1 techniques:1 phases:4 satisfying:2 definite:3 tend:2 envelopes:1 between:3 drawn:1 champagne:1 conditions:5 2αv:2 notice:1 terms:9 hereman:1 however:2 vanishing:1 solv:1 article:2 both:3 cos:5 2n:1 limits:2 many:2 3j7:1 nserc:2 propagation:1 expression:1 baltimore:1 otherwise:1 arbitrarily:1 fcar:1 16n:1 relevant:1 cn:2 point:4 asymptotically:1 harmonic:7 dimensional:2 r44:1 pole:1 grants:1 simply:2 polynomial:2 moreover:4 basis:1 three:8 been:2 defined:2 reduction:4 ph:1 harmonics:1 families:5 restrictions:1 jacobi:1 agrawal:1 2n2:1 2n1:1 c0:49 present:1 case:25 p0:1 p1:1 look:1 comput:2 single:1 value:1 will:5 b02:2 shift:2 situation:1 property:6 guide:1 procedure:2 engineers:1 a20:2 a21:1 larger:1 coupled:2 vi:1 thus:6 iv:1 ii:1 vt:1 triple:3 ib:2 containing:1 generic:3 recursion:2 belong:1 locking:2 same:2 shifts:1 stimulated:1 complex:5 φk:1 difficult:1 used:2 see:5 cubic:1 hand:2 resonance:3 ablowitz:2 schr:2 reobtain:1 modeled:1 well:2 analysis:5 levi:4 academic:1 materials:3 solve:3 coordinate:1 position:1 arising:1 subgroup:2 cosh2:2 just:3 being:2 obtain:14 using:1 4a0:2 alternative:1 scattering:3 kluwer:1 conclusions:1 had:1 signals:1 interested:1 conjugated:1 lett:7 guarantees:1 real:12 possible:1 corresponds:1 possibly:1 know:2 background:1 integer:2 variants:1 meaning:1 necessary:1 helpful:1 reduces:5 menyuk:7 separately:1 imposes:3 yields:2 either:2 2a2:1 arbitrary:12 r41:1 conclusion:2 essential:1 because:1 methods:1 phenomena:2 supplementary:2 b0:33 b2:1 specified:1 multiple:3 specific:1 describing:3 centre:2 integration:5 comments:1 sr2:1 does:2 expressing:1 indication:1 6a0:2 3b0:1 algorithmic:1 integrals:1 analysed:1 expansion:2 properties:3 tanh2:1 diego:1 constraint:2 coexist:1 discriminant:1 discussed:1 chance:1 reduced:2 compatible:1 mutually:1 range:1 important:2 greatly:1 introduced:1 soc:2 own:1 previously:2 into:3 numerically:1 right:2 raises:1 elementary:5 proportional:1 acknowledgements:1 van:2 initial:2 transform:1 ωp0:1 handbook:1 m1:5 was:2 function:10 eal:3 form:4 some:4 memory:1 but:2 construction:1 dissipative:1 ωx:1 wish:1 up:1 us:8 different:1 dordrecht:1 below:3 limit:1 similar:2 called:1 interval:1 constant:11 ωxx:1 ln:2 int:1 certain:2 ak:4 am:2 general:6 globally:2 engineering:2 exist:3 corresponding:1 physical:1 again:3 functions:7 integrability:1 no:3 werner:2 when:2 field:1 other:7 electrical:1 neighbourhood:2 solitons:2 test:1 eiφ2:2 nice:1 separate:2 rv:1 a1:9 a0:65 generated:2 a2:11 a5:1 a7:1 a6:2 algebraic:2 implies:4 faster:1 algorithm:1 assume:1 required:1 stegeman:3 together:1 4m:1 time:1 recherches:1 sin:9 4b:1 original:2
|
solv-int9812014.txt |@word scl:7 partial:1 consider:4 remarkably:1 inverse:2 hump:2 lillo:2 tn:5 under:2 tf:7 hibbs:1 straightforward:3 choice:1 exact:4 condition:6 presented:2 ref:1 notes:1 shock:2 solution:34 t0:1 solved:1 small:1 linearizing:1 zn:10 eωt:1 dealing:2 cosh:1 burger:1 integrability:1 equation1:1 theory:1 bdg:1 nonlinear:5 section:3 celebrated:2 henceforth:1 above:1 3b:3 3a:1 method:5 supporting:1 discontinuity:1 respectively:2 illustration:3 sinh:24 path:11 sine:1 equations:7 institute:1 drs:1 krohn:1 action:14 jalan:1 via:2 9a:1 9c:1 9b:2 apply:2 derivatives:1 use:1 eω:1 would:2 type:5 theoretical:1 separated:1 ti:7 odinger:1 berlin:1 appendix:5 basically:1 known:5 iii:4 rδ:1 springer:1 rη:1 dodd:1 equation:28 erf:3 values:2 following:5 ivp:7 dec:1 compare:1 give:1 calculation:1 expanding:1 xcl:4 dxn:1 νa:2 sense:1 verlag:1 motion:1 discussion:1 pure:2 instead:3 profile:2 simplicity:1 may:2 after:1 dx2:1 dx1:1 waves:1 summarize:1 wave:1 constants:2 natural:1 outline:1 explicit:2 secs:2 so:1 pleasure:1 prefactor:1 zen:2 paper:3 through:2 mentioned:1 satisfies:2 cole:8 its:2 thank:1 acknowledge:1 chosen:2 solving:2 coordinates:1 lect:1 choose:4 non:1 motivated:1 obtaining:1 dxδ:1 2t:1 2u:1 term:10 2s:2 sobczyk:5 2f:1 2a:3 found:1 2k:1 homogeneous:6 differential:2 formulate:2 related:2 inhomogeneous:17 static:2 expect:1 quantum:1 our:1 eq:7 special:1 er:1 space:1 rep:1 since:2 rev:1 research:1 transforming:1 hill:1 formula:1 evaluation:1 math:5 wiley:1 linear:13 8b:1 abramowitz:1 8a:1 quart:1 york:4 derivation:2 kivshar:1 keep:1 counterpart:2 gordon:1 first:2 there:1 xn:7 xf:3 directly:2 illustrate:1 given:8 their:1 introduction:1 1a:1 obtainable:1 1b:2 πt:1 zϕ:1 gives:3 tfi:2 exactly:3 whitham:1 airy:2 x2:2 x0:1 x1:1 2ax:2 kind:1 unfortunately:1 aai:2 see:1 limiting:1 project:1 were:1 enables:2 7b:2 7a:2 rewrite:1 linearizable:1 academic:1 lim:2 take:1 xi:3 green:2 coincide:1 kac:7 what:1 simplify:1 pair:1 acknowledgements:1 considered:2 adopt:1 steady:3 feynman:9 exp:8 physics:2 fact:2 dover:1 directorate:1 show:1 attempts:1 solutions:5 12v:1 substituting:7 d2:5 find:1 enough:1 should:1 integrable:1 hopf:8 continuity:1 dependent:1 itb:2 de:2 dx:8 dy:3 applying:5 dt:2 net:1 coth:1 evolution:2 qt:2 qx:1 arxiv:1 mapped:1 fixed:1 nε:1 kernel:7 namely:2 sec:3 result:2 terms:2 still:1 state:5 simplest:1 boundary:4 conditions:4 email:2 qt2:2 extend:1 complementary:1 ωn:1 however:1 comm:1 solv:1 taking:1 according:4 separation:1 taylor:1 simply:1 lagrange:1 respect:1 throughout:1 second:1 considering:2 pp:3 proceeded:1 transformations:1 bbi:2 been:1 ai:5 much:1 sachdev:1 define:1 generating:1 arises:1 corresponding:23 new:4 6x:1 albeverio:1 present:4 case:4 look:1 tanh:2 5a:1 value:12 choices:1 will:5 while:2 5c:1 error:1 va:1 formulation:1 thus:3 encouragement:1 iv:3 ii:3 vt:1 conf:1 technology:1 id:2 education:1 verified:1 descent:1 beside:1 several:1 higher:1 independent:1 used:1 trivially:1 purpose:1 hans:1 ablowitz:2 prescribed:1 lower:1 mech:1 schr:1 indonesia:2 well:3 obviously:2 burgers:14 solve:5 being:1 stegun:1 obtain:6 scattering:2 λn:2 adv:1 had:1 international:1 source:4 lett:1 solvable:1 transformation:12 euler:1 5b:1 around:1 2v:17 press:1 using:5 mod:1 bobby:1 follows:2 reduces:2 integrals:2 arbitrary:2 mcgraw:1 reduced:1 mathematical:2 classical:7 kdv:1 manipulations:2 2xy:1 prof:1 method1:1 bn:3 bi:5 expansion:1 although:1 properties:1 simpler:1 obeys:1 shared:1 into:7 integral:10 references:1 initial:18 question:1 transform:1 quadratic:3 handbook:1 malomed:1 was:3 function:6 form:4 but:2 dξe:1 heat:11 delta:1 made:1 compute:1 whether:1 ωt:11 us:6 freddy:1 limit:4 steepest:1 va2:1 problem:11 mechanics:1 ac:1 ab:2 constant:8 int:1 abstract:1 general:3 single:4 laboratory:1 ax:2 formalism:2 proceeds:1 functions:3 rederive:1 no:1 republic:1 department:1 forcing:5 nice:1 superposition:1 4v:1 4b:1 dτ:34 required:1 time:3 appl:4 4d:1 starting:1 4c:1 4a:1
|
solv-int9812015.txt |@word miwa:5 concept:1 consider:3 desirable:1 results:2 commute:1 research:1 row:1 particles:5 preserves:1 sogo:1 calculate:1 tn:5 charge:1 manifolds:1 th:1 under:2 presentation:1 fay:2 string:25 differently:1 geometrical:2 every:2 difference:2 matrices:2 deformations:1 condition:1 dim:2 annihilated:1 riemann:1 solves:1 presented:1 did:1 turns:1 notes:1 t2:7 solution:1 t0:5 t1:9 discrete:18 vector:7 science:1 manifestly:1 relation:1 enjoy:1 zn:3 unexpected:1 oscillation:1 za:3 zb:3 zc:3 sergeev:1 integrability:1 linear:1 bilinear:3 established:1 what:1 appear:1 section:2 brief:1 version:1 net:13 congruences:1 nakamura:1 satisfy:1 simultaneously:1 qµν:6 tangent:6 xν:1 directions:1 ratio:1 along:3 sine:1 equations:7 z1:3 z2:4 z3:2 metro:1 shift:4 study:1 studied:2 prior:1 therein:1 rdn:2 f0:8 pinkall:1 santini:4 sgn:1 total:2 unit:1 takes:1 would:1 prove:1 covariant:5 positive:1 negative:1 sports:1 therefore:3 type:1 theoretical:1 more:1 brings:1 operators:1 curvature:1 eν:4 bogdanov:1 projective:1 must:1 springer:1 quantized:1 tokyo:2 recall:1 equation:13 work:1 reviews:1 values:2 rewritten:1 following:4 dec:1 example:1 beautiful:1 korepanov:1 share:1 saito:3 verlag:1 lame:1 darboux:3 verify:1 discussion:1 acts:2 write:1 iso:1 map:4 levy:1 after:1 fg:8 date:2 summarize:1 revealed:1 realized:2 natural:4 dynamical:1 grant:1 lines:3 parameterized:1 so:2 fundamental:2 correlation:8 wiegmann:2 interpretation:4 hierarchy:7 developed:1 satisfied:3 interpreted:5 paper:1 including:1 statistical:1 japan:2 satisfies:3 nets:5 its:3 before:1 thank:2 ln:1 coordinates:2 forms:1 parts:1 systems:4 mail:1 main:1 might:1 deformation:2 correspondence:3 introduce:1 invitation:1 they:3 eµ:15 rotation:5 now:1 several:1 characterizes:1 university:1 backgrounds:1 found:1 extentions:1 characterized:2 constraints:1 differential:3 directly:1 related:1 t3:7 elementary:1 toda:1 changed:1 quantum:1 our:1 operation:2 out:3 shown:4 jimbo:2 matrix:6 space:11 since:1 rev:1 denotes:1 rd:1 geom:1 rm:2 correct:1 math:3 common:1 theory:11 associate:1 νth:1 quite:3 publication:1 zjn:1 interaction:1 language:1 ministry:1 geometry:7 turn:1 lµ:3 place:1 gordon:1 assumed:1 hence:2 first:1 zl:2 variables:7 general:1 another:2 given:9 zj:3 similarly:2 introduction:1 system:1 relations:1 their:5 identity:1 kµ:2 realization:7 satoru:1 relationship:1 alonso:1 continuous:1 part:2 somewhat:1 translation:1 was:6 imply:1 torus:1 amplitude:1 enables:1 kashiwara:1 argument:2 curves:1 say:1 conjugate:21 need:1 any:1 tρ:1 depending:1 describe:1 convenient:1 bµν:2 k3:3 k2:12 k1:12 subjects:3 generalized:1 surfaces:1 exactly:1 opposite:1 algebraic:1 propagate:1 nothing:2 kc:7 kb:7 ka:7 tν:4 observation:2 kk:2 kj:6 calculated:1 kn:12 kl:2 points:2 ohta:1 exp:5 physics:6 fact:2 show:3 nρ:2 supported:1 multicomponent:1 wµ:4 spaces:1 gauge:5 solutions:1 analogue:1 find:1 ground:1 q1:1 q2:1 based:2 jap:1 only:1 explicitly:1 integrable:5 do:2 his:1 means:4 report:1 lattices:3 zabrodin:2 dr:1 gen:1 becomes:1 continuum:1 fields:1 arxiv:1 qd:1 analytical:1 through:2 implication:1 view:1 coefficient:2 set:1 exists:1 hν:7 culture:1 see:2 recently:1 bobenko:1 subject:1 uν:2 qµ:2 interacting:1 review:1 lµν:1 state:3 various:2 between:2 theta:1 notice:1 terms:4 manas:2 component:1 jp:1 however:1 comm:1 key:1 solv:6 configuration:1 uρ:1 limits:1 many:1 according:3 laplace:4 etc:1 hρ:4 expression:1 among:2 point:1 quadrilateral:7 dimensional:5 moreover:1 throughout:1 kp:12 lect:1 described:1 second:1 addition:1 three:1 been:6 defined:2 workshop:1 combined:1 define:3 direction:2 arises:1 corresponding:1 understand:1 external:5 denote:2 present:1 qνµ:1 tetrahedron:2 will:4 while:1 suppose:1 aid:1 property:1 planar:1 tµ:9 metropolitan:1 jpn:5 thus:1 surface:2 itself:5 owes:1 compactified:1 different:4 combining:1 make:1 belong:3 same:2 shifts:1 complex:1 physical:2 higher:3 independent:1 grassmann:1 hand:3 moment:1 purpose:1 focal:3 recent:1 center:2 acknowledgement:1 well:1 tsujimoto:1 consistency:1 coordinate:1 model:5 left:1 proposed:1 profs:1 obtain:1 rest:1 bµ:2 correspondences:1 integer:1 momenta:6 previous:1 infinitely:1 interprete:2 had:1 coplanar:1 lattice:22 setting:1 lett:3 easy:1 theorem:2 rectilinear:2 solvable:2 transformation:7 momentum:5 take:2 rules:1 fusion:1 know:1 background:3 vacuum:2 using:1 intersection:1 necessary:1 like:4 particle:5 follows:1 yields:1 invariants:1 translated:1 mathematical:2 because:1 often:1 classical:2 kashaev:1 some:5 draw:1 acad:1 diff:1 proper:1 happens:1 does:1 proc:1 scientific:1 shifting:1 proceed:1 comparison:1 extension:3 discussed:3 o:2 extensions:2 konopelchenko:1 organizers:1 jν:1 soc:5 doliwa:8 into:6 functional:1 right:1 references:2 operator:12 proportional:1 transfer:2 there:2 transform:1 way:1 sections:1 naturally:1 function:8 form:2 soliton:7 but:5 change:2 wρ:1 us:5 krichever:1 embedded:1 problem:2 called:4 ac:1 associated:1 int:6 certain:1 abstract:1 congruence:3 hµ:7 single:2 imai:1 education:1 identities:1 constructed:1 again:1 functions:7 no:2 uµ:1 whereas:1 when:2 other:5 solitons:1 department:1 conclusion:1 picture:1 briefly:2 elements:2 models:4 hirota:5 vertex:4 medina:1 includes:1 meaning:1 vectors:1 variable:1 together:1 neighbouring:1 mass:2 time:1 strings:3 once:1
