text
stringlengths 0
190k
|
|---|
solv-int9507005.txt |@word limited:1 lakshmanan:1 consider:3 magnetic:2 varying:1 results:1 fluids:1 research:1 whose:1 ohya:1 answered:1 those:2 stochastic:1 te:6 division:1 amplitudes:3 rise:3 account:1 wave:9 electron:6 summarized:1 difference:1 exact:2 condition:2 treating:1 hamiltonian:24 t2:2 applicable:1 enon:9 large:3 involution:1 angelis:1 small:2 inspection:1 upper:20 force:3 occurrence:1 haar:1 dealing:1 sign:3 integrability:14 alfv:1 earth:1 qualitatively:1 dynamics:5 canonical:3 nonlinear:14 developed:1 appear:1 trivial:1 section:1 expressed:1 above:2 contrast:1 coefficient:1 simultaneously:2 respectively:2 reported:1 free:1 along:2 equations:26 change:1 obtained:7 derivable:3 geophys:1 shift:4 studied:2 chang:1 suitable:1 changes:2 heiles:10 useful:1 propagations:1 modulated:2 decrease:1 redefining:1 unit:1 dne:2 plot:2 use:1 takes:1 ωh2:1 positive:12 ωh0:2 coupled:20 negative:12 next:1 mori:1 therefore:2 m2:1 type:2 theoretical:1 tions:1 odinger:4 berlin:1 normalized:3 particular:2 known:4 cases:5 hold:1 ahmedabad:1 potential:4 me:3 k02:3 equation:14 work:1 mi:2 mt:1 values:12 following:1 example:1 ions:1 figure:8 give:3 arise:1 india:1 high:4 minimum:1 ter:1 allowed:2 normalize:1 needs:1 boussinesq:9 painlev:3 navrangpura:1 xˆ:1 regions:2 ordinary:1 parameter:17 may:3 ωe0:2 earlier:3 derived:4 containing:2 consequence:1 shukla:1 waves:18 henon:1 correspond:1 so:1 order:1 cs2:1 indeed:1 satisfied:3 years:1 symbols:1 thermal:3 motions:1 omitting:1 captions:1 kinetic:7 still:2 write:1 group:13 directional:3 dr:1 zˆ:2 coordinates:1 systems:4 defining:1 non:2 good:1 thereby:2 investigated:1 band:1 identically:1 vm2:2 represents:1 term:2 magnetoacoustic:10 always:2 presented:1 mode:10 each:1 acoustic:1 2n:1 side:1 homogeneous:1 differential:1 energy:8 reduce:2 related:3 frequency:16 laboratory:1 approximated:1 eq:22 special:3 shown:1 space:2 res:1 furthermore:2 since:4 rev:2 denotes:3 increase:1 investigation:1 π2n:3 ref:1 math:1 shows:1 linear:4 interactions:1 differ:1 governing:5 standard:1 completely:4 necessarily:1 finite:2 e2:2 derivation:1 similarly:1 but:3 motion:8 equa:1 hence:2 first:1 number:4 2a2:2 directly:1 open:1 given:6 perturbation:2 πe:3 introduction:1 eqs:8 πn:3 system:3 relations:1 their:1 perturbations:3 structures:1 gives:2 a31:1 exactly:2 x2:4 x3:1 x4:1 kind:1 second:2 classes:2 amplitude:2 rao:5 vte:4 conjugate:1 need:1 clearly:2 complete:2 latter:5 δne:1 k0:3 absorbed:1 generalized:7 electric:1 normal:3 any:1 goldman:1 beta:1 regular:1 2vm:4 letter:1 mach:3 soliton:1 considered:1 gyro:1 physica:4 points:1 electrons:1 exp:1 narrow:1 velocity:1 vries:1 fact:4 show:2 relation:3 solutions:4 substituting:1 d2:8 d0:16 ratio:1 parameters:11 should:4 only:2 explicitly:6 coefficients:2 factor:1 integrable:8 hamiltonians:3 dn:2 get:1 dependent:1 de:6 fluid:1 dv:7 dt:2 admissible:1 d52:1 stability:1 evolution:1 continuum:1 fields:2 arxiv:1 analytical:3 satisfy:1 exists:1 frame:1 signs:2 observed:1 discussions:1 cold:3 invoked:1 definite:5 written:2 determined:1 various:1 boundary:2 conditions:3 terms:5 nature:1 however:2 eb0:1 modulational:1 solv:1 separately:1 both:4 essentially:1 many:1 stenflo:4 conclusions:1 propagation:8 uni:2 magnetosphere:1 temporal:1 otherwise:1 relevant:2 cn:4 conclude:1 corresponds:6 dimensional:4 cs:3 respect:3 rep:1 indefinite:4 due:1 been:8 defined:2 magnetized:10 describes:1 slowly:1 expected:1 direction:2 6d:1 coherent:1 external:1 astron:1 plasmas:8 present:3 case:13 kaufman:1 novel:3 unlike:2 pram:1 value:1 while:1 b02:1 replaced:1 christiansen:1 cva:1 va:2 a22:1 a24:1 vg:2 chaotic:1 thus:1 vm:6 different:5 author:1 radiation:1 