|
solv-int9812016.txt |@word consider:3 chain:1 similarity:1 alg:1 results:2 generalize:1 go:1 expressions:1 whose:2 certainly:1 depend:1 calculate:1 fellowship:1 tu:1 finally:3 contours:1 under:1 te:3 amplitudes:7 string:14 orthogonal:1 very:3 geometrical:3 witten:1 difference:1 condition:3 riemann:1 solves:1 tokyo:3 solution:2 deals:1 involution:1 manifestly:1 deleting:1 ten:1 dealing:1 eλs:5 sign:2 sergeev:2 integrability:3 sbcd:2 pass:1 remarkably:1 scientific:1 bilinear:1 will:5 what:2 abc:2 abd:2 minami:1 section:6 axes:1 expressed:1 version:2 new:2 satisfy:2 degree:3 respectively:1 κa:1 here:7 following:2 l22:1 κx:1 groups:7 address:3 represented:2 path:2 along:1 strong:1 equations:4 interpret:1 obtained:2 metro:1 shift:1 suggests:3 published:1 opinion:1 changes:1 uniquely:2 namely:2 explained:1 univ:1 linearly:1 readily:1 additive:1 chelyabinsk:2 commun:2 nucl:1 relativistic:1 taken:1 themselves:1 type:3 theoretical:1 diagrams:2 more:5 duality:16 becomes:1 clue:1 fixed:5 rigid:1 particular:2 known:7 ural:1 hold:1 glad:1 must:2 account:1 coefficient:1 integrating:1 equation:18 acd:2 theories:3 remain:1 obvious:2 believed:1 sabc:2 dec:1 example:2 abcd:2 compare:1 korepanov:2 figure:27 december:1 choice:2 saito:6 professor:1 numbers:11 want:1 enslapp:1 yang:3 fpe:9 rather:1 verify:1 discussion:1 means:1 feature:1 write:2 how:1 axis:1 sin:4 product:1 mat:2 replacing:1 max:2 after:1 diagram:7 modest:1 plane:5 law:1 2l1:1 compatibility:2 natural:2 grant:1 lines:3 yielding:2 element:1 hachioji:1 so:7 fundamental:1 koba:1 vary:1 course:1 paper:2 including:1 looks:2 y1:2 japan:2 y2:2 its:10 ohsawa:1 derive:1 outer:1 acknowledge:1 fiz:2 forms:1 permanent:1 choose:2 mail:2 correspondence:2 them:1 greater:1 pentagons:1 finitedimensional:1 mention:1 they:1 rotation:1 now:1 resonance:2 equality:2 university:3 obius:1 possibilities:1 l4:8 l5:8 l2:19 l3:24 l1:18 crossing:2 rising:1 mean:1 baxter:3 ed:1 hard:2 idea:1 related:2 measure:2 quantum:15 our:5 regge:1 special:1 out:1 ru:1 shown:1 matrix:2 discrete:1 nuovo:1 rev:3 research:2 transforming:1 acting:1 rational:1 reader:1 formula:7 issue:1 math:3 foundation:1 theory:6 diagonal:2 possibility:1 put:2 pairs:1 interaction:1 agree:1 teor:2 generalizations:2 south:1 researcher:1 variables:4 number:3 l32:1 another:2 angular:5 given:8 necessarily:1 sheet:1 reference:1 similarly:1 introduction:2 relations:9 assumption:1 satoru:1 structures:1 final:1 mostly:1 explanation:2 exactly:1 rejected:1 authors:1 x2:2 tacitly:1 believe:3 than:1 coefficients:4 wide:2 determines:1 behaved:1 require:1 see:6 determined:4 amplitude:11 providing:1 russia:1 projections:1 igor:2 zamolodchikov:1 argument:1 generalization:2 correspond:1 any:4 lie:4 generalizes:1 constructions:5 angle:2 min:2 studying:1 responsible:2 mechanism:3 note:3 k2:21 k1:14 internal:2 take:3 k5:21 k4:14 schematically:1 green:1 analogs:1 heisenberg:2 algebraic:5 nonlinear:1 connected:2 formulae:2 nothing:3 analytically:1 why:2 soliton:2 kj:1 clear:3 coincides:1 vertices:1 ckj:1 feynman:1 proceedings:1 points:3 diagonals:4 physics:3 fact:7 joining:1 saying:1 phenomenon:1 show:1 random:1 notations:1 relation:7 solutions:4 carefully:1 substituting:1 find:1 x1:2 based:1 explain:2 written:2 topological:1 values:1 only:1 integrable:2 local:1 do:1 dl:1 his:1 triangle:3 get:1 between:1 overall:1 ones:1 invariant:1 gen:1 processes:1 prima:1 fields:2 arxiv:1 through:2 cycles:2 valid:1 view:2 body:1 multiplying:1 constructing:2 exists:1 frame:1 differentials:1 connections:1 depends:1 geometrically:1 result:1 existence:2 close:1 dµ:6 analog:1 acquires:1 satisfying:2 dk3:3 ways:2 pictures:1 away:1 symmetric:2 state:1 hopefully:1 probably:1 geometric:4 ends:1 terms:5 jp:1 however:2 multiplier:1 solv:3 group:7 both:5 cos:4 reverse:1 many:1 taking:1 minus:2 dl3:3 argue:1 expression:2 comment:1 ci:1 relevant:1 point:11 simple:4 corresponds:4 quadrilateral:3 dimensional:6 superstring:1 sequences:1 associated:1 kp:1 conference:1 described:3 transformations:5 basis:1 three:2 been:1 reduction:1 production:1 change:2 interest:1 basic:1 reggeized:1 sogo:1 direction:1 arises:1 corresponding:4 sufficient:1 dramatic:1 external:3 angles:2 57a:1 present:2 case:1 straight:1 tetrahedron:5 value:4 aim:1 euclidean:6 while:1 suppose:3 irrespective:1 maximal:2 metropolitan:2 vol:1 surface:2 dual:3 ave:1 movements:2 different:2 akj:1 lengths:7 belong:1 same:6 poincar:2 complex:1 quadrilaterals:1 arguments:1 finite:2 used:1 singapore:1 trajectories:1 edges:3 hospitality:1 infinite:2 nevertheless:1 disappears:1 ıvely:1 well:5 edge:4 english:1 coordinate:2 model:2 parametric:2 usual:2 ruegg:1 just:2 generally:1 obtain:2 world:2 scattering:2 k3:21 preprint:1 seems:1 parametrization:1 other:2 garbaczewski:1 b12:1 solvable:1 transformation:5 k6:21 real:1 nielsen:1 big:1 term:1 finding:1 five:2 goebel:1 press:1 using:3 sakita:1 semiclassical:1 like:4 particle:3 follows:2 28b:1 yields:1 schwarz:1 arbitrary:1 multiplicative:2 mathematical:3 lenin:1 classical:3 kashaev:4 plausible:1 some:14 algebraically:1 examples:2 choosing:1 convex:1 l6:15 tmu:1 integration:4 l12:1 does:1 virasoro:1 minimal:2 obey:1 intimate:1 equivalent:1 host:1 shifting:1 although:1 properties:1 central:1 extension:1 most:3 freedom:1 dependence:1 compatible:1 dilogarithm:1 range:1 obeys:2 soc:1 cambridge:1 into:3 within:1 functional:6 references:1 pentagon:14 acknowledgements:1 area:1 assumed:1 support:1 there:5 transform:2 start:1 way:3 forward:1 sections:1 naturally:1 function:5 form:5 regard:1 but:3 construction:1 russian:1 line:1 raising:1 evident:1 versions:1 characteristic:1 attached:2 up:3 us:8 bcd:2 below:2 those:1 demonstrate:2 similar:3 called:1 distance:2 strongly:1 ac:2 constant:2 int:3 abstract:2 general:2 exist:5 triangles:4 dα:1 cim:1 no:1 na:1 when:2 interested:2 role:1 papers:1 department:1 mathematics:1 picture:1 draw:2 kinds:1 provided:1 models:5 hirota:1 generated:2 important:2 sides:11 structure:3 dimensions:1 assume:2 veneziano:8 curve:1 together:2 having:1 implied:1 time:1 far:1 strings:3 once:1
|
solv-int9812017.txt |@word consider:8 rev:1 results:5 gd:12 computation:2 edu:2 follow:2 equivalences:1 whose:2 depend:1 superspace:1 tw:2 show:4 reductions:2 finally:2 δhk:8 present:1 th:1 ti:1 analogous:1 case:4 string:3 straightforward:1 far:1 focus:1 difference:1 manin:5 presented:2 turns:2 dig:1 t1:1 science:1 brunelli:1 diu:1 superalgebras:4 originally:1 akns:1 compensated:1 consistent:2 direct:2 literature:2 sign:3 past:1 second:31 further:1 nemeschansky:1 odd:8 panda:1 canonical:2 residue:1 what:1 brackets:21 giving:1 section:3 xφ:1 expressed:2 ˆb:1 version:1 above:4 ˆi:1 method:2 coefficient:5 respectively:4 realizations:2 modify:1 here:2 reported:1 identifications:1 supermultiplets:1 address:2 concluding:2 quite:2 equations:15 z2:1 obtained:8 remark:1 antisymmetric:3 kanno:3 study:2 resulting:2 poisson:28 chang:2 suitable:1 makes:1 relation:2 equivalence:4 2φd:2 virasoro:2 use:2 would:2 prove:1 2u:3 contains:1 1x:2 next:2 few:2 nucl:1 call:1 therefore:5 type:3 ψd:2 more:2 yes:1 becomes:4 operators:17 under:2 v0x:2 4ad:1 appendix:2 particular:3 known:6 cases:2 iii:2 springer:1 v1x:2 recall:1 equation:6 work:5 modified:4 theories:4 reviews:1 remain:1 infinitesimal:1 dxdθ:1 mr:19 following:9 modifies:1 dec:1 example:2 proof:2 compare:5 gallot:2 give:2 calculation:1 share:1 explorations:1 δv2:2 council:1 sense:1 ϕx:5 goal:2 provide:3 verify:1 means:1 write:3 superstrings:1 answer:1 instead:2 verlag:1 parameter:1 map:10 mas:1 express:1 description:1 v02:1 φ2k:2 derived:1 φ2n:4 lax:44 popowicz:1 representations:3 choice:1 parallel:1 transposed:1 natural:1 dynamical:1 third:3 φx:2 so:2 fundamental:2 correlation:1 definitions:1 order:9 hierarchy:44 inami:3 spectral:1 satisfied:1 gauged:1 paper:3 through:2 2v:2 signs:1 satisfies:3 still:2 its:7 before:1 ld:1 lb:3 thank:1 maps:9 lm:6 boson:2 li:3 forms:2 lt:5 systems:13 lp:2 jacobi:6 derivative:3 main:1 h0:1 lx:1 them:5 nsc:2 motivated:1 introduce:2 primary:1 yields:1 they:2 u2n:8 now:2 φj:3 possess:1 dj1:1 easily:3 february:1 φk:1 university:2 hamiltonian:65 identified:1 2d:4 theory:1 2b:1 each:2 2n:16 referred:2 homogeneous:3 differential:7 chung:1 series:1 related:4 extended:1 quantum:1 our:6 eq:9 brings:1 out:7 shown:9 ψxx:1 rq:1 space:1 gradient:1 res:7 furthermore:2 since:6 crucial:1 u2k:1 replacing:1 denoted:2 induced:2 math:11 qd:2 belief:1 contain:1 free:2 standard:1 ramos:4 besides:1 ask:1 omit:1 linearized:1 δij:2 chiao:1 hence:6 first:16 xk:1 formulas:1 organize:1 features:1 xl:1 miura:11 variables:2 number:2 clear:1 aratyn:3 another:1 precisely:1 between:5 illustrate:1 given:23 1v:1 introduction:1 leading:1 adjoint:3 construct:3 1a:1 their:4 dt2:2 dt1:4 variational:1 structures:26 δjk:1 supermanifolds:1 gives:2 relationship:1 serve:1 kupershmidt:2 part:2 dˆi:2 than:1 coefficients:2 dˆb:2 dtk:9 dt0:2 skdv:30 effective:1 stb:7 namely:1 preparation:1 str:8 enables:2 minus:1 perturbative:1 motivation:1 symmetries:1 rewrite:2 generalization:3 ming:1 manuscript:1 constrained:8 hsien:1 any:1 viewed:1 wilson:1 triggered:1 zero:1 convenient:1 latter:1 note:1 liu:2 generalized:12 pφφ:2 even:6 begin:1 shall:3 most:2 remarks:3 nctu:1 class:2 kb:25 ka:42 constructed:5 especially:1 dordrecht:1 ki:22 flow:1 typeset:1 bracket:11 exp:3 vries:1 sum:1 fact:6 3v1:3 oevel:3 dickey:2 leibniz:1 supported:1 ending:1 gauge:26 solutions:1 decompositions:1 substituting:5 find:3 decade:1 figueroa:4 based:1 knowledge:2 should:2 only:2 explicitly:1 aϕ:1 2ax:3 indeed:2 integrable:9 hamiltonians:1 achieve:2 dl:15 cheng:1 viewpoint:1 di:5 df:5 dg:1 de:1 db:12 da:12 ones:4 φxx:1 new:1 dv:3 ϕd:6 dt:3 du:3 represented:1 qp:1 evolution:1 δφi:2 qt:1 explore:1 fields:5 arxiv:1 factorization:1 summary:1 investigate:1 common:2 mapped:2 including:1 view:3 requirement:1 tu1:1 national:3 j1:5 morosi:1 relative:2 see:4 sec:6 result:4 discussions:1 nonstandard:8 satisfying:1 dlg:1 away:1 functionals:7 written:1 hsinchu:1 identification:1 simplest:4 progress:1 reading:1 approach:4 farrill:4 notice:2 terms:1 attention:1 2ux:1 however:2 key:1 solv:2 jc:9 received:1 kluwer:1 desired:1 many:2 according:1 ϕxx:1 etc:1 admit:1 superdifferential:3 mean:1 comes:1 otherwise:1 comment:1 huang:2 point:1 v2x:4 superfield:1 factorize:1 superstring:1 stanciu:1 governed:1 polynomial:1 proved:2 v2n:4 kp:7 mathieu:3 described:2 transformations:3 delduc:2 due:2 been:5 int:4 reduction:5 much:1 change:1 basic:1 pi:3 define:4 v23:1 v22:4 direction:1 describe:1 supersymmetric:28 both:2 θb:1 quantities:1 concerning:1 mail:2 berezin:1 worked:1 denote:2 former:1 those:2 applied:1 will:6 replaced:1 supersymmetry:1 situation:1 conformal:1 vi:3 thus:3 non:1 iv:3 ii:2 tu:3 ik:4 ax:1 ready:1 superconformal:2 different:2 shaw:4 grant:1 perform:5 acknowledgments:1 make:1 formulations:2 connection:1 same:3 paa:2 antisymmetry:1 φd:15 φi:6 hierarchies:25 several:3 subalgebra:1 φn:2 difficult:1 investigated:1 imply:2 flows:5 hand:6 v0:18 v1:18 v2:15 purpose:2 infinite:2 sres:25 tung:1 δv1:2 identity:6 recent:1 relies:1 off:2 ccu:1 jcs:1 well:1 coordinate:1 supertrace:1 dki:3 usual:2 unified:1 gelfand:2 just:4 less:1 being:2 das:3 obtain:6 ldl:3 via:3 drinfeld:1 transforms:1 facts:1 taiwan:3 previous:2 skp:4 generator:1 infinitely:1 seems:1 discuss:1 transformed:5 lett:10 easy:1 theorem:1 sokolov:1 guarantees:1 transformation:22 eigenfunction:4 represents:3 read:2 supercovariant:2 term:3 using:4 unique:1 mod:7 dimensional:1 modifications:1 seperate:1 imposed:1 like:2 δv:2 follows:6 dv0:1 δl:1 δv0:2 korteweg:1 δh:23 arbitrary:2 δf:6 δg:1 mht:1 reduced:6 δa:2 therein:1 parity:2 methods:1 classical:2 people:1 ψx:1 some:2 calculated:1 examples:5 moreover:3 kdv:12 grading:1 huitu:1 superfields:1 provides:8 steps:1 dda:1 tk:3 inserting:1 obey:4 equivalent:3 bi:1 q2n:3 constructive:2 multiplicative:1 step:1 binomial:1 revtex:1 polynomials:1 although:1 super:43 properties:1 constraint:3 commun:5 discussed:2 o:5 compatible:1 extensions:2 obeys:1 2k:3 automatically:2 unexplored:1 own:1 ηb:1 ηa:1 h2:1 into:9 h1:2 integral:2 functional:1 ηi:2 suppl:1 down:3 δui:1 2v1:2 δuk:3 references:2 operator:24 bosonic:1 descriptions:1 hep:1 weight:1 assumed:1 there:3 u0:4 describes:1 way:1 ed:1 was:2 function:1 form:8 soliton:1 covariantizing:1 but:3 δki:1 hk:8 construction:1 hl:2 encoded:1 highest:1 algebras:2 applying:2 ux:1 versions:1 whether:1 up:2 us:5 below:1 un:2 ui:8 uk:3 similar:1 called:3 detailed:1 associated:25 defined:26 abstract:1 pseudodifferential:2 general:2 conserved:1 together:1 formulation:7 corresponding:4 dδ:3 check:2 defines:4 grassmann:1 functions:6 no:1 whereas:2 when:1 field:3 other:7 dj0:3 department:2 mathematics:2 dv1:3 shows:2 dv2:2 briefly:1 elements:1 models:1 radul:5 variation:1 helpful:1 a1:1 a3:2 a2:2 a4:2 variable:2 algebra:2 structure:19 matrix:1 algebraic:2 implies:2 factorized:1 dψ:9 dφ:6 dτ:1 pseudo:2 rule:1 dϕ:6 starting:3 having:1 4a:2
|
solv-int9812018.txt |@word solv:1 int:1 arxiv:1 dec:1
|
solv-int9812019.txt |@word represent:1 ui:1 homomorphism:1 consider:9 chain:2 rev:2 global:1 edn:1 results:7 four:4 commute:5 montr:2 go:2 gn:59 expressions:1 gl:2 devoted:2 inverse:1 depend:25 concerned:1 equivalence:2 tn:3 neighbours:1 γn:15 under:15 te:2 supported:2 very:1 rise:1 translations:2 conditions:3 additional:7 entries:1 specific:1 nieto:1 difference:6 matrices:2 condition:1 entire:1 presented:1 positions:2 list:7 solution:2 discrete:42 convenience:1 vector:14 progress:1 relation:1 shows:2 ville:1 mn:7 ten:1 direct:5 consists:1 second:5 follow:1 further:22 substitute:2 canonical:3 even:1 aim:1 nonlinear:7 plays:1 stands:1 invertible:2 brackets:1 section:15 d3:3 run:3 goes:3 new:5 method:1 body:3 edited:1 κn:4 simultaneously:1 respectively:4 l1:1 here:6 atoms:4 explore:1 objects:1 groups:9 indecomposable:16 represented:1 const:4 along:2 standard:1 equations:26 interpret:1 mez:1 obtained:13 arrive:2 involved:1 study:4 studied:2 allows:4 leaving:1 decouple:1 makes:1 tt:1 involves:4 genuinely:1 via:1 classification:6 requiring:3 seven:1 specified:7 translational:1 total:1 establish:2 research:1 linearly:6 derivatives:3 use:11 proceed:2 would:2 prove:1 contains:6 finally:2 next:2 ψk:1 ψn:35 completes:1 taken:3 survive:1 means:1 type:11 until:1 possible:6 preserved:1 standardized:1 thus:4 operators:10 site:2 correspondingly:1 particular:2 cases:11 iii:4 must:20 none:5 isomorphism:1 subcases:1 equation:2 work:2 det:2 ρn:12 following:7 nonsingular:1 dec:1 decoupled:3 nearest:1 figure:1 abelian:3 rodriguez:1 introduces:1 preserving:1 table:16 involve:7 cartan:1 allowed:25 exclude:1 species:2 dim:2 rather:3 six:2 write:3 nontrivial:3 pair:3 instead:2 sin:7 classify:3 product:1 express:1 algebra:78 treatments:1 ζn:9 biophysics:1 succ:1 representations:3 types:3 realized:3 short:2 λ2n:2 outline:1 imply:5 grant:1 correspond:2 element:4 hospitality:2 ones:2 spain:1 sn:9 allow:3 sl:89 representation:5 restriction:2 least:5 interpretation:1 indeed:2 over:1 b33:1 satisfied:1 already:2 through:3 y1:3 existence:1 y2:1 its:6 ld:4 derive:1 group:9 lc:18 τi:1 chosen:1 lm:1 li:9 forms:2 absence:1 according:4 tenenbaum:1 systems:41 derivative:1 dges:1 conjugacy:1 semisimple:2 split:1 maximal:3 them:2 yn:2 saff:10 outlined:1 introduce:2 functional:1 mention:1 they:11 now:4 yu:44 integrability:2 nor:1 above:5 2t:3 articles:1 february:1 several:2 always:3 b3:3 possibilities:4 l2:1 sim:1 2b:8 each:12 universit:1 pb95:1 characterized:2 gazeau:1 arxiv:1 successively:1 formulate:1 dorodnitsyn:2 t2:13 journ:1 used:1 investigated:1 our:3 summary:3 eq:82 special:6 canada:2 shown:3 matrix:6 space:2 restricted:4 rep:1 since:6 induces:1 λ1n:2 denotes:2 particles:1 include:1 acting:3 constants:15 rn:11 ref:3 occurs:1 math:10 rk:5 fiber:1 linear:12 interactions:28 contain:1 ısica:2 diagonal:1 departamento:2 quite:2 completely:6 vinet:4 york:1 put:4 subalgebras:4 e1:1 finite:7 irreducible:2 e2:1 pairs:2 interaction:61 r1:1 r2:1 determining:5 could:2 impose:4 gaff:14 levi:8 turn:1 universidad:2 hence:11 βn:5 qn:24 onto:1 first:15 xi:1 xn:1 symmetry:78 radical:4 variables:31 number:5 rank:2 restrict:4 done:1 unspecified:2 precisely:6 given:6 necessarily:2 similarly:1 introduction:1 eqs:1 b2:4 system:8 construct:2 their:9 fn:55 statement:1 dt2:2 molecular:2 independant:1 relations:7 listed:1 floreanini:2 calculations:1 continuous:1 negro:1 2at:2 authors:1 x2:16 x3:15 x1:16 than:2 specify:2 dynamical:40 kind:1 double:1 require:1 namely:23 winternitz:7 matter:1 classes:5 gives:1 powers:1 fcar:1 symmetries:51 few:1 say:1 manner:2 2t2:2 need:1 any:9 complete:2 lie:34 zero:1 depending:5 partly:2 convenient:3 jacobson:1 note:4 instance:2 ideal:2 take:11 forces:4 finding:1 so:5 specifying:1 exactly:1 shall:12 singlet:3 algebraic:1 involving:8 plus:1 reducible:1 future:2 intrinsic:1 deviations:2 annul:1 prolongation:2 considered:1 γun:1 into:23 coincides:3 kn:34 kt:2 χn:13 physics:1 sum:6 fact:1 dover:1 λkn:1 show:1 labels:1 b48:1 notations:1 spaces:1 gauge:2 solutions:2 centralizer:8 substituting:1 d4:3 d5:3 d2:2 find:9 d1:2 parameters:1 homomorphic:1 should:2 only:25 explicitly:2 coefficients:2 molecules:1 ematiques:2 capel:1 equilibrium:1 dn:12 do:15 his:2 dk:3 notation:2 get:1 dependent:5 de:7 aα:3 cannot:3 conjugate:2 words:3 tranformations:1 during:1 dt:7 du:1 gen:1 quispel:1 qu:1 fields:7 µ2n:1 differential:7 consisting:1 qc:1 mapped:1 semidirect:1 scott:1 fixed:1 doublet:2 crm:2 satisfy:5 set:5 exists:6 ωt:4 see:10 individual:1 result:3 y0:8 discussions:1 inequivalent:3 acts:1 satisfying:1 commutation:8 pattern:1 uα:4 sites:1 written:3 µn:52 µk:3 between:2 invariant:46 approach:2 αn:5 preserve:1 notice:1 triplet:1 terms:4 complementary:1 ullate:1 however:7 concentrate:2 tun:4 solv:1 article:5 thank:2 both:6 cos:7 σn:10 ωe:2 taking:1 la:1 c5:2 3j7:1 ısicas:1 ωd:4 ln:4 figures:1 quantites:1 otherwise:3 ck:2 affine:2 cn:24 point:4 simple:3 continuation:1 ca:2 others:1 cohomology:1 corresponds:6 dimensional:43 distinguish:1 simply:3 bα:3 modeling:1 respect:3 ucm:1 throughout:1 pr:2 singlets:6 transformations:18 basis:3 addition:1 locally:2 copies:1 been:2 strategy:1 defined:1 combined:3 algebras:64 pn:28 abstract:1 choose:3 dots:2 θk:5 generating:1 adopted:2 corresponding:6 commutes:1 quantities:2 bulk:1 implied:1 c9:2 c8:2 func:1 c3:2 c2:2 c1:2 denote:2 c7:2 c6:4 present:1 c4:2 case:19 c10:6 pacs:1 transformation:8 will:23 while:1 replaced:1 many:2 orica:2 procedure:3 vn2:2 h3c:1 generate:1 larger:4 coupled:4 vi:3 vk:22 tions:1 non:1 vn:201 iv:15 ii:10 itself:5 properties:1 nserc:1 vanish:1 alone:1 containing:13 verified:1 etc:1 perform:3 make:2 same:3 shifts:1 arguments:1 largest:1 dilations:2 verification:1 φk:1 subalgebra:5 φn:34 higher:5 independent:9 literature:1 maeda:1 sums:2 diml:2 hand:1 doublets:7 purpose:1 dgu:1 infinite:8 invariance:8 interested:1 recent:1 task:1 vα:5 campa:1 analysis:1 obviously:1 solve:4 components:3 coordinate:1 model:1 dimension:5 realised:1 λa1:2 φtt:2 just:5 obtain:12 summed:3 λk:2 λn:104 down:1 previous:3 adding:6 diffeomorphisms:1 generator:1 conclusions:1 character:1 except:2 lattice:1 add:11 other:9 transformed:1 lett:4 easy:1 theorem:1 c12:3 c11:2 yv:44 solvable:4 remaining:2 identical:1 aspects:1 depends:1 ebec:1 unlimited:1 term:1 possibly:3 five:1 ciencias:1 using:2 ams:1 λan:1 helpful:1 like:3 follows:1 tables:2 separately:3 ai:19 continue:1 either:8 arbitrary:16 accelerations:1 upshift:1 classical:1 madrid:2 phenomena:1 back:1 ideals:1 b5:3 b6:3 tvn:4 equivalent:2 b1:3 tvk:1 moreover:4 oscillations:1 extended:2 absent:1 provided:1 dimensions:1 lead:4 centre:3 comments:2 providence:1 does:4 decomposition:11 provides:2 chains:1 2a:11 gratitude:1 algorithmic:1 bc:1 bn:77 view:1 bk:3 step:4 although:1 stay:1 entirely:2 takes:1 about:1 extension:2 simplify:2 column:2 discussed:1 dependence:3 o:1 compatible:2 mutually:2 ξk:22 extensions:2 greatly:1 act:1 2x2:1 ηe:1 presence:3 ηn:8 umontreal:2 ηk:18 isomorphic:4 three:1 b7:3 variable:15 appropriate:1 references:1 determine:2 sov:1 operator:5 actually:2 refined:1 substitutions:1 a3:6 acknowledgements:1 span:1 centralizers:2 eleven:1 assumed:1 there:7 available:1 transform:5 long:1 start:3 restricts:2 facultad:1 strong:1 series:15 call:1 was:6 a2:51 treat:1 function:5 transformable:1 eak:1 arise:1 eal:2 form:43 ean:14 some:4 restrictions:4 but:11 change:1 japan:1 properly:1 hn:28 he:1 b4:2 annihilate:1 ωs:4 up:10 us:11 different:5 below:5 un:202 those:4 decomposable:11 uk:18 ωn:5 problem:4 more:4 similar:2 called:2 mechanics:1 constant:2 pτ:1 int:1 certain:1 ak:17 describe:2 general:5 single:2 exist:7 formulation:1 θn:7 constructed:2 again:3 functions:43 know:2 no:14 when:2 field:6 priori:3 role:1 es:1 becomes:1 elements:15 complutense:2 pronounced:1 symbol:1 setting:1 ragnisco:1 includes:2 a1:58 commutator:1 generated:2 important:2 allowing:1 ξn:109 dissipation:1 structure:4 implies:10 imposes:1 algorithm:1 assume:5 typically:1 together:3 neighbouring:2 time:10 recherches:2 requires:1 original:2