same:3 wherein:2 shifts:1 complex:1 dimensionless:1 physical:1 used:1 hand:5 driven:14 ion:4 recent:1 weakly:3 schr:4 modes:4 keeping:1 acknowledgement:1 well:4 analysis:3 sets:1 coordinate:3 ae:4 usual:4 when:3 obtain:5 thanks:1 λe:1 turbulence:2 momenta:3 speed:5 yet:1 note:6 density:5 seems:1 weiss:1 source:1 other:6 plasma:11 take:1 march:1 around:1 possible:3 possibly:1 fusion:1 using:1 necessary:1 like:2 particle:1 follows:3 reduces:1 specific:1 korteweg:1 either:3 integrals:1 arbitrary:6 become:2 stationary:9 reduced:2 indications:1 right:1 classical:2 some:2 springer:1 b0:3 b2:6 scripta:3 provided:2 lead:1 shall:1 extensively:3 conservative:1 wavenumber:3 does:1 yields:1 meanings:1 tabor:1 bn:4 bi:1 pressure:2 instability:1 super:1 fordy:1 sub:1 theorems:1 lieberman:1 remains:2 important:1 introduced:1 considerations:1 significant:1 maxwell:1 into:1 integral:4 three:1 en:2 references:1 determine:1 letts:2 there:2 question:2 reduction:1 long:2 dispersion:20 quadratic:1 low:6 function:2 elsewhere:1 form:8 jul:1 longer:1 qualitative:1 ponderomotive:3 ωh:5 below:2 limit:3 va2:1 called:1 regimes:8 bearing:1 associated:6 int:1 abstract:1 general:2 dξ:12 together:1 wavelength:2 corresponding:3 regime:1 functions:2 no:1 whereas:5 hybrid:20 ne:2 field:5 valid:2 details:1 spatial:1 kinds:1 problems:1 a2:2 bounded:1 fedele:1 4πn0:2 independently:1 lichtenberg:1 2d0:1 physics:1 pseudo:1 governed:5 mass:1 vg2:1 time:1 n0:1 having:2
|
solv-int9507006.txt |@word partial:1 consider:8 pointing:1 magnetic:3 nauchn:1 results:1 leads:2 commute:1 generalize:2 montr:1 ga:1 primes:1 inverse:1 const:3 calculate:3 aug:1 δhk:2 present:3 th:2 under:7 semenov:2 analogous:1 γf:2 case:9 g2:12 g1:17 very:1 multi:1 geometrical:1 witten:1 every:3 matrices:1 deformations:1 condition:3 hamiltonian:28 turns:1 dif:5 itep:1 solution:1 try:2 vector:5 science:1 small:2 reyman:2 wronskian:2 integrability:3 odd:1 theory:3 established:2 appear:4 brackets:7 deeply:1 section:7 above:1 3b:3 3a:2 method:1 exercise:1 body:1 component:2 water:2 groups:3 represented:1 blinov:1 equations:14 change:2 deduced:1 shansky:2 institute:2 lomi:1 leaves:1 allows:2 reports:1 leaving:1 loop:3 poisson:13 pick:1 action:14 useful:1 projection:1 family:7 explained:1 f2:18 univ:1 virasoro:7 derivatives:3 takes:1 would:2 prove:2 substitutions:1 approach:1 therefore:4 associated:1 theoretical:1 sort:1 nauka:1 operators:11 occurred:1 correspondingly:1 particular:2 projective:1 iii:5 td:1 springer:1 isomorphism:1 recall:1 equation:21 antonov:1 infinitesimal:1 obvious:1 marshakov:1 following:6 making:1 arrive:2 example:1 stimulating:1 proof:2 f1:23 compare:2 give:1 preserving:4 suggestions:1 lψ:1 procesi:1 occur:2 coalgebra:7 end:1 dww:8 rather:1 s1:11 get:4 write:3 maps:1 ordinary:1 parameter:1 csp:3 classify:1 product:10 algebra:28 may:5 orbits:13 residues:1 lax:9 waves:2 multiplication:1 representations:1 types:1 fordy:1 dynamical:7 third:7 element:11 so:3 representation:7 first:11 af1:2 help:2 hierarchy:3 developed:1 versal:1 choose:1 rubtsov:2 paper:4 mentioned:1 existence:1 its:6 before:1 derive:2 group:9 thank:1 interesting:4 affine:3 forms:2 kuznetsov:1 systems:17 derivative:1 main:1 might:1 marshall:1 non:6 combination:3 introduce:2 isomorphic:2 mention:3 das:1 now:3 transparent:1 kirillov:2 concini:1 february:1 invariants:1 presented:2 hepth:1 2f:10 ussr:1 l2:4 l3:3 2b:2 l1:3 found:2 notes:1 mean:2 arxiv:1 resλ:1 series:1 energy:1 related:6 used:1 our:11 mdw:1 special:1 out:3 ru:1 shown:1 lazutkin:1 matrix:6 space:19 res:3 since:1 denotes:1 hill:3 lecture:1 math:7 semidirect:9 sympletic:1 linear:7 associate:1 free:1 standard:6 tian:2 clarify:1 ect:4 subalgebras:1 anal:1 