|
solv-int9812020.txt |@word limited:1 partial:3 consider:9 alh:70 caused:1 lack:1 results:15 leads:9 ciudad:1 proposition:1 grateful:1 types:1 sci:1 expressions:4 devoted:1 looking:1 inverse:8 depend:3 chain:3 c0n:1 ty:2 editors:1 nonlocal:2 recurrence:1 quasi:1 spain:2 th:7 under:2 analogous:4 multilinear:1 divergent:1 2rn:1 fay:5 straightforward:1 returning:1 choice:2 difficult:2 discretizations:3 difference:11 matrices:17 rn:107 condition:3 four:1 solves:3 presented:12 bn:33 vertex:1 solution:11 leave:1 discrete:35 hospitality:1 equation:24 akns:5 upper:1 mn:17 zj:5 zk:19 dealing:2 seventies:1 direct:2 past:1 elegant:1 zero:14 ǫm:1 further:4 oneself:1 ρn:37 odd:2 linear:9 even:3 aim:4 what:3 nonlinear:10 plays:1 appear:2 brackets:1 section:18 analogously:3 expressed:1 subspaces:1 new:6 construction:2 method:4 ˆn:1 pioneering:1 compact:1 condensed:1 simultaneously:1 component:1 here:7 objects:1 possibility:1 address:5 directions:1 ratio:1 restricts:1 equations:105 z1:7 z2:6 z3:2 ukraine:1 institute:1 involved:1 study:1 studied:1 completely:1 periodic:2 resulting:2 action:5 shifting:2 history:1 studies:3 york:1 formulated:2 useful:3 projection:3 elaborated:3 jimbo:1 namely:1 ipn:4 till:1 analyzing:1 summation:1 glance:1 tools:1 standing:1 derivatives:1 use:5 expresses:1 proceed:1 analytic:2 remains:1 positive:11 negative:12 next:1 few:5 noting:1 ψn:18 expanding:4 taken:1 themselves:6 type:1 theoretical:1 more:8 introducing:2 started:1 solitons:4 expose:1 mozilla:2 odinger:5 curvature:9 introduces:1 bogdanov:2 known:4 cases:1 effort:2 springer:1 r2:1 indicates:3 originally:1 work:9 det:1 modified:4 salam:2 remain:1 values:2 columns:1 following:13 making:1 my:2 example:4 proof:1 f0:1 tau:18 compare:1 indicated:1 give:3 calculation:2 december:1 sense:1 purposes:1 2cq:1 trieste:1 o:1 want:2 arise:1 overbar:1 verlag:1 compatible:2 needs:1 end:3 goal:1 provide:2 verify:3 discussion:1 acts:1 range:1 write:2 how:7 extended:1 get:1 instead:1 parameter:4 sato:1 map:1 product:4 express:3 description:4 information:1 replacing:1 ζj:5 after:13 derived:7 mapping:1 applications:2 ζr:1 lax:1 multiplication:1 law:2 compatibility:2 constants:5 λ2j:6 ot:1 natural:3 third:1 maybe:1 author:1 eliminated:3 summing:1 element:1 interpolates:1 rather:7 spectral:1 ones:2 used:6 definitions:1 subsequently:1 z2k:5 order:5 davey:8 cofactors:1 restriction:1 evolutionary:5 words:4 summands:1 hierarchy:37 developed:3 over:3 move:1 discretization:4 produced:1 redefinition:1 mathematicians:1 paper:19 through:1 mentioned:2 satisfies:2 still:1 its:6 before:3 τn:145 derive:16 group:1 la:1 chosen:1 interesting:5 conjugation:1 writing:1 forms:1 systems:5 nf1:1 omitted:5 derivative:5 hidden:2 main:8 decades:1 easier:1 them:8 crucial:1 return:1 pure:1 combination:2 universality:1 acklund:1 introduce:2 framework:4 a0n:1 they:6 nov:1 now:13 yu:2 discuss:5 possess:1 easily:4 ϕn:4 castilla:1 hereafter:1 designation:3 hamiltonian:3 2d:4 2f:3 each:2 found:1 βnk:2 quarter:1 side:4 2j:13 mean:3 subsystem:1 differential:17 directly:1 series:17 revised:1 idea:1 related:8 toda:4 gaps:1 combining:1 our:10 ζm:5 beyond:1 out:2 large:1 shown:6 divide:1 matrix:15 space:1 res:1 since:4 squared:1 f1:1 studying:1 acting:1 stud:1 electronics:1 math:9 ζk:3 theory:8 associate:1 contain:2 divergence:1 diagonal:1 departamento:1 standard:2 expansion:2 approaches:1 surely:1 counterparts:1 τn2:6 publ:1 generate:1 additional:1 definition:2 derivation:3 language:2 ζq:2 determining:1 ist:2 motion:3 turn:1 universidad:1 hence:7 inst:1 βn:3 onto:1 first:9 already:3 xn:9 manuscript:1 zm:3 feel:1 relate:2 variables:5 number:7 philadelphia:2 restrict:2 done:3 relations:9 another:6 avenida:1 equating:2 given:5 rewritten:3 fˆn:1 introduction:3 system:22 construct:7 their:9 appl:2 fn:34 calculations:2 realization:1 d0n:1 siam:2 scheme:4 structures:2 speaking:2 gives:2 ictp:1 grant:1 mostly:1 tool:1 continuous:4 eliminates:1 multicomponent:1 part:2 july:1 representing:2 than:1 coefficients:3 character:1 begins:1 wide:1 kind:3 determines:1 kharkov:1 sections:1 integrability:2 aims:1 limiting:1 lim:3 were:8 embody:1 discretetime:1 enables:3 powers:2 perspective:1 shifted:3 rewrite:8 explicit:4 unchanged:1 modern:4 mind:1 matem:1 say:7 close:1 need:3 seen:1 seem:2 obviously:1 clearly:2 viewed:7 lie:1 subsystems:1 αn2:1 depending:1 general:1 convenient:1 self:1 ideas:1 note:7 square:1 take:1 simplified:2 so:17 subject:1 εa:1 adopted:1 δnj:17 bilinear:4 exactly:1 established:1 object:1 gλ:4 vnj:9 newell:1 most:1 qˆn:1 regular:1 formulae:14 nothing:2 acknowledgements:1 intrinsic:1 class:1 stands:1 constructed:2 consequences:3 δn2:1 considered:7 kj:2 calculated:1 flow:10 kp:4 free:1 exp:1 hn:3 left:3 physics:3 fact:1 laws:10 nls:8 akhiezer:1 show:2 γnl:1 supported:1 γnj:11 γnk:2 least:2 discovered:1 miwa:19 relation:9 solutions:10 miller:1 substituting:2 careful:1 d2:4 find:3 help:1 q2:3 based:2 knowledge:2 copyright:1 title:1 representation:39 behind:2 jap:1 should:4 2bn:1 only:7 explicitly:2 indeed:5 integrable:21 hamiltonians:1 local:4 γn:5 hope:1 dn:40 do:6 insight:1 dj:4 irn:8 viewpoint:1 means:6 de:5 straightforwardly:1 cannot:1 radiophysics:1 closely:1 suris:6 combinations:2 during:2 gen:3 differentiating:2 qr:9 determinants:1 twice:1 conditions:10 arxiv:1 fixes:1 cela:1 baker:1 investigate:1 common:1 grassmannians:1 wish:1 identify:1 fixed:1 qn:113 satisfy:3 set:5 above:4 ser:1 acknowledged:1 operates:1 connections:1 differs:1 see:13 result:4 terms:21 nonlocality:1 techniques:1 krichever:1 imposition:1 consequence:2 yet:1 written:12 various:1 jth:1 ladik:39 between:6 boundary:9 reading:1 approach:11 tz:16 jos:1 recently:1 importance:1 attention:2 analogues:1 however:12 gratefully:1 jn:3 concentrate:1 comm:1 key:2 jk:6 solv:1 article:2 received:2 essentially:1 last:3 σn:41 many:1 vanishing:1 dissatisfaction:1 etc:5 context:2 attributes:1 genus:3 whole:1 cj:4 cn:31 point:3 appeared:1 had:1 others:1 corresponds:2 dimensional:2 z4:1 exploit:2 consideration:2 polynomial:2 respect:6 considers:1 considering:3 pq:2 described:1 transformations:2 second:4 lattice:3 equivalent:7 been:19 b0n:1 defined:6 reduction:1 much:4 combined:3 abdus:2 basic:1 algebras:1 pn:27 define:1 wants:2 obtained:8 generating:6 enable:1 corresponding:8 restrictions:1 quantities:10 sufficient:1 maps:2 observe:1 yk:6 stems:1 c2:1 c1:1 determinantal:1 former:2 present:8 case:12 exception:1 appearance:1 value:1 choices:1 will:2 while:8 replaced:1 shift:9 investigating:1 procedure:2 adjusts:1 century:1 almost:2 vj:4 thus:15 vm:1 vn:15 ii:14 ym:1 cumbersome:1 binary:1 different:4 italy:1 sensitive:1 determinant:2 same:2 shifts:17 complex:1 arguments:5 widely:2 hierarchies:9 finite:6 φn:10 higher:6 status:2 independent:1 literature:3 embedding:1 i1:2 i2:1 upon:2 nj:5 flows:14 hand:11 usually:3 moment:1 uses:2 purpose:1 ˇn:1 infinite:11 invariance:1 ablowitz:40 idn:2 identity:2 recent:1 ministerio:1 fourier:1 schr:5 nevertheless:1 expression:4 modeled:1 well:7 spent:1 analysis:1 double:3 without:3 solve:4 consistency:1 firstly:2 model:2 possesses:2 usual:3 proposed:2 among:1 being:5 resp:2 obtain:27 distant:1 questions:1 facts:1 alternative:1 scattering:12 λn:2 stewartson:8 previous:5 bullough:1 density:2 zakharov:2 conclude:2 seems:2 qn2:1 transparent:1 jost:4 simple:1 transformed:3 lett:1 aticas:1 usage:1 generalized:1 real:1 σn2:1 depends:4 iξ:11 situation:3 big:1 decomposed:1 possible:2 iζ:10 know:2 δnl:2 using:19 accepted:1 formal:9 modifications:1 imposed:1 like:3 differentiations:1 identifying:1 follows:10 noted:2 δn:6 continue:4 yields:1 δnk:6 arbitrary:2 become:8 works:3 stationary:1 reduced:4 replacement:1 mathematical:1 βnj:12 because:3 2qr:1 classical:3 βnl:1 affects:1 interrelations:1 some:36 global:1 deduce:1 acad:1 examples:3 zcr:3 nondiagonal:1 proper:1 kdv:4 manifest:1 ourselves:1 generates:1 separately:1 describing:3 both:2 lead:4 establish:1 avoid:1 centre:1 cφ:1 manipulations:1 quickly:1 does:3 eliminate:1 provides:3 korteweg:1 proc:1 forgets:1 demonstrated:1 lowest:1 pr:2 plu:1 camilo:1 2q2:1 power:4 simultaneous:1 kyoto:1 journal:1 aj:3 bj:3 cλ:1 viewpoints:2 substitution:2 standpoint:1 motive:1 stay:1 properties:4 earlier:1 about:2 carried:2 algebraic:2 column:2 discussed:6 dependence:4 2cr:1 practical:4 2cn:1 plus:1 konopelchenko:2 2k:1 consequently:1 considerations:1 raised:1 previously:1 into:6 obtaining:1 functional:51 latter:4 down:1 remarks:1 right:7 references:1 operator:7 proportional:4 lastly:1 ercolani:1 technically:1 deal:2 strictly:2 there:2 question:7 transform:3 long:1 start:1 appears:2 conservation:12 physicists:1 way:7 crucially:1 forward:1 closed:4 was:8 function:9 complete:2 form:15 but:11 volume:1 properly:1 grassmannian:1 gain:1 δn1:1 segur:1 considerable:1 factorized:1 absent:3 october:1 embedded:1 characteristic:1 interest:2 up:1 us:6 ciencia:1 international:1 ul:2 below:1 un:24 limit:4 levermore:1 ωn:17 demonstrate:3 problem:16 similar:6 called:6 bearing:1 constant:11 ln:4 int:1 abstract:2 describe:4 am:1 direction:2 textbook:1 hardly:1 2qn:1 conserved:2 referee:2 dλ:1 dζ:18 partly:1 identities:11 simplest:6 fill:1 again:1 functions:27 rederive:1 no:1 index:1 commutes:1 when:7 vanishes:1 rewriting:1 field:1 finish:1 other:22 role:1 mathematics:2 2dn:3 operators:1 conclusion:1 elements:1 may:1 superposition:9 separate:1 models:2 symbol:1 time:23 problems:5 polynomials:4 includes:1 deriving:1 important:1 ξm:2 variable:1 proceeding:2 sides:5 structure:4 ago:1 auxiliary:6 vries:1 αjn:5 hnj:2 together:6 original:2 hirota:3 n1:2 quantity:3 starting:5 having:2 once:3
|
solv-int9812021.txt |@word represent:3 consider:6 chain:11 rev:3 global:2 results:4 leads:7 proposition:16 computation:3 expressions:1 whose:1 depend:5 calculate:9 contained:1 quasi:13 petersburg:2 th:2 analogous:3 norm:3 applied:1 r12:1 particularized:1 very:2 δµj:1 entries:1 zeitschrift:2 difference:6 matrices:8 hamiltonian:5 turns:1 anisotropy:1 solution:10 large:1 solved:2 vector:1 small:2 eigenvalues:3 takhtajan:1 cosh:2 second:2 masson:1 further:4 odd:1 fonction:1 spectral:9 aim:1 what:1 invertible:1 section:4 expressed:3 maillet:3 poles:1 sup:1 values:3 contributes:1 erieure:1 method:1 groupe:1 respectively:3 here:5 ansatz:8 sinh:7 address:1 represented:5 based:1 quite:1 equations:12 δλk:4 logarithmic:4 obtained:7 remark:1 institute:1 involved:1 study:1 kitanine:2 periodic:12 products:2 procedure:3 action:1 suitable:1 makes:1 quotient:1 uniquely:1 iδab:1 merely:2 limm:1 total:2 derivatives:1 use:8 prove:5 remains:1 positive:3 finally:2 france:4 approach:1 call:1 therefore:2 m3:1 m2:1 associated:1 bethe:23 more:5 introducing:1 continue:1 fontanka:1 ecole:1 becomes:2 operators:4 vm:5 appendix:10 normalized:1 particular:1 eζ:2 defines:1 equation:15 work:1 det:19 obvious:1 following:21 dec:1 spontaneous:11 example:1 proof:9 compare:3 give:2 calculation:3 december:1 organized:1 generically:1 states:13 allowed:1 enslapp:3 µj:16 yang:4 particularize:1 s0:5 orthogonality:1 evidently:1 how:1 ens:4 liniger:1 ct96:1 parameter:2 sin:71 stand:1 product:5 v00:2 communicating:1 replacing:1 thermodynamic:22 earlier:1 derived:2 residues:1 constraint:1 maa:2 hence:7 mab:2 mae:1 physik:2 representations:1 associ:1 constants:1 sz:9 explicit:1 korepin:2 element:3 rather:1 so:1 inhomogeneity:1 representation:4 order:11 typical:1 acts:1 paper:5 london:1 thesis:1 signs:1 existence:1 steklov:1 its:4 diagonalized:2 derive:1 thank:1 la:1 ln:7 actually:1 permanent:1 derivative:4 main:1 defining:1 them:2 introduce:3 functional:3 framework:4 half:1 now:4 possess:1 easily:3 2v:3 2q:1 2x:1 each:1 found:1 2n:8 side:3 baxter:13 ei:1 formulate:1 ee:2 series:5 energy:1 reduce:1 fr:5 ec:1 obtains:8 quantum:3 our:1 out:1 w2:2 ru:1 shown:1 jimbo:1 matrix:25 factors:2 u2m:5 since:7 parametrizing:3 fellowship:2 acting:4 rational:6 denoted:1 formula:13 math:3 after:1 linear:3 reformulated:1 diagonal:9 standard:1 admits:4 complicated:3 york:1 estimate:1 care:1 parametrized:2 could:1 similarly:5 length:2 exponentially:2 corrections:6 first:11 staggered:1 kernel:3 variables:7 number:1 rank:2 done:1 directly:2 precisely:1 size:5 given:8 rewritten:3 their:2 introduction:1 πk:1 least:1 fmrx:1 identity:4 calculations:1 gives:2 shifted:1 m0:4 exactly:2 representing:1 coefficients:1 see:8 determined:1 developping:1 were:1 treated:1 russia:1 perturbative:2 rewrite:2 sab:1 correction:3 generalization:1 summing:1 ras:1 vn0:2 st:2 any:6 zero:2 convenient:3 physique:2 note:6 take:3 φab:1 degenerated:1 modulus:1 heisenberg:4 even:1 cnrs:2 algebraic:8 involving:1 successive:1 phase:2 vk2:14 concerning:1 ura:1 calculated:1 coincides:1 kn:2 points:4 exp:13 sum:4 fact:3 quantity:2 supported:1 12m:1 functionals:2 notations:2 miwa:1 spaces:3 relation:2 solutions:3 ground:30 q2:4 ratio:3 onde:1 parameters:11 distributed:1 written:2 should:3 only:10 explicitly:3 factor:6 local:3 do:3 his:1 means:6 dg:1 σ1a:1 de:4 ϕm:4 mention:2 new:2 du:1 dq:4 determinants:9 µa:6 arxiv:1 qj:7 qm:13 inside:1 coefficient:2 set:9 computed:5 exists:1 namely:4 bare:1 result:6 w1:2 dµ:3 lyon:6 satisfying:1 tensor:2 sites:1 λn:2 µm:2 state:22 µn:1 µk:35 between:3 boundary:1 conditions:1 email:1 µb:4 multiplied:1 terms:8 reproduced:2 wj:1 r02:1 δab:3 solv:1 both:4 last:2 cot:4 σm:15 ua:1 region:1 equal:7 contract:1 minus:1 energies:2 present:3 expression:10 mechanics:1 conclude:1 simple:3 corresponds:1 dimensional:1 taylor:3 simply:1 moreover:3 slavnov:2 iψ:1 δλj:3 due:1 been:2 int:1 anisotropic:1 xab:1 determinant:6 corresponding:7 xxz:6 m1k:1 recalled:1 c2:7 c1:3 general:1 spin:5 those:1 case:5 p0:17 look:1 exponential:2 evaluated:1 transformation:4 will:8 replaced:3 monodromy:2 shift:2 property:1 taking:7 pdmi:1 dλ:10 vi:1 vk:2 thus:11 non:2 according:1 itself:1 im:1 different:3 terras:2 same:2 orders:1 pauli:1 qab:1 proved:3 finite:11 higher:1 development:1 independent:3 used:4 rmatrix:1 parametrizes:2 laboratoire:1 nj:3 hand:5 v0:3 v1:1 v2:1 compared:1 infinite:5 normalization:1 recent:1 normale:1 fourier:5 eorique:1 nevertheless:1 well:2 analysis:1 academic:1 sets:1 model:3 left:2 r01:1 surveys:1 magnetization:11 just:1 being:2 obtain:6 λb:8 λa:57 immediately:2 λk:49 λj:53 momenta:3 scattering:2 eigenstates:2 λm:2 previous:1 density:1 lattice:4 other:1 easy:1 propositions:2 iπ:1 solvable:1 eigenstate:1 momentum:1 depends:2 evaluate:1 sums:4 term:1 iζ:46 department:1 know:1 press:1 using:8 ams:1 unique:3 r0m:2 insert:1 follows:6 separately:1 homogeneously:1 integrals:3 arbitrary:1 spins:1 mathematical:1 right:1 deal:1 formulas:1 some:2 begin:1 gaudin:5 nonzero:1 tmr:1 does:3 provides:1 faddeev:1 interval:2 step:1 2m:1 integers:2 ferromagnetic:1 most:1 column:1 commun:1 discussed:1 o:42 plus:1 fredholm:6 lieb:6 homogeneous:5 convergent:1 previously:1 lenght:1 within:1 integral:11 isomorphic:3 references:1 operator:14 proportional:2 next:1 vˆ:2 vab:2 there:4 italie:1 was:2 iˆ:9 function:26 form:20 enough:1 differences:1 but:3 cedex:1 related:2 hm:3 ph:2 compute:2 consist:1 2πk:4 2πm:5 up:3 us:10 2πn:1 um:2 limit:23 russ:1 distribution:2 similar:1 detailed:1 ac:1 ab:2 ordered:1 defined:5 abstract:1 denote:2 dν:1 exist:1 rule:1 identities:5 constructed:2 nab:3 again:2 functions:16 naa:1 no:2 whereas:2 when:1 valid:1 ferent:1 really:1 izergin:2 stat:2 elements:12 kinds:1 models:2 vertex:1 ξm:1 u2a:8 regime:1 auxiliary:2 statistical:1 space:4 together:1 remarkable:1 once:2
|
solv-int9812022.txt |@word represent:1 concept:1 consider:9 results:1 scalar:1 generalize:1 computation:1 expressions:1 compact:1 inverse:1 superspace:2 subjected:1 alvarez:2 θt:6 under:1 must:2 kanno:1 g4:1 proved:1 g2:3 very:4 wave:2 every:2 matrices:1 hamiltonian:1 turns:1 solution:11 discrete:1 manifestly:1 relation:2 der:1 dealing:1 direct:1 zero:1 displays:1 iσ2:2 implemented:1 odd:4 bilinear:36 nonlinear:14 diag:1 section:4 ˆb:3 version:2 above:3 method:1 3d:1 coefficient:1 condensed:1 sincere:1 here:2 water:2 ansatz:1 sawada:6 consideration:1 sine:9 equations:20 antisymmetric:1 leutwyler:1 institute:2 shift:1 study:2 larger:2 allows:2 completely:1 ekx:1 hospitality:1 fourier:1 yamada:1 useful:1 apply:1 tools:1 virasoro:1 derivatives:2 use:2 proceed:1 prove:1 covariant:5 nucl:2 going:4 type:7 theoretical:2 introducing:2 formally:1 anticommuting:3 solitons:2 operators:9 odinger:1 instrumental:1 eθ:5 particular:1 known:1 eη:2 iii:2 fermionic:9 ramani:6 mg:1 valued:1 φdφ:1 equation:18 work:2 values:1 concepts:1 following:18 dec:1 proof:1 solved:1 expanding:1 organized:1 numbers:1 want:1 sense:4 needs:1 boussinesq:1 darboux:1 verify:1 acts:1 write:1 far:1 nontrivial:1 pair:4 pure:1 parameter:3 sin:4 product:1 express:1 ft:1 description:1 algebra:1 fx:2 after:1 variant:1 lax:4 sx:4 dα:1 kulish:4 light:1 author:1 rather:1 used:1 sn:6 representation:1 order:6 hierarchy:4 inami:1 satisfied:1 b309:1 paper:5 its:1 mod2:1 how:1 interesting:1 affine:1 forms:3 d4x:1 systems:2 mail:1 eη1:5 supersymmetry:5 them:2 motivated:1 acklund:1 introduce:3 obeyed:1 mention:3 they:3 singularity:1 yu:1 discuss:1 vecchia:1 articles:1 2p:2 d3x:1 s11:1 university:1 presented:1 e2θ:2 2d:5 ifa:1 found:2 2i:6 constraints:1 spinor:2 square:1 there:4 journ:1 related:2 constitute:1 operator:8 extended:1 obtains:1 quantum:1 our:2 special:1 out:2 df:4 space:3 kotera:6 rev:1 research:1 collisions:1 investigation:1 emerged:1 conjectured:2 ro:1 math:9 theory:4 given:3 standard:6 reason:2 ask:2 interaction:3 derivation:1 ferrara:1 linearized:1 gordon:10 consequence:2 inst:1 generalizations:1 first:2 romania:1 xi:1 xn:1 roelofs:1 variables:3 number:3 clear:1 kersten:1 done:1 relations:1 little:1 introduction:1 system:4 construct:1 their:1 c2n:3 progr:1 ζˆi:6 alonso:1 shallow:1 part:2 supergauge:1 x2:6 x1:4 than:1 coefficients:1 kink:2 were:2 usefulness:1 seminal:1 ueno:1 ann:1 manner:1 further:1 lie:1 generalizes:1 depending:1 fxt:1 able:2 note:1 instance:1 k1:18 generalized:1 so:3 kac:4 even:6 multiple:1 shall:8 algebraic:2 multisoliton:5 phase:2 acknowledgements:1 xµ:4 soliton:9 observation:1 prolongation:1 kj:15 ki:23 partition:1 kp:3 principle:3 exp:12 hietarinta:2 kx:3 physics:3 fact:3 nls:1 oevel:1 supported:1 anyway:1 gauge:10 solutions:6 find:7 proposed:2 romanian:1 jap:1 stud:1 only:6 anticommutes:1 factor:1 integrable:7 dn:1 do:2 his:1 klein:1 means:2 dependent:1 dg:4 µj:4 itoyama:1 liu:1 dx:12 probably:1 dt:14 procedures:1 reveal:1 evolution:4 fields:2 arxiv:1 leur:2 switzerland:1 requirement:1 imposing:1 namely:2 result:1 theoretic:1 best:1 subject:1 nuclear:1 supergravity:1 kj2:4 written:4 µi:8 between:2 c2j:8 invariant:7 c2i:10 approach:4 notice:1 terms:1 extend:2 however:1 comm:3 solv:1 σi:1 last:1 kjj:1 many:2 infinitely:1 linears:3 etc:2 admit:1 mct:1 context:3 expression:4 otherwise:1 ci:6 point:1 superfield:5 mkdv:1 moreover:2 ddφ:1 mcarthur:4 mathieu:2 described:1 transformations:2 aˆ:1 due:1 been:5 defined:3 interest:1 algebras:1 choose:2 wants:1 θk:2 supersymmetric:13 cos:1 versions:4 derivative:4 c0:7 present:2 θu:1 case:11 k2:18 manes:1 will:1 dept:1 aij:7 di:1 property:1 conformal:1 leaves:2 launched:1 studied:2 coupled:1 ki3:3 ki2:5 metric:1 thus:1 iv:2 ii:2 converts:1 cone:1 susy:39 uxxx:2 ig:2 different:1 φt:5 grant:1 s2n:1 connection:1 same:5 shifts:1 emphasize:1 pauli:1 hierarchies:3 several:2 yung:5 independent:1 investigated:1 see:1 satsuma:6 effect:1 kii:1 invariance:7 identity:1 popowicz:1 schr:1 epx:1 framework:1 well:1 analysis:1 de:2 solve:1 components:2 exponentials:2 usual:1 φtt:1 just:1 grammaticos:2 obtain:8 thanks:1 integer:1 scattering:1 adv:1 application:1 seems:2 lett:7 easy:1 theorem:4 5d:1 transformation:5 take:1 real:2 depends:1 easily:2 possible:1 know:2 using:9 mod:2 follows:1 reduces:1 δp:3 manas:1 bucharest:1 parity:1 gaume:2 because:2 classical:3 understood:1 examples:1 respect:1 kdv:18 ourselves:1 though:1 integration:1 comments:1 prof:1 majorana:1 power:1 equivalent:1 expansion:2 step:1 binomial:2 medina:3 although:4 substitution:5 exemple:1 relating:1 refers:1 super:33 properties:1 about:2 extension:8 extending:2 discussed:2 remains:1 extensions:2 introduced:2 mathematical:1 soc:1 φxx:1 into:2 ηi:15 martinez:1 lies:1 references:1 paradigmatic:1 eη2:2 bosonic:8 van:2 log:6 initial:1 long:1 dispersion:1 accordingly:3 quadratic:2 way:1 was:7 function:6 form:20 but:1 bern:1 compute:1 leclair:2 ut:2 6uux:2 ωt:4 assume:1 limit:3 define:3 similar:2 called:1 b1:1 ibort:1 constant:1 int:2 certain:2 abstract:1 pseudodifferential:1 deep:2 general:5 engineering:1 sxt:3 formulation:1 formalism:12 physical:3 grassmann:10 functions:7 integrability:3 no:2 field:8 other:1 papers:1 nr:1 theor:2 quadrilinear:1 briefly:1 a12:6 radul:1 ξt:1 polynomials:1 manin:1 commutator:1 generated:2 important:2 θθf:1 variable:3 b314:1 structure:2 implies:1 coupling:1 dφ:1 requires:1 dot:1 hirota:18 starting:1 having:1
|