derivation:1 geometry:3 could:2 motion:2 place:1 βm:1 fian:1 generalizations:1 βi:2 purpose:1 indebted:1 there:3 symmetry:1 miura:4 variables:2 number:1 rosly:1 angular:1 zap:1 dispersive:2 given:3 introduction:1 adjoint:1 cheremushkinskaya:1 system:31 relations:3 their:1 conservation:1 expand:1 variational:3 structures:6 gives:4 pare:1 2ab:2 academy:1 moscow:2 kupershmidt:2 differentiate:1 authors:1 coefficients:3 ivanov:1 kind:1 was:5 second:12 were:1 powers:1 russia:1 w1:1 rewrite:3 unchanged:1 modern:1 generalization:4 eal:1 lie:13 take:4 coincide:1 kac:2 gδ:1 olshanetsky:1 normal:1 algebraic:1 connected:2 plan:1 pair:2 consequences:1 reminds:1 considered:3 clear:1 coincides:2 order:1 bracket:8 principle:1 physics:2 sum:1 dot:1 laws:2 show:4 reductions:1 recipe:1 spaces:1 find:5 q1:4 q0:2 q2:2 should:2 lemma:1 only:1 explicitly:1 indeed:1 integrate:1 integrable:8 circle:2 hamiltonians:11 local:1 centrally:5 continuity:1 his:1 means:5 df:2 de:2 aβ:1 closely:1 dw:2 densities:1 fields:2 differential:5 consisting:1 bf1:1 qk:1 fixed:2 crn:1 moduli:1 set:1 exists:1 variations:1 namely:2 w2:1 eliminating:2 discussions:1 sem:1 λi:3 analog:1 tensor:1 αz:1 written:2 between:5 αi:2 invariant:4 conditions:3 email:1 multiplied:2 terms:2 analogues:1 flow:1 vanishing:2 comm:1 jk:1 solv:1 configuration:2 inertia:1 restrictions:2 whole:2 experimental:1 ck:4 aa:3 diffeomorphisms:2 gorsky:2 conclude:2 simple:3 enriquez:1 cf:2 dimensional:1 mkdv:5 dependent:1 proved:3 cp:2 cv:5 described:1 publishing:1 geometries:1 skew:1 three:9 defined:1 reduction:1 describes:3 treat:2 algebras:1 define:1 dots:1 corresponding:9 formed:1 curves:1 func:1 c0:1 those:1 applied:2 p0:7 p1:3 arnold:1 will:2 while:2 replaced:2 momentum:1 situation:1 procedure:1 ix:1 orientation:4 coupled:1 vol:4 ir:5 them:1 ii:10 cocycle:2 dual:2 technology:1 different:1 author:2 formulations:1 same:6 parts:1 arguments:1 modification:1 hierarchies:1 higher:1 independent:1 extended:8 see:14 cocycles:6 flows:5 possible:1 moving:1 hydrodynamics:3 infinite:2 identity:1 expression:1 well:1 analysis:1 coordinate:1 dh2:1 dh1:1 subgroup:1 manifold:1 just:3 less:1 moments:1 obtain:3 actions:1 world:1 alternative:4 segal:1 preprint:2 classification:6 iω:1 add:1 transformed:1 lett:1 easy:3 theorem:2 mod:1 transformation:6 euler:3 generalized:5 real:1 aspects:1 integrals:1 supervisors:1 using:8 arbarello:1 moody:1 like:5 identifying:1 reduces:1 δl:5 δh:13 arbitrary:2 immersions:4 δb:6 δa:13 mathematical:1 methods:2 classical:4 sequence:2 some:2 back:1 elements:10 b2:2 b3:1 oscillations:2 kdv:16 ςi:3 comments:1 eliminate:1 2a:1 ba:3 bl:2 equivalent:3 each:2 bi:4 substituted:1 substitution:2 subtract:1 properties:1 central:5 extension:3 column:3 commun:3 dependence:1 compatible:4 extensions:3 introduced:3 conserving:1 h2:5 h3:1 h0:5 h1:9 functional:1 due:2 phase:3 appropriate:1 square:1 references:1 determine:1 operator:6 matrixes:1 hep:2 log:1 iβ2:1 pairing:3 u1:1 transform:1 u2:1 quadratic:2 way:3 scientific:1 resolvent:1 dx:13 combined:1 function:1 complete:1 form:12 but:2 hk:2 so3:2 construction:3 russian:2 line:1 he:1 made:1 orlov:1 smooth:5 up:1 us:14 problem:4 mechanics:3 ab:3 constant:1 ad:9 ag:7 af:1 int:2 certain:2 abstract:1 fχ:3 coadjoint:23 denote:1 conserved:2 exist:1 formulation:1 khoroshkin:1 formalism:1 commuting:8 check:2 physical:1 tedious:1 again:1 functions:5 no:5 when:6 application:1 setting:1 papers:1 mathematics:1 theor:1 ag1:1 conclusion:1 repeat:1 models:1 radul:1 polynomials:2 commutator:1 meaning:1 a2:13 structure:15 coupling:1 harnad:1 pseudo:2 orbit:1 χj:3 vishik:1 χi:6 appl:1 starting:1 original:1
|