solv-int9812023.txt |@word partial:1 consider:4 remarkable:4 funct:2 rx:1 results:9 four:3 olive:1 scalar:4 grateful:1 consists:3 follow:2 expressions:1 research:2 dα:1 row:1 compact:2 zuckerman:7 certainly:1 inverse:20 depend:3 calculate:2 re:2 tt:1 provisions:1 editors:2 nonlocal:28 passage:3 presents:1 kβ:2 finally:5 present:5 elliptic:2 under:1 kκ:1 δhc:1 me:1 rαβ:1 expressing:1 advantage:1 very:2 dq:6 rise:3 multi:5 fadeev:1 geometrical:2 witten:7 entries:1 redefinition:1 invert:1 matrices:1 2rr:2 condition:3 tri:3 leads:1 annihilated:1 riemann:2 immediately:2 hamiltonian:154 turns:1 notes:2 nucl:2 list:1 solution:2 hereafter:1 solved:1 vector:20 science:1 indices:1 c01:1 div:1 refer:2 deleting:1 noted:1 degeneracy:1 application:6 δu:8 neighborhood:5 coordinate:1 lecture:2 coefficient:1 morozov:2 jc:2 elegant:1 zero:4 enclosed:1 involution:2 qualitatively:1 dynamics:1 dqx:4 conclusion:1 µq2:2 canonical:7 even:1 index:1 nonlinear:9 plays:1 appear:1 brackets:12 section:13 bergman:1 rome:1 henceforth:3 nondegeneracy:1 version:2 above:5 method:1 new:3 consisting:1 multitude:1 satisfy:4 full:1 led:1 gravitation:1 degree:4 respectively:4 l1:2 component:2 richest:2 here:1 water:1 reported:1 tangent:1 possibility:1 groups:1 others:2 xβ:1 based:3 along:1 xα:1 equations:51 appears:1 change:3 suggest:1 obtained:13 derivable:1 remark:2 institute:1 vectors:1 disadvantage:1 reason:4 suggests:1 accomplished:1 resulting:4 poisson:15 factored:1 conveniently:2 fourier:2 makes:2 glu:2 montreal:1 york:2 pxx:8 useful:8 family:12 extra:3 private:1 brought:2 texts:1 santini:2 opportunities:1 summation:2 total:12 univ:1 unit:4 readily:5 derivatives:5 use:11 y2:1 proceed:1 would:1 prove:1 covariant:2 contains:4 kα:2 next:1 linear:5 h1k:3 examination:1 therefore:5 taken:1 associated:2 simpler:1 type:7 boiti:1 more:2 introducing:2 sons:2 excluded:1 px3:3 px2:10 operators:68 itak:1 pairs:1 curvature:2 invoking:2 introduces:1 particular:4 known:1 mokhov:4 cases:2 hold:3 potential:1 qdx:1 must:6 nutku:8 springer:3 valued:2 integrating:1 recall:1 equation:33 det:4 modified:1 ere:24 ρr:3 values:1 following:7 dec:1 specialized:1 example:6 proof:5 zametki:1 νq:1 exterior:4 indicated:3 give:1 calculation:3 ηxx:1 distributions:1 sense:2 sokolov:2 purposes:1 monge:24 uxn:1 pq2:1 his:1 o:6 degenerate:11 qq2:1 uab:1 gervais:2 verlag:2 information:2 dh:2 newell:1 ahler:1 rather:1 verify:3 discussion:4 acts:1 xκ:1 feature:1 write:7 maps:1 syst:1 manipulating:1 instead:2 those:1 parameter:1 specializations:3 product:1 express:1 ft:1 mat:1 algebra:12 may:5 max:1 earlier:1 derived:1 gardner:2 consequence:1 lax:4 dokl:2 summarize:1 choice:5 qqx:2 types:3 introduced:3 natural:1 remember:1 third:3 δi:3 lines:1 element:4 manipulated:1 so:6 lα:4 definitions:3 lκ:6 order:21 typical:1 evolutionary:1 interpretation:1 evident:1 considerations:1 hierarchy:4 indeed:1 over:8 satisfied:3 years:1 furnishes:1 combinations:1 paper:2 through:4 p1x:8 existence:6 satisfies:5 still:1 its:11 mathematics:1 swank:1 thank:1 δiµ:4 fix:1 writing:1 forms:8 omitted:1 degrees:4 systems:16 frech:1 jacobi:14 derivative:10 shabat:1 main:1 defining:3 arguments:1 correspondence:1 closure:1 non:4 good:3 return:1 combination:3 ya:3 conversations:1 amenable:1 school:1 introduce:4 number:8 framework:1 hamilton:8 they:6 kkj:1 now:3 provision:1 discuss:2 considerably:1 heaviside:1 term:1 φk:3 dirac:30 name:1 traced:4 2x:1 identified:1 privileged:1 possibilities:1 l2:1 l3:1 qx:66 kerf:1 found:4 side:4 constraints:26 homogeneous:15 lectures:1 arxiv:1 directly:6 ee:1 series:1 sov:2 reduce:2 principles:1 related:6 inverted:3 elementary:1 mdx:1 expect:1 entering:2 quantum:1 our:5 eq:45 regge:1 out:5 category:2 emerges:1 shown:4 matrix:6 rr:1 space:2 restricted:1 furthermore:3 since:5 lagrangian:30 denotes:4 increase:1 similarly:1 stud:1 denoted:1 constants:2 2k:1 correct:1 math:19 shows:3 wiley:2 theory:12 kaup:1 divergence:3 free:1 quite:4 admits:3 completely:4 complicated:1 counterparts:1 attendant:1 monographs:1 anal:3 definition:5 enormous:1 r2:6 applications:2 lincei:1 could:1 transition:1 obstacle:1 motion:17 turn:3 lµ:4 place:2 δij:1 hence:5 first:22 origin:1 indebted:1 ukt:1 graduate:2 symmetry:1 miura:4 variables:23 geodesic:10 sssr:2 ranges:1 xx:9 simplified:2 construct:2 another:5 carry:2 xp:1 precisely:2 several:1 xu:1 given:39 necessarily:1 backbone:1 interesting:1 hyperbolic:2 introduction:2 eqs:26 πi:2 system:11 relations:4 compatibility:3 their:5 πp:3 πq:6 master:5 1d:1 statement:6 πu:3 hundred:1 variational:12 structures:7 gives:3 holomorphic:1 calculations:1 sl:1 shallow:1 serve:1 kupershmidt:1 immediate:2 direct:3 part:1 because:4 x2:3 x3:1 x0:1 than:1 coefficients:3 dynamical:2 finitely:1 scheme:2 determines:1 acknowledgement:1 second:11 goddard:1 αc:1 classes:4 doubly:1 were:2 enables:1 distinguished:2 galv:3 generality:1 rewrite:2 explicit:1 unchanged:1 θxx:2 argument:2 generalization:1 already:3 qpx:1 further:3 need:7 seen:1 constrained:1 any:8 hessian:1 lie:1 generalizes:1 depending:1 convenient:1 latter:4 responsible:2 dispersionless:1 note:6 sciences:1 densities:3 take:2 xi:1 techniques:1 kac:7 spectral:1 akad:2 shall:23 kosmann:1 magri:9 falls:1 most:6 3x:1 ht:2 representation:1 pair:12 class:11 divergences:1 volume:2 tκ:1 tλ:1 considered:7 kj:1 clear:1 incompatible:1 flow:19 km:5 lλ:8 bracket:18 principle:5 h2k:1 quadratic:1 physics:3 sum:1 fact:7 quantity:1 sundermeyer:1 particularly:1 show:8 jµ:8 prime:1 ending:1 ki:1 relation:3 solutions:1 carefully:1 range:1 find:16 principal:2 q1:1 current:3 q2:6 ratio:1 eαβ:1 outside:1 contraction:1 should:4 lemma:4 only:7 explicitly:1 geodesics:2 rich:1 integrable:11 circle:3 hamiltonians:6 local:32 pointed:1 dn:1 do:3 dm:1 establishes:1 notation:4 get:3 dependent:1 familiar:2 simplest:9 methods:1 remedy:1 cannot:3 dz:3 dx:96 report:1 dw:1 dt:1 du:4 dr:1 dp:10 secondary:2 qq:8 qp:2 evolution:11 determinants:1 qt:13 qy:1 fields:6 differential:4 yield:5 dpx:2 twice:1 nauk:2 hydrodynamic:1 contain:6 qi:3 qm:4 qn:3 hκ:3 hλ:3 requirement:1 set:2 modulo:3 constructing:2 exists:1 δji:1 differentials:1 j0:12 j1:12 morosi:1 namely:3 result:9 eliminating:1 semmes:3 terms:2 analog:1 subject:6 surfaces:2 hilbert:1 satisfying:1 µq:32 functionals:1 written:3 determined:1 various:5 closed:6 between:1 limit:1 approach:4 law:2 available:1 publishers:1 recently:1 uk:2 cern:1 2px:1 vinogradov:2 however:11 vanishing:2 concentrate:1 comm:1 extent:1 solv:1 tub:1 jetp:1 utx:2 factorization:1 both:7 essentially:1 pempinelli:1 cardinality:1 emes:1 xλ:1 many:17 density:11 according:4 admit:2 symplectic:30 casimir:4 σq:3 expression:6 finds:1 comes:1 among:1 ci:2 relevant:1 point:3 simple:1 had:3 lagrangians:3 corresponds:4 satisfaction:2 alone:1 maintained:2 simply:6 lagrange:4 respect:4 actually:1 factors:1 schwarzbach:1 turkey:1 dui:2 duj:1 strong:2 pt:8 fairlie:5 yau:1 simplification:1 px:81 py:1 three:4 been:2 dux:1 int:2 κr:5 hawking:1 basic:3 expected:1 prototype:1 pn:4 pm:3 direction:1 arises:1 families:2 restrictions:1 quantities:7 offered:1 iµ:1 covariance:2 belfer:1 θx:10 determination:1 func:1 olver:4 c2:2 c1:2 hµ:2 standard:3 instructive:1 case:12 exception:1 macfarlane:1 unlike:1 checking:2 dorfman:3 straight:2 appearance:6 value:1 choices:1 will:14 cast:6 while:4 kjk:1 situation:3 skewsymmetric:1 property:1 procedure:1 rename:1 ix:6 lenard:2 credence:1 zenith:1 vol:2 soliani:1 refs:1 prr:1 thus:12 them:2 uxx:22 ii:1 ik:7 itself:4 dual:1 vx:5 teitelboim:1 mod:2 vanish:1 different:5 verified:6 specialization:2 generic:3 recursion:23 make:2 belong:1 connection:1 same:1 proceeds:1 member:1 read:1 complex:4 split:1 pξ:1 modification:1 φi:5 finite:2 composition:4 higher:3 independent:2 ux2:1 see:1 jα:2 interscience:1 flows:2 hand:8 kik:1 kij:1 purpose:2 infinite:12 ablowitz:1 cµ:1 courant:1 suitable:1 off:1 center:1 parantheses:1 nevertheless:1 no:3 well:9 analysis:2 de:2 without:1 neveu:1 components:4 µqq:2 dimension:4 manifold:1 generally:2 obtain:4 infeld:2 underlying:2 using:11 momenta:5 qξ:1 scattering:3 fokas:3 adv:1 preprint:1 infinitely:16 zakharov:2 yu:1 ease:2 character:2 qx2:6 source:1 belongs:1 transformed:1 treatment:2 theorem:4 pointing:1 uαβ:2 hat:1 transformation:5 scientific:1 generalized:1 real:21 iκ:2 aspects:1 increased:1 depends:1 alternatively:1 rules:2 spatial:1 possible:3 naz:1 rµν:1 press:1 amp:24 unique:2 string:1 moody:7 loss:1 necessary:1 δx:3 δy:4 follows:10 reduces:1 velocities:2 δr:2 exploit:1 δp:5 manifest:2 discarded:1 yields:5 δk:1 integrals:1 arbitrary:42 qxx:2 works:1 essential:1 amd:1 lends:1 mathematical:2 calculus:1 right:4 often:1 sequence:3 sequences:5 some:2 back:5 born:2 acad:1 kdv:2 δq:8 df:4 provided:2 primary:3 dimensions:12 lead:2 opposite:1 hodge:1 does:1 exposition:1 linearly:1 provides:3 assuming:1 minimal:1 either:5 presented:1 object:3 δh:1 annal:1 poincar:4 retains:1 equivalent:3 each:4 continuing:1 bi:3 illustration:1 step:1 variation:2 references:1 th:2 properties:3 takes:1 comparison:1 clarifying:1 world:1 simplify:2 column:1 freedom:8 completing:1 basis:2 discussed:1 dependence:4 recognized:1 2i:1 compatible:15 carries:1 kµ:1 stand:1 referred:1 skew:1 automatically:1 δux:2 jν:2 rev:1 jθ:1 jι:2 jκ:4 presence:1 einx:1 communication:1 into:11 integral:1 functional:1 jβ:2 due:1 lies:1 appropriate:9 square:2 bihamiltonian:1 determine:1 formidable:1 operator:78 proportional:1 ηx:9 developable:1 there:19 u1:5 transform:1 u2:5 start:2 accordingly:1 conservation:2 editor:1 way:3 forward:2 assumes:2 function:25 survives:2 complete:3 form:54 simplifications:1 hq:1 but:10 δki:1 σpx:1 repeated:4 construction:5 hn:1 hc:1 segur:1 level:1 true:1 factorized:1 etrie:1 commun:2 algebras:3 uy:1 ux:27 consist:2 understood:1 ut:13 smooth:1 up:1 differentiable:6 ur:9 h0k:2 discarding:1 below:2 un:4 ui:5 verification:1 utt:2 dv:3 problem:3 similar:5 called:1 ex:1 mechanics:2 interval:1 constant:8 defined:7 universal:4 am:3 israel:1 ao:3 general:4 dξ:3 conserved:18 exist:6 uit:3 formulation:11 corresponding:5 gradients:2 identities:14 check:5 defines:3 incorrect:1 again:13 functions:25 us:2 integrability:3 variety:3 nonlinearities:1 when:2 vanishes:1 multipliers:4 field:17 other:12 role:1 brings:1 department:1 nq:2 concerning:1 govaerts:5 rt:2 star:1 generates:2 0th:1 why:1 remarked:1 consideration:1 includes:1 manin:1 convention:1 important:3 variable:3 hanson:1 ωc:2 structure:28 independently:1 auxiliary:1 algorithm:1 dω:1 assume:1 starting:4 required:1 eom:1 notion:2 factorizes:1 implied:1 dvx:1 time:8 far:1 appl:4 reserve:1 requires:5 lett:5 once:5
|
solv-int9812024.txt |@word sci:1 consider:7 chain:2 global:1 results:2 leads:2 lecture:1 montr:3 follow:1 gi:1 compact:1 certainly:1 hold:2 depend:2 calculate:1 paris:6 concerned:2 γu:1 containing:1 finally:1 according:1 th:8 under:3 multilinear:24 p2:2 g3:1 g2:1 g1:1 far:2 account:1 choice:1 every:2 fall:2 matrices:2 tri:1 dij:1 turns:2 occurs:2 large:1 discrete:20 vector:6 8x:1 anal:1 stay:1 programme:1 des:1 10b:1 mi:11 10a:1 translating:1 painlev:18 pour:1 further:1 odd:1 ode:1 canonical:1 bilinear:2 established:1 what:6 nonlinear:3 appear:1 giving:1 section:3 selected:1 m33:1 m32:1 expressed:3 above:2 new:2 coefficient:1 full:1 led:2 degree:14 respectively:1 never:2 component:2 richest:1 here:6 papageorgiou:1 behaviour:1 dover:1 bj:1 groups:1 address:1 directions:1 κu:1 along:2 equations:17 appears:2 change:1 obtained:8 study:6 studied:1 allows:1 subcase:1 contradiction:1 resulting:1 formation:1 suitable:1 ratios:1 classification:5 vii:2 engineering:1 analyzing:1 names:1 linearly:2 use:3 towards:1 additive:1 would:5 prove:4 recalling:1 contains:2 france:3 m1:37 m2:21 type:4 more:7 possession:1 formally:2 ecole:1 initial:1 regrouping:1 particular:4 known:1 projective:29 cases:2 encountered:2 must:4 ramani:8 keeping:2 include:1 word:1 science:1 equation:43 mn:8 det:5 mk:2 mu:2 following:5 dec:1 f1:1 f2:1 f3:1 f4:1 indicated:1 give:2 calculation:1 confused:1 generically:1 caution:1 performed:1 council:1 information:6 fonds:1 divided:1 get:5 write:11 how:1 criterion:1 behave:1 acta:3 ordinary:1 constraints:1 undertook:1 belongs:1 express:1 tried:1 singular:3 replacing:1 coined:1 after:1 singularities:2 mapping:30 produce:1 ζu:1 coming:1 fi:1 types:2 third:2 computations:1 lines:2 trilinear:1 ones:3 lhs:1 enter:1 definitions:1 acknowledges:1 order:26 excepted:1 holds:2 help:1 indeed:8 satisfied:4 course:2 paper:2 through:10 satisfies:1 still:1 its:8 la:2 interesting:8 solving:1 actually:2 forms:5 permanent:1 systems:18 fij:1 ours:1 main:2 fin:1 ince:1 non:2 combination:3 amenable:1 chercheurs:1 p11:1 p12:1 p13:1 they:3 identically:1 singularity:11 now:3 realize:1 easily:3 term:17 2w:3 always:3 classified:1 2a:1 2b:1 each:1 found:1 universit:3 higher:8 mean:1 homogeneous:1 downshift:1 arxiv:1 ei:1 independent:9 ed:1 reduce:1 w12:1 related:1 aide:1 inhomogeneous:2 expect:2 our:5 meth:1 beyond:1 nonlinearities:1 special:2 out:6 canada:2 shown:5 matrix:4 u2n:1 since:9 rev:2 research:1 content:1 rational:5 formula:1 linearisable:6 suffices:1 integrated:2 math:3 shows:1 linear:9 8b:2 8a:2 free:2 approaches:1 complicated:1 york:2 βu:1 m21:1 m22:1 turn:1 hence:3 first:21 already:2 variables:7 number:1 carry:1 precisely:4 open:1 illustrate:1 given:4 checked:1 rewritten:1 their:1 introduction:1 leading:3 system:25 least:2 indicate:1 assumption:1 inversion:4 1k:1 1j:21 recovered:1 1n:14 recursively:1 continuous:28 somewhat:1 appearence:1 x3:1 translation:3 x1:12 than:4 coefficients:4 kind:1 sections:1 namely:1 winternitz:2 matter:2 contrary:1 were:3 gives:1 treated:1 fcar:1 lowest:1 etage:2 rewrite:1 acknowledged:1 linearizable:4 turned:1 aw2:1 say:1 seen:1 clearly:1 complete:3 6w:2 mij:1 mappings:12 zero:2 depending:3 studying:1 latter:2 inv:1 note:3 instance:2 absorbed:1 take:1 jacobian:4 so:3 even:1 begin:1 exactly:2 shall:3 track:1 denominator:1 diminishing:1 riccati:8 most:5 involving:1 acknowledgements:1 class:4 singled:1 fjn:1 nonlinearity:3 coincides:1 physica:2 points:1 principle:1 hietarinta:1 fact:6 quantity:1 precise:3 saying:1 show:4 saga:1 3w:1 fifty:1 x2:1 solutions:2 d4:1 find:5 d1:1 ear:1 based:1 writes:1 enough:1 should:4 analytic:3 only:19 explicitly:1 factor:3 integrable:15 local:1 do:6 his:3 dominant:9 dk:1 notation:1 means:5 dependent:3 de:5 soon:1 subdominant:1 cannot:2 invariant:3 dw:1 du:3 differentiating:1 evolution:1 qu:2 settings:1 differential:9 investigate:1 predicted:1 contain:2 fixed:1 crm:1 satisfy:1 set:1 exists:2 imposing:1 national:1 cin:1 depends:2 w4:1 w3:1 w2:27 w1:105 springer:1 satisfying:1 subsequent:1 definite:1 written:6 convince:1 wn:19 limit:11 conditions:4 terms:22 extend:2 wk:4 analogues:1 however:5 wi:11 wj:27 ww:3 implementing:1 solv:1 problem:1 5x:1 concentrated:1 both:6 recherche:1 last:1 limits:3 gratefully:1 f2j:2 3j7:1 contract:1 tour:2 context:1 fnn:1 contribution:4 expression:10 fnj:1 comes:3 generalisation:1 relevant:1 cn:11 point:6 simple:2 others:2 corresponds:2 dimensional:2 m13:1 m12:2 simply:2 solve:1 polynomial:6 moreover:3 cw:2 cv:1 cu:1 considering:2 second:9 pu:1 due:1 been:2 defined:2 reduction:1 much:1 combined:2 goes:1 expected:1 ph:1 ak:2 define:4 corresponding:3 quantities:1 confinement:3 derivative:1 those:2 θu:1 case:33 p3:2 multi:1 p1:2 exponential:1 examine:1 value:1 will:10 while:3 situation:1 property:5 guide:1 procedure:1 h3c:1 vi:5 thus:15 them:1 vn:26 f2n:1 middle:6 reads:4 examined:2 nserc:1 vanish:2 worry:1 different:2 integrodifferential:1 chazy:1 make:1 lett:3 same:4 orders:2 member:2 shifts:2 palaiseau:1 potentially:2 arguments:1 largest:1 difficult:1 fairly:1 see:6 cubic:1 absorb:3 v0:14 v1:23 v2:22 unmanageable:1 3x:1 fully:1 disappears:1 min:1 well:1 analysis:1 obviously:1 without:1 gambier:4 components:5 very:1 loss:1 calogero:2 scholarship:1 just:4 unshifted:1 linearisation:1 grammaticos:8 obtain:5 rest:1 homogeneity:2 integer:1 yet:2 previous:3 enters:2 family:2 zakharov:1 alternate:1 character:1 except:1 quadratures:1 source:1 setting:3 treatment:1 5e:2 doctorat:1 adj:3 transformation:2 secondorder:1 showing:1 disagreement:1 possible:4 confines:1 quest:1 confined:3 using:3 like:1 c1j:5 necessary:1 c1n:1 lost:2 follows:2 reduces:1 specific:1 ai:1 cx:1 steps:1 polytechnique:1 arbitrary:2 multiplicative:1 become:1 works:1 reduced:1 terminology:1 upshift:4 right:1 methods:1 some:6 cnrs:1 b4:2 b5:1 b6:1 b7:1 b1:2 b2:2 b3:2 b8:1 b9:1 nonzero:1 scholarships:1 lead:2 umr:1 though:1 ese:1 does:5 eliminate:2 ebec:2 prob:1 either:3 object:1 lose:1 bi:3 m11:2 bk:1 translated:1 step:6 bw:2 although:1 p32:1 p33:1 p31:1 bx:2 between:1 about:2 freedom:3 discussed:1 dependence:1 o:6 introduced:3 considerations:1 subclasses:1 into:6 within:2 obtaining:1 three:8 acad:1 references:1 inverting:1 isospectral:1 financial:1 mere:1 suffice:1 there:6 u1:7 m31:1 start:2 anderson:1 quadratic:1 low:1 way:1 was:2 function:4 eal:3 form:22 regenerating:1 w13:1 but:5 construction:2 elimination:1 highest:4 true:1 uu:1 cij:3 up:2 us:2 harnad:1 un:26 ui:3 autonomous:1 similar:2 examples:1 detailed:3 associated:1 play:1 int:1 abstract:1 u2:6 proven:1 general:20 single:13 exist:2 rule:2 aw:3 av:1 simplest:1 again:4 functions:8 integrability:12 no:2 when:3 ourselves:2 other:2 role:1 conclusion:1 symposium:1 elements:1 kinds:1 surprise:1 time:1 polynomials:2 εw:2 a1:2 a0:2 a3:1 a2:1 a4:1 variable:17 sides:1 structure:4 independently:1 implies:3 assume:3 cpt:1 together:1 hirota:1 appl:1 backward:1 starting:1 having:1
|
solv-int9812025.txt |@word externally:1 partial:12 remarkable:2 similarity:3 unel:1 people:1 results:2 fluids:1 eds:4 computation:1 edu:2 sci:1 expressions:2 research:2 inverse:2 chain:1 paris:1 dickey:2 finally:1 th:1 under:2 stochastic:4 analogous:1 applied:1 random:2 rational:1 advantage:1 zhang:3 very:2 tends:1 springer:2 focus:1 lecture:2 ma:1 continued:1 deformations:1 condition:1 entire:2 europhys:1 wetensch:2 solves:1 purely:1 did:3 turns:1 notes:2 solution:9 t0:8 large:1 discrete:1 vector:1 dix:1 anal:4 originally:1 concluded:1 force:3 disciplines:1 øksendal:4 direct:1 burger:2 zero:1 displays:1 concludes:1 further:1 dynamics:1 linear:8 even:1 will:2 what:2 nonlinear:12 appear:1 celebrated:1 http:2 brief:1 expressed:1 above:1 new:7 etheridge:1 method:3 satisfy:1 weikard:2 full:1 deduces:1 respectively:3 republished:1 equals:2 here:3 water:1 simon:4 free:1 nonsingular:1 represented:2 standard:1 equations:38 appears:1 change:1 great:1 generalizing:1 involved:1 introductory:1 studied:1 periodic:3 published:1 therein:1 proof:2 der:1 polonica:1 brought:1 analyzing:1 forefront:1 univ:1 derivatives:2 ψx:8 would:1 positive:11 etc:2 quasi:4 ψt:27 next:2 calculation:2 ust:1 telegraph:1 associated:3 noisy:1 type:5 until:1 subcritical:1 more:3 introducing:2 gohberg:1 started:1 becomes:1 ee:1 odinger:4 validity:1 berlin:1 appel:1 eθ:2 particular:4 known:2 escaped:1 account:1 valued:2 defines:1 ed:1 science:2 equation:73 modified:11 london:2 zhao:2 renders:1 solitaire:1 resembles:1 following:3 strategies:1 dec:1 mo:1 history:2 dedicated:1 process:1 beals:1 sokolov:1 states:3 council:1 advancing:1 jensen:1 motion:3 boussinesq:4 straightforward:1 rather:2 describes:1 how:4 nontrivial:1 ntnu:2 pure:3 instead:1 simplicity:2 fr:1 replacing:1 algebro:3 earlier:1 derived:2 gardner:4 consolidation:1 applications:7 birthday:1 lax:5 mag:1 waves:4 dibenedetto:1 derives:1 constants:1 branches:1 liquid:1 whenever:3 quoted:1 explicit:4 green:3 sect:3 fundamental:2 decreasing:1 pleasure:1 order:6 se:1 restriction:1 deck:1 hierarchy:12 indeed:1 insight:1 mainly:1 years:1 paper:1 including:2 statistical:2 existence:2 satisfies:13 cole:27 its:5 solitary:1 rapidly:1 thank:1 ln:5 interesting:1 solving:2 writing:1 systems:3 researches:1 covered:1 norway:2 setting:1 non:1 pego:2 return:1 auto:2 acklund:3 introduce:2 scaling:1 mention:2 they:2 acta:1 trondheim:1 multidimensional:1 yu:1 developments:1 deift:1 2v:2 finite:1 dirac:1 name:1 goldstein:1 always:1 university:6 revert:1 perturbing:1 sufficiently:1 bielefeld:1 die:1 found:1 2n:1 differential:25 edinburgh:1 doing:1 series:2 idea:1 related:3 inverted:1 isospectral:1 toda:3 literature:1 obtains:2 funct:3 our:5 out:1 shown:1 ψxx:3 nonoscillatory:1 space:3 gradient:1 restricted:2 furthermore:2 since:3 rev:3 denotes:1 drazin:1 may:1 acting:1 investigation:2 rb:1 surprise:1 rn:17 ri:1 math:26 shows:2 illustrating:1 theory:8 singularities:1 surveys:1 gesztesy:21 quite:1 quart:1 nth:1 york:3 monographs:2 bulla:1 v0:4 pairs:1 r2:4 could:1 omit:2 counterpart:2 turn:2 assumed:1 hence:3 generalizations:3 first:5 origin:1 already:4 xn:2 reveals:1 miura:22 variables:2 number:1 moritz:1 restrict:1 instances:1 xx:3 another:1 calculational:1 precisely:2 open:1 illustrate:1 given:2 nullspace:1 introduction:3 eqs:1 system:3 relations:4 their:2 appl:5 vxx:1 calculations:3 realization:1 zxx:1 siam:1 structures:1 final:1 observations:1 holden:16 relationship:1 johnson:1 shallow:1 serve:1 teschl:2 part:3 x2:3 x3:1 translation:1 x1:1 convinced:1 than:2 vxxx:1 diffusion:2 treatise:1 showed:1 dans:1 limiting:1 preparation:1 classes:1 were:1 kumei:1 seminal:1 motivation:1 symmetries:1 rewrite:1 footnote:1 boston:1 topics:1 generalization:1 factorizations:1 seen:1 null:1 clearly:1 karl:1 blaszak:1 florin:2 petviashvili:6 concrete:1 studying:1 60th:1 note:6 instance:3 potential:4 so:1 analogs:1 rediscovered:3 kac:3 formulas:1 continuous:2 multiple:1 trace:1 investigations:2 viscosity:3 birkh:4 most:1 boltzmann:2 involving:1 germany:2 preliminary:1 pair:2 probabilistic:1 exact:1 soliton:2 prolongation:2 considered:3 clear:1 later:3 flow:1 schweiger:1 wick:2 points:1 exp:7 occasion:1 physics:3 bateman:2 fact:2 laws:4 precise:2 emerging:1 nonuniqueness:1 bluman:1 show:2 german:1 supported:1 analogously:1 rediscovery:1 focusing:1 relation:2 solutions:20 wahlquist:1 principal:1 impact:1 based:2 knowledge:1 title:1 basel:3 lemma:7 only:4 going:1 coefficients:1 developed:1 parabolic:1 hopf:28 his:6 notation:1 dependent:1 cannon:1 de:10 fluid:2 ssr:1 closely:1 dy:5 dt:1 ds:1 reveal:1 evolution:10 kadomtsev:6 