solv-int9508002.txt |@word partial:1 consider:2 remarkable:1 maximum:1 trigonometric:6 eds:2 scalar:1 proposition:10 2ig:5 consists:2 expressions:2 nwo:1 inverse:3 depend:1 calculate:1 aug:1 tv:1 equivalence:1 should:2 presents:1 finally:2 does:1 tj:6 petersburg:3 under:2 eliminate:1 applied:1 conjecture:6 orthogonal:2 far:2 kω:1 continues:1 springer:1 choice:1 wishes:1 jack:15 lecture:1 difference:1 continued:1 condition:2 groups:1 differentiated:1 conjugating:1 riemann:1 hamiltonian:1 turns:1 notes:2 sklyanin:3 t2:4 solution:8 t1:6 leave:2 vector:1 progress:1 eigenvalues:3 equation:17 still:1 heckman:1 sin2:15 direct:2 sign:1 second:1 further:2 quite:1 theory:1 even:1 hide:1 section:4 selected:1 while:1 expressed:3 henceforth:1 version:1 poles:4 above:5 fractional:2 new:4 3g:26 equivalent:1 contrast:1 coefficient:1 degree:2 respectively:6 here:3 canonically:2 separation:12 q12:12 sing:2 november:1 strong:1 equations:3 change:4 z3:1 obtained:1 antisymmetric:3 institute:2 study:6 vectors:1 allows:5 expression:1 suggests:1 permutation:1 action:3 wetenschappelijk:1 uniquely:1 schur:8 via:2 transformations:1 n2j:2 substitution:4 replace:1 yitp:1 total:1 circumvent:1 linearly:3 tn:8 conventional:1 tn1:7 takes:2 would:2 analytic:1 distinct:1 positive:1 contains:3 uniqueness:1 next:1 few:1 m1:6 therefore:3 m3:5 m2:8 taken:1 onderzoek:1 simpler:1 type:1 theoretical:1 tk:10 separated:6 compositio:1 formally:2 fontanka:1 brings:1 operators:17 y2j:2 curvature:1 virtue:3 particular:3 known:7 cases:1 sekiguchi:2 graphical:1 none:1 tokyo:4 ed:3 h12:1 work:1 det:2 mj:1 erd:2 ms:1 learn:1 following:5 field:1 root:5 mo:1 proof:11 f1:4 f2:5 omit:1 challenging:1 calculation:3 permutations:2 validates:1 states:1 aomoto:1 caution:1 degenerate:1 sense:1 ratio:1 needs:1 gh1:2 gh2:1 rather:3 verify:1 discussion:3 orthogonality:1 mj1:1 pure:1 ordinary:2 parameter:3 sin:57 product:1 proc:1 description:1 algebra:1 may:2 after:2 singularities:2 plane:3 coming:2 fn:9 goal:1 eiky:1 natural:1 effective:1 light:1 mjk:1 bunkyo:1 provide:1 so:5 sn:7 allow:1 representation:5 integrand:1 order:7 prescription:1 restriction:1 produces:1 inami:1 over:1 choose:1 paper:1 through:1 y1:26 satisfies:7 y2:29 its:4 group:3 thank:1 singular:1 chosen:1 interesting:1 fix:1 conjugation:1 actually:1 kuznetsov:2 parts:2 systems:6 gel:1 deformation:2 them:1 yj:15 yn:2 safe:1 introduce:1 essex:1 mention:1 oxford:1 now:6 hall:1 wetensch:1 inversion:2 finite:2 always:1 university:3 2g:25 2b:1 each:1 2l:2 monomials:1 side:3 2k:1 subset:1 lectures:1 en:1 england:1 weight:1 series:5 hypergeometric:12 idea:1 used:1 t3:2 operator:16 qjk:2 obtains:2 quantum:14 our:4 beyond:1 special:1 out:1 conjectures:5 space:3 rep:2 since:7 acting:1 hill:2 rational:4 formula:8 rn:1 math:5 shows:2 inevitably:1 linear:3 2h1:1 qf:1 surveys:1 standard:6 completely:1 complicated:1 put:1 intermediate:1 publ:1 monographs:1 generate:1 definition:2 pairs:1 fixed:2 derivation:1 could:2 impose:1 excluding:2 voor:2 times:1 obscure:1 hence:1 guesswork:1 generalizations:1 strictly:1 first:5 origin:1 ϕn1:7 simplifies:2 symmetry:1 pn1:3 variables:21 rank:1 restrict:1 another:1 ring:1 precisely:1 sutherland:5 ser:1 given:12 rewritten:2 needed:1 families:1 unknown:1 adjoint:3 vandermonde:1 system:6 construct:2 their:2 assumption:1 calculations:1 exponents:3 speaking:1 terminates:1 explanation:1 ih1:4 contribute:1 immediate:1 calogero:5 part:1 differentiate:1 pnn:4 x2:4 x1:4 sˇ:1 separability:1 coefficients:3 third:1 zero:1 nederlandse:1 retracing:1 providing:1 distinguished:1 w2:2 supplement:1 motivation:1 w1:2 rewrite:1 cohen:1 argument:1 generalization:2 lin:1 already:1 tables:1 need:2 seen:2 st:3 any:1 tρ:2 lie:3 depending:1 convenient:2 self:2 converges:3 note:4 k2:1 generalized:2 finding:2 8m1:1 spectral:1 acquire:1 olshanetsky:2 shall:3 denominator:1 sequence:1 polynomiality:1 algebraic:3 beta:1 satisfying:1 remarks:1 analytically:2 fand:1 acknowledges:1 laurent:10 surprising:1 considered:1 torus:1 later:1 universiteit:1 points:3 ku:1 wiskunde:1 physics:5 sum:1 fact:4 drastically:1 akhiezer:1 12g:1 purely:1 spaces:2 solutions:2 organisatie:1 dimension:2 ground:2 q1:13 q3:11 q2:13 based:1 q4:1 parameters:5 than:4 moments:1 only:3 transcendental:1 factor:6 integrable:9 constant:7 achieve:1 do:1 dm:3 dominant:1 notation:4 dg:2 ϕn:7 dx:3 dy:1 geometric:1 dq:2 differential:17 factorization:2 method:2 common:2 characteristic:2 analytical:1 qk:2 qj:9 qn:2 riemannian:1 kernel:5 set:2 constructing:1 exists:2 j0:1 j1:3 j2:1 up:4 differentiation:2 see:8 w3:2 result:2 eliminating:1 ge:1 y3:2 steklov:1 eigenfunctions:5 fn1:9 subsequent:1 review:1 symmetric:13 state:2 use:2 simplest:1 probably:1 boundary:5 conditions:1 preserve:1 notice:1 triplet:1 terms:8 rims:1 iky:1 ikx:1 however:5 jn:8 jk:2 solv:2 come:1 regular:2 originates:1 cos:4 last:2 cot:18 limits:2 xλ:5 many:1 fuchsian:2 vanishing:1 russia:2 hψ:1 iv:1 oshima:1 whole:3 ck:7 cj:2 q13:9 simple:4 dimensional:2 simply:1 coordinates:2 sequences:2 cs:2 moreover:2 speak:1 considering:2 longman:1 pp:1 described:1 commutative:1 differs:1 n1n:1 invert:1 locally:1 three:2 int:2 calculi:1 arxiv:1 interest:1 pj:1 conjugated:2 algebras:2 topics:1 define:3 koornwinder:1 determinant:1 describe:3 corresponding:8 finishes:1 6g:1 sufficient:2 coherence:1 body:2 gen:1 observe:1 kalnins:1 2n2:1 2n1:1 general:3 present:2 case:23 pitman:1 p0:2 handling:2 akad:1 easier:1 will:2 technical:1 sln:1 replaced:2 evaluating:1 property:2 identical:1 changed:1 n2n:1 vol:4 vk:1 thus:6 yk:1 according:3 ii:5 reads:1 obstacle:1 jn1:3 ready:1 qj1:2 qj2:1 zonal:2 ig:3 containing:1 generic:1 make:2 same:3 weyl:1 complex:4 invariant:1 several:1 higher:2 independent:4 extended:1 singapore:1 published:1 nj:14 hand:3 parametrized:3 changing:1 n21:1 opportunity:1 normalization:5 eigenvectors:5 nevertheless:1 safely:1 well:3 obviously:1 academic:1 utrecht:1 coordinate:1 model:2 parametric:1 latter:1 usual:1 spherical:2 just:1 among:1 being:11 resp:2 shilov:1 obtain:3 valuable:1 transforms:2 using:3 hongo:1 scattering:2 previous:1 4m1:1 like:1 preprint:2 integer:4 sciences:1 tn2:4 macdonald:2 book:2 transformed:2 easy:3 theorem:12 dqn:2 skn:1 transformation:1 momentum:2 take:1 real:1 available:1 eigenfunction:3 read:3 results:2 possible:1 nonpolynomial:1 vacuum:6 press:2 immediately:1 unique:2 mod:1 meaning:1 ψn1:7 necessary:1 dq1:2 particle:1 follows:4 performing:3 ignore:1 deltafunction:1 steps:1 sesquilinear:1 reduced:5 mathematical:5 parity:1 satisfactory:1 right:3 classical:4 formulas:4 lagrange:1 some:3 algebraically:1 polynomial:26 trends:1 q23:9 b1:17 b2:4 dense:1 univ:3 though:2 integration:3 everything:1 behave:1 select:1 assuming:1 adjoints:1 scientific:2 power:1 kyoto:2 bn:8 q2m:5 bj:7 nederl:1 explicitely:3 feb:1 hilbert:1 stage:1 integers:6 about:3 world:1 mcgraw:2 prove:2 numerator:1 dependence:2 o:1 remains:1 a2:20 slightly:1 elyi:2 gamma:1 perelomov:2 computational:1 h2:19 h3:9 into:4 h1:24 integral:18 functional:1 suppl:1 hermitian:1 square:1 references:1 inverting:1 elementary:4 amsterdam:2 van:1 formulate:2 prepare:1 assumed:2 support:2 there:2 question:1 transform:2 pochhammer:1 workshop:1 low:1 way:3 triplets:1 ψn:18 sections:2 cancel:1 function:17 complete:3 form:10 denoting:2 but:2 hk:27 construction:2 hn:2 related:2 throw:1 regularized:1 informatica:1 wish:1 ωt:1 us:4 gindikin:1 international:1 liouville:2 limit:1 integrating:1 problem:10 more:12 