textbooks:1 arxiv:1 acknowledgments:1 nauk:2 characteristic:1 uncover:1 solitons:2 kernel:1 requirement:1 constructing:1 exists:1 see:9 result:2 discussions:1 close:2 best:1 lancaster:1 satisfying:4 commutation:2 away:1 irrotational:1 eorie:1 mem:2 trans:2 between:9 geometric:3 reading:1 approach:1 discovery:2 notice:1 recently:1 uux:4 extend:2 nature:2 importance:1 p2n:4 however:4 vanishing:2 comm:3 solv:1 modeling:1 amer:6 ker:1 both:2 reverse:1 limits:1 many:2 taking:1 display:1 2θx:1 connection:1 became:1 forsyth:5 ernst:1 decreusefond:1 expression:8 monograph:1 cj:1 ch:2 abbreviate:1 simple:3 address:2 corresponds:1 dimensional:6 analyzed:1 mkdv:24 moreover:3 throughout:2 diff:1 society:1 pp:5 transformations:9 monthly:1 moerbeke:3 distributional:1 due:1 been:6 defined:1 much:1 interest:1 collected:1 ph:1 pn:2 treatment:1 oth:1 addison:1 direction:1 corresponding:2 misprint:1 tomei:1 concerning:1 remark:4 gap:1 greifswald:1 fritz:7 observe:1 6v:2 mail:2 c2:1 c1:1 careful:2 those:1 case:8 p3:1 multi:5 p1:1 akad:3 value:3 rectangular:1 aim:1 while:4 suppose:3 behavior:1 applies:1 revisited:1 study:2 procedure:1 coupled:1 vol:4 vi:1 formulation:2 thus:1 uxx:1 iv:1 ii:3 soils:1 reads:6 uhe:1 vt:12 ramifications:1 vx:10 technology:1 different:2 φt:1 grant:2 φx:6 potthoff:1 thesis:1 lett:3 shorter:1 html:1 arguments:1 hierarchies:6 several:2 ludwig:1 development:2 independent:3 used:1 columbia:1 context:2 functions:1 µxx:1 possible:1 driven:1 norwegian:1 moving:1 purpose:1 student:1 infinite:2 frequently:1 identity:4 recent:3 shortly:1 no:6 well:4 analysis:2 obviously:1 burgers:27 without:2 components:1 convenient:1 landmark:2 model:4 dimension:1 gelfand:2 just:2 being:1 generally:1 underlying:2 drinfeld:1 immediately:2 comput:1 scattering:2 yet:1 kondratiev:1 preprint:1 sciences:1 auser:4 had:4 operator:2 book:1 extends:1 board:1 easy:1 theorem:9 prominently:1 extensive:1 transformation:29 real:1 race:2 aspects:1 advances:1 term:3 cf:7 background:1 press:3 turbulence:3 bit:1 occurring:1 acquainted:1 follows:6 reduces:1 exploit:1 communications:1 korteweg:8 integrals:1 evolutions:1 become:1 stationary:1 mathematical:6 reidel:1 www:2 representation:1 methods:5 classical:2 lectures:1 some:16 acad:1 respect:2 kdv:38 proofs:1 ourselves:1 scale:1 uniqueness:1 phenomenal:1 onde:1 though:1 schr:4 benth:2 providence:1 critical:1 connecting:2 assuming:4 yields:1 proc:2 saab:1 biology:1 noise:1 kruskal:4 use:1 wesley:1 nederl:2 although:2 relating:4 properties:1 simpler:1 usa:1 extension:3 algebraic:1 discussed:2 o:2 ou:1 introduced:2 considerations:2 soc:7 cambridge:6 kuznetsov:2 into:2 schappacher:1 integral:1 functional:1 appropriate:1 weather:1 references:2 url:2 elementary:2 actually:1 techn:1 canal:2 van:3 additional:2 transfer:4 there:2 question:1 transform:1 long:3 start:1 conservation:4 aerodynamics:1 notices:1 viscous:4 was:10 unal:1 function:16 considerably:2 form:4 mehmet:1 denoting:1 but:5 gaussian:1 volume:1 heat:13 construction:2 russian:1 line:1 he:5 instructive:1 uu:1 ut:4 up:1 dordrecht:1 liouville:1 un:1 limit:2 time:1 problem:4 define:9 similar:1 called:3 sturm:1 phil:1 proved:2 int:1 countably:1 abstract:1 proven:1 twist:1 engineering:1 initial:3 relates:1 supersymmetric:1 curl:1 identities:1 constructed:1 helge:6 streit:5 fixing:1 when:2 detail:3 application:3 interested:1 details:3 papers:1 department:2 mathematics:2 er:1 operators:3 tic:1 cauchy:1 thereafter:1 missouri:4 problems:2 polynomials:1 n0:1 generated:1 dekker:1 implies:1 using:2 assume:3 vries:8 equivalently:1 estabrook:1 demonstrates:1 far:1 dover:1 requires:1 rep:1
|
solv-int9812026.txt |@word ptn:4 sci:1 consider:4 secondly:1 skii:1 eds:2 2ig:1 gn:38 expressions:1 research:2 ptr:1 whose:1 inverse:1 zone:1 equivalence:9 tr:113 tn:34 finally:4 c5:2 elliptic:1 under:1 analogous:1 pickering:2 g3:1 g2:1 g1:1 g0:2 linked:1 reader:1 choice:1 ma:1 emphasized:1 exact:3 pt1:1 pt0:1 generalised:1 entire:1 dubrovin:3 riemann:4 solves:4 hamiltonian:1 notes:1 enol:1 solution:8 t0:69 leave:1 vector:2 science:1 relation:6 div:2 originally:2 solutions:32 zn:2 employing:2 consistent:2 edu:2 direct:1 modified:1 second:4 follow:3 further:2 canonical:2 bilinear:1 established:2 fℓ:4 invertible:1 section:13 http:2 gj:3 poles:1 new:5 ˆj:1 method:3 ˆn:1 satisfy:2 homology:1 degree:2 mem:1 respectively:6 equals:1 here:1 water:1 address:2 along:1 equations:19 obtained:5 remark:2 divisor:1 studied:3 periodic:4 g2n:1 geng:3 pxx:4 classification:1 technique:1 treatment:1 ipq:3 apply:1 univ:1 ψx:6 usa:1 recalling:2 contains:1 quasi:3 ψt:2 next:12 few:5 linear:1 krishnan:1 conservation:1 type:2 vj:1 more:3 introducing:1 th:1 gohberg:1 solitons:2 ap0:13 hydrodynamique:1 odinger:5 curvature:7 pfn:3 ip2:2 berlin:2 appendix:1 normalized:1 particular:4 known:1 hold:2 springer:2 valued:1 gℓ:4 integrating:1 recall:1 equation:23 det:2 reads:5 remain:1 nonlinear:9 starts:1 following:6 nonsingular:3 dec:1 mo:1 proof:8 f0:2 f1:2 f2:1 speciality:2 chosen:1 calculation:1 cited:1 smirnov:2 numbers:1 council:1 sense:2 conversely:2 algebrogeometric:4 νj:3 boussinesq:41 compactify:1 painlev:2 provide:3 holds:2 maps:1 ntnu:2 e2n:2 parameter:2 r2n:9 express:1 singular:1 suppose:7 after:1 derived:2 treatments:1 residues:1 cubic:1 applications:2 lax:2 coming:1 pqx:1 representations:3 fj:1 derives:2 data:1 compatibility:1 fn:14 recursive:3 sx:6 clarkson:1 third:1 explicit:4 yielding:1 su:6 st:1 rather:1 fundamental:3 definitions:2 subsequently:3 vhn:2 order:3 ito:1 closely:1 duke:1 hierarchy:45 developed:2 satisfied:2 japan:4 satisfies:13 still:1 its:10 solitary:1 derive:5 decay:1 ln:10 fix:1 solving:4 li:1 previously:1 html:1 choose:1 jacobi:1 mail:2 secondary:1 norway:2 deformation:2 yi:2 them:1 outlined:3 introduce:7 band:1 sψ:2 effects:1 trondheim:1 now:1 qhn:1 discuss:1 developments:1 easily:3 february:1 university:3 2d:2 2f:1 2g:1 2a:1 2b:1 2c:4 previato:1 found:1 2n:7 2h:1 2i:19 em:6 differential:2 related:2 operator:2 toda:3 literature:1 obtains:2 2hn:3 funct:2 our:3 special:2 er:3 matrix:6 space:1 furthermore:1 since:1 rev:1 denotes:3 content:1 sciences:1 adapt:1 rb:1 algebro:15 denoted:3 lecture:1 math:12 rational:2 wiley:1 theory:3 variant:1 enforcing:1 kaup:7 gesztesy:14 effect:1 nth:20 completely:1 base:1 nonspecial:2 york:1 dx:5 e0:13 definition:2 cycles:1 eriodiques:1 derivation:1 geometry:1 phrases:1 noted:2 turn:1 hence:7 inst:1 first:10 initial:1 symmetry:1 wave:3 waves:1 primary:1 date:1 xx:6 wronskian:1 ihn:3 ψxt:1 given:14 rewritten:3 similarly:1 introduction:1 πi:1 system:32 construct:1 their:5 appl:4 zeros:2 constants:13 brevity:2 hyperelliptic:6 vxx:2 holden:14 holomorphic:2 progr:2 recursively:2 proving:2 immediate:1 whitham:1 teschl:2 part:2 authors:1 x2:3 x0:63 vxxx:4 varieties:1 kind:3 fortschr:1 eor:1 was:2 stn:2 integrability:1 2fn:3 preparation:1 determined:1 were:2 symmetries:1 generality:1 ann:1 curves:1 sv:2 20a:3 20c:2 20b:2 need:1 seen:1 presque:1 any:1 zero:7 vanishes:2 latter:1 propagation:1 ideas:1 note:2 instance:2 104a:1 best:1 analogy:1 kawamoto:1 interior:1 kac:1 formulas:5 abbreviate:1 trace:1 normal:1 systems:3 birkh:1 algebraic:2 hirota:3 connected:1 representation:3 pair:4 homogeneous:2 contain:1 class:3 soliton:2 ifn:2 url:2 into:1 later:1 kn:46 physica:1 points:1 tech:1 exp:11 fact:1 laws:1 precise:1 akhiezer:3 reductions:2 supported:1 rth:2 implying:3 gauge:13 akns:44 uxx:2 βhn:1 find:1 principal:3 q1:2 q0:1 based:2 knowledge:1 basel:1 stud:1 lemma:1 only:4 explicitly:4 threefold:1 ambiguity:1 employed:1 circle:1 abelian:3 notation:3 means:1 dependent:11 familiar:1 between:5 aim:2 integrable:4 words:1 applying:1 ds:1 dp:2 dq:5 evolution:2 qt:1 qx:6 arxiv:1 factorization:1 contrast:1 ut:2 cℓ:1 fixed:2 musette:2 qn:2 body:1 bulla:1 set:3 qtr:1 differentials:4 connections:1 see:5 result:1 qtn:3 close:1 αp0:7 sel:1 bobenko:1 analog:1 subject:1 lancaster:1 αv:10 review:1 symmetric:1 written:1 un:1 various:1 µj:4 theta:8 geometric:15 approach:6 meromorphic:5 matveev:4 terms:3 shabat:1 qt0:1 qt1:1 uj:2 however:1 dµˆ:6 ωp:17 vanishing:1 no:4 key:1 solv:1 amer:1 last:1 many:1 wu:3 mathematical:2 etc:9 connection:3 poincar:1 contribution:1 genus:3 finds:2 monograph:1 otherwise:1 cj:8 cn:7 point:2 simple:1 cf:3 simply:1 polynomial:6 cr:2 considers:1 appeared:1 kp:1 specializing:1 pp:2 pq:4 transformations:1 pt:1 basis:3 addition:3 px:11 due:2 been:3 int:1 reduction:1 basic:1 utilizing:1 ak:1 define:11 conte:2 corresponding:9 quantities:2 xxx:1 2ip:4 2iq:4 fritz:2 observe:2 systematic:1 c3:1 c2:9 c1:22 careful:1 present:1 c4:2 case:11 p0:17 will:5 near:5 replaced:1 revisited:1 property:1 iy:2 real:2 iz:12 vf:1 iq:6 ip:7 ivn:1 thus:5 non:1 vn:15 iv:1 ii:1 ih:1 vr:2 vt:1 vx:8 technology:1 ig:2 compactified:1 develop:3 grant:2 φx:1 recursion:10 corresponds:1 lett:2 clearly:2 verifies:4 hierarchies:11 finite:4 higher:1 used:2 columbia:1 vvx:4 helge:1 norwegian:1 purpose:1 invariance:2 ablowitz:1 normalization:1 recent:3 schr:5 variety:2 well:2 ξp0:7 analysis:2 obviously:1 burgers:2 de:2 without:1 sets:2 lin:1 2gn:4 spherical:1 manifold:1 being:2 reviewed:1 transforms:1 tilde:1 λj:2 alternative:1 scattering:1 previous:1 adding:1 preprint:3 liu:2 zakharov:1 hℓ:4 auser:1 theoret:3 lattice:1 setting:1 combine:1 board:1 theorem:12 constant:2 dqn:1 operators:2 transformation:6 identical:2 aspects:1 eigenvalue:1 read:5 advances:1 inversion:1 period:1 finding:1 mathematics:3 confined:1 using:13 variants:2 intersection:1 mod:2 loss:1 dq0:2 dq1:1 identifying:1 follows:3 reduces:2 specific:1 δj:2 integrals:1 arbitrary:1 qxx:4 stationary:23 therein:3 www:2 leningrad:1 classical:35 people:1 some:4 2iα:2 b1:1 moreover:3 kdv:4 revs:1 explode:1 vol:2 scale:3 integration:15 does:1 eliminate:1 yields:3 refer:1 inserting:1 power:1 equivalent:7 dissection:1 use:1 bj:6 bk:1 inherent:1 properties:3 eaire:1 theorems:1 discussed:2 o:6 aℓ:1 regular:1 ψtr:2 ic1:1 introduced:2 moerbeke:1 considerations:1 soc:5 h2:1 h0:3 h1:2 sachs:2 references:3 sov:1 elementary:4 abel:1 methods:2 outline:1 van:1 additional:1 explict:1 there:1 u1:1 u0:3 start:2 ut1:1 sections:1 naturally:2 function:13 complete:1 form:1 simplifications:1 denoting:1 but:1 hu:1 hj:8 construction:3 hn:37 compute:2 ux:5 2πi:4 characteristic:2 uv:5 utn:2 ludlow:1 cim:1 ur:3 krichever:1 ωk:1 ωj:3 ωn:2 similar:1 detailed:1 dafermos:1 associated:6 defined:6 abstract:1 aj:5 35q55:1 denote:1 ap:2 periods:1 dζ:2 formalism:10 defines:1 again:2 functions:5 broer:1 polygon:1 ingredients:1 index:2 when:1 detail:1 interested:1 details:3 department:2 ign:11 νˆj:1 igj:1 νˆn:1 briefly:2 elements:1 missouri:4 problems:1 polynomials:2 a1:1 anal:3 gap:2 svn:4 independently:1 monic:2 assume:5 baker:3 curve:7 equivalently:3 35q53:1 time:11 n0:19 vestnik:1 starting:3 nuovo:1
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.