similar:1 called:2 selects:1 detailed:3 proved:1 defined:6 abstract:1 aj:6 direction:1 denote:2 dξ:7 examine:1 nankai:1 relates:1 dη:2 face:1 commuting:5 sasaki:1 constructed:3 tedious:1 again:1 functions:15 nk:1 nl:1 nn:24 no:1 whereas:2 when:6 nx:1 acknowledgments:1 finish:1 other:4 statement:1 es:1 becomes:2 department:2 mathematics:1 company:2 expected:1 briefly:1 intend:1 models:1 symbol:1 become:1 problems:1 polynomials:31 lot:1 a1:19 a3:4 important:1 allowing:1 4g:4 variable:6 structure:4 opdam:1 bcn:1 factorized:5 assume:2 baker:1 factors:3 dσ:1 n1:36 n2:48 n3:19 having:1
|
solv-int9508003.txt |@word secondly:1 logarithms:2 partial:1 consider:5 corps:1 discards:1 7z:1 global:13 four:3 eds:1 generalize:1 computation:4 go:1 whose:2 certainly:1 system:3 aug:1 paris:3 eα:1 quadruple:1 does:3 erentiels:1 present:3 determinations:1 under:1 fronti:1 spec:1 divergent:2 ramani:2 contopoulos:1 very:2 implicitly:1 every:4 chapters:1 condition:3 solution:29 gauthier:1 small:1 relation:1 mati:1 smaller:2 neighborhood:2 zi:3 cosh:1 painleve:1 cost:2 j23:1 pass:1 rigorous:1 fonction:2 canonical:1 even:1 established:1 nonlinear:11 giving:1 annali:1 section:4 while:2 3u:2 3i:1 annals:1 poles:3 sur:6 establishes:1 sup:1 3c:2 new:5 method:12 satisfy:2 erieur:1 here:3 behaviour:1 favourable:1 les:2 sinh:4 represented:1 equations:21 change:2 conte:8 search:1 study:3 studied:3 allows:4 leaving:1 implement:1 settled:1 york:4 useful:1 family:6 requiring:1 merely:1 seven:1 scaled:1 emoire:1 natuurkunde:1 linearly:2 derivatives:1 asymptotic:2 would:1 prove:1 remains:1 positive:2 pedagogical:1 france:2 call:1 therefore:3 8u:1 type:5 more:3 lowering:3 formally:2 excluded:1 initial:1 envelope:1 tested:1 accept:1 particular:8 known:6 detects:2 iii:3 must:3 logarithm:4 valued:10 defines:1 recall:3 equation:37 des:5 mi:2 values:2 following:1 making:1 root:1 example:6 proof:3 f1:2 persists:1 cosmological:2 share:1 generically:4 respective:1 effectively:1 numbers:1 sense:1 times:1 evidently:1 guarantee:1 information:2 available:1 cours:1 requirements:1 painlev:25 provide:1 purpose:1 di:1 feature:4 occur:1 located:4 pura:1 types:2 ordinary:3 parameter:4 erale:3 irrational:1 singular:24 may:3 after:1 singularities:7 movable:19 applications:1 tries:1 plane:1 discard:1 constants:2 short:2 natural:2 clarkson:1 third:3 brussel:2 maybe:1 classe:2 cosmology:1 chazy:5 si:1 ones:1 so:3 fundamental:5 correlation:1 representation:3 order:19 restriction:1 seeing:1 indeed:4 despite:1 soon:2 course:3 london:1 motions:1 mentioned:1 existence:3 still:1 its:8 before:1 sciences:2 le:1 rapidly:2 thank:1 la:5 solving:1 fruitful:1 detected:1 parts:1 constitutes:2 main:1 defining:1 non:21 greater:1 cea:1 propose:1 sooner:1 number:2 framework:3 mezincescu:1 they:3 acta:2 singularity:10 now:2 possess:3 2u:2 february:1 finite:12 classified:1 2a:3 2b:1 each:5 soc:1 mean:2 arxiv:1 detect:1 ee:1 series:13 revised:1 ea:1 applicata:1 inhomogeneous:2 yvette:2 our:6 happen:1 extract:1 event:2 special:1 etat:1 analytic:1 space:1 robert:1 since:3 w5:1 reader:1 denoted:2 ref:7 math:7 shows:1 sinh2:1 earlier:1 linear:6 barrier:1 given:5 quite:1 admits:2 difficulty:2 reason:1 belgique:1 term:1 ask:1 detecting:1 e0:1 forbids:2 additional:1 definition:1 created:1 geometry:1 starts:1 could:1 rejects:2 linearized:12 place:1 twenty:1 consequence:1 first:8 already:2 features:1 symmetry:1 coming:1 powerful:1 etudes:1 rank:3 linking:1 peculiarity:1 simplified:2 unperturbed:1 impossible:1 xv:1 illustrate:1 differ:1 perturbation:10 service:1 similarly:1 introduction:2 leading:2 theoretische:1 least:3 eqi:1 their:3 perturbations:1 too:2 exponents:1 holomorphic:1 untractable:1 moscou:1 exactly:3 immediate:1 assumption:1 part:2 editions:3 x2:3 x3:1 x0:15 x1:4 than:9 x4:1 distance:9 showed:1 fuchs:8 require:7 second:6 future:1 contrary:1 sophie:1 perturbative:6 exhibit:2 table:1 concludes:2 needs:1 discussions:1 multivalued:2 null:2 any:3 emes:2 generic:1 oeuvres:1 depending:2 physique:1 isolated:1 note:1 instance:1 k1:14 εn:2 build:4 sufficiency:1 green:1 mir:1 εa:1 said:1 cnrs:1 sure:1 allow:1 centre:1 who:1 fails:1 algebraic:8 champs:1 regular:5 letter:3 remarks:1 analytically:1 class:2 laurent:3 χq:1 χp:1 considered:2 sometimes:2 physica:1 universiteit:1 points:18 physics:1 notion:1 reprinted:1 dover:2 probl:2 12c:3 particularly:1 cyclically:2 multicomponent:1 joshi:2 solutions:28 keywords:1 d2:1 find:1 principal:3 ses:1 waves:1 based:1 parameters:3 title:1 much:2 explain:1 should:1 lemma:8 only:10 going:1 integrate:1 xvii:3 local:7 do:1 ordre:3 above:2 notation:1 means:1 syst:1 de:7 likely:1 cannot:2 dz:1 negative:1 dx:1 expresses:1 dt:1 du:4 coth:4 eme:4 evolution:1 mixmaster:2 approach:1 differential:19 fixes:3 remove:1 qi:3 fixed:10 musette:3 coefficient:3 requirement:1 set:6 modulo:1 longmans:1 summed:1 detection:1 edition:2 depends:2 computer:1 radius:2 fail:1 paul:1 eres:2 permuted:1 satisfying:1 equal:1 eorie:1 smallest:1 bureau:11 lifshitz:1 closed:2 between:3 geometric:1 conditions:2 meromorphic:1 terms:2 august:2 nature:1 however:1 solv:1 group:1 received:1 cos:1 c21:1 classique:1 irregular:5 extracts:1 according:1 sensitive:1 connection:1 expense:1 comment:1 among:1 autour:1 english:1 co:1 conclude:6 simple:1 period:1 pole:4 polynomial:1 respect:1 diff:4 egrale:3 pp:8 addition:2 chapitre:1 locally:5 absence:5 been:1 int:4 cauchy:1 dont:3 logarithmic:1 interest:1 basic:1 empty:1 location:1 obtained:4 arises:1 families:6 xxv:1 both:1 imin:2 sufficient:2 2iu:1 remark:2 neumann:1 xλi:1 6u:1 bull:1 c3:1 c2:2 c1:1 denote:1 those:3 case:7 k2:9 exception:1 pacs:1 chap:2 value:1 will:1 near:6 suppose:1 applies:1 revisited:1 property:4 uniforme:1 ix:5 generate:1 vol:1 thus:3 them:2 4c1:1 ii:1 properties:1 examine:1 2uu:1 perform:1 recursion:1 same:5 poincar:2 shorter:1 complex:5 ince:2 units:3 several:2 higher:2 independent:3 used:1 infinity:4 occurence:1 v1:1 v2:1 introduce:1 characters:1 n23:2 landau:1 ablowitz:1 solide:1 nevertheless:1 well:2 analysis:3 without:7 solve:1 greatest:1 easily:1 model:4 arising:1 possesses:7 generally:1 grammaticos:1 obtain:1 proposes:1 bessis:1 immediately:1 λk:2 λi:2 yet:1 2k1:1 adding:1 villars:1 fuchsian:34 point:21 explanatory:1 except:1 quadratures:1 pickering:5 lett:2 easy:1 theorem:1 ruled:1 useless:1 vrije:1 around:2 represents:1 showing:1 possible:2 admitting:3 plenum:1 know:1 vacuum:2 integer:3 accepted:1 formal:5 necessary:3 follows:1 reduces:1 yields:4 arbitrary:5 xsi:1 essential:4 accessible:3 because:5 old:1 methods:11 classical:3 back:1 examples:4 moreover:1 est:2 kowalevski:1 erentielles:3 fixe:1 resonances:1 investigations:1 cχ:4 integration:2 2c2:1 ese:1 critical:16 critiques:3 refer:1 algorithmic:2 power:1 sixth:1 kruskal:2 2c:3 step:2 th:2 dictated:1 fordy:4 analysing:1 integers:1 about:1 extension:7 most:2 universe:1 ϕij:4 accepts:1 o:3 deserves:1 recherche:1 insufficient:1 book:1 converging:2 mathematical:2 mechanics:1 letters:1 presence:3 orders:2 into:1 three:4 en:3 references:1 often:3 acknowledgements:1 log:8 assumed:1 there:8 question:3 u0:1 long:1 pages:1 gif:2 bianchi:5 goursat:1 namely:2 ed:2 examination:1 was:1 function:2 hypergeometric:1 form:4 differences:1 analyse:1 but:6 failure:7 cedex:1 matematica:1 convergence:2 χs:1 segur:1 highest:1 rotation:1 evident:1 whether:1 multiplicity:1 avec:1 us:4 un:2 multivaluedness:1 boldface:1 detectable:1 define:2 called:1 detailed:2 taylor:4 indices:8 defined:2 abstract:1 troisi:1 general:11 globally:3 single:10 proves:2 exist:3 integrable:1 formalism:1 knows:1 compared:1 ematique:1 integrability:2 no:10 index:4 when:2 application:2 other:7 branch:1 test:17 mathematics:1 dienst:1 concerning:1 conclusion:1 requested:1 briefly:1 generates:1 vocabulary:1 condens:1 preceding:1 taub:1 a2:1 needed:1 structure:1 implies:1 practically:1 assume:2 4u:2 saclay:2 bulletin:2 volumes:1 imax:2
|
solv-int9508004.txt |@word consider:9 maximum:1 results:10 existing:2 continual:1 mild:1 grateful:1 constants:1 perturbations:9 gkσ:1 revealed:1 localized:18 gh:1 whose:1 uneven:3 aug:1 graph:1 stably:4 finally:1 present:1 under:4 ζx2:2 case:10 amplitudes:3 account:2 wave:4 affect:1 exact:1 adaptive:1 condition:3 presented:8 proc:1 solution:11 travels:5 small:3 lapse:1 force:1 consistent:1 pulse:10 cosh:6 go:1 second:1 traveling:2 dynamics:1 amplified:2 44d:1 even:1 nonlinear:6 section:7 near:3 expressed:2 above:1 3b:1 3a:3 method:11 coefficient:1 calculations:1 degree:3 climbs:1 mei:1 2kz:1 amplification:1 bj:1 sinh:1 concluding:2 along:3 equations:19 appears:2 change:1 spite:1 study:1 studied:2 2µx:1 ignoring:1 periodic:1 professor:2 resonance:1 suitable:2 studies:2 spatially:1 extra:1 explained:1 santini:2 rρ:1 select:1 derivatives:2 use:4 would:2 intensively:1 positive:2 jpn:5 single:2 negative:3 next:4 few:2 going:4 ayy:2 reductive:4 tell:1 more:1 fractions:1 introducing:1 solitons:6 stable:5 envelope:1 odinger:2 curvature:1 a21:1 trail:1 normalized:2 known:2 iii:1 logarithm:2 none:1 ρg:1 tokyo:3 equation:14 london:2 gathers:1 values:12 following:1 example:3 performed:3 control:1 give:1 calculation:2 pξ:4 organized:1 indicates:2 recognized:1 keep:1 occur:1 axis:1 decaying:2 travel:3 acts:1 feature:1 how:2 varies:1 fourth:2 instead:1 parameter:4 tension:1 express:1 may:1 after:8 derived:3 lump:1 taha:1 plane:2 ζt:1 deviates:1 faculty:2 ζx:1 ζy:2 summarize:1 data:1 parallel:1 engineering:2 explicit:1 bunkyo:1 complexity:1 martina:1 inhomogeneity:4 keeps:3 order:5 davey:4 typical:2 xj:1 least:1 pointed:1 displayed:1 soc:7 stability:8 paper:5 pulses:2 during:1 japan:3 satisfies:2 its:3 before:1 wadati:2 derive:2 group:2 decay:13 chosen:2 coordinates:1 fruitful:1 systems:5 mail:2 main:8 setting:1 them:5 runs:1 introduce:1 scaling:1 yz:1 effects:2 they:9 focus:1 grows:1 rotation:1 now:3 discuss:1 developments:4 term:11 finite:1 hereafter:2 university:3 hamiltonian:1 asano:1 sufficiently:2 2g:1 2a:3 2b:4 each:4 break:1 found:2 side:1 mean:4 development:3 square:1 ei:3 used:1 inhomogeneous:1 decays:5 our:1 out:1 shown:1 space:5 since:5 rev:3 iizuka:2 particles:1 get:2 ref:3 occurs:2 math:2 shows:4 linear:2 interactions:1 asz:1 midpoint:1 free:1 quite:5 mmm:1 clarify:1 reason:1 base:2 region:1 inevitable:1 nishi:1 interaction:1 derivation:1 recipes:1 computers:1 kivshar:1 ds1:7 motion:1 length:1 exponentially:6 hence:3 undergo:4 neglect:1 first:6 origin:4 initial:7 ono:1 feel:1 researches:1 variables:6 waves:1 number:1 philadelphia:1 restrict:1 xx:1 meshes:1 boiti:1 ky2:1 horizontal:1 size:1 sech2:3 given:3 perturbation:31 introduction:1 unknown:1 system:6 relations:5 1a:2 their:1 1c:3 1b:3 listed:2 monotonously:1 iat:3 siam:1 scheme:2 structures:10 final:1 store:1 1d:1 passed:1 discussion:3 incompressible:1 segur:1 authors:1 x2:1 x1:1 than:2 coefficients:1 determines:4 roles:1 kakutani:1 future:1 supposed:1 amplitude:3 gives:1 iωi:1 2kω:1 behaviors:2 fig:11 comput:1 rewrite:1 say:1 conjugate:1 tells:1 acceleration:1 quadrant:1 εy:1 petviashvili:1 gravity:1 yajima:5 potential:2 take:2 accuracy:2 gζ:1 play:1 experienced:1 shall:2 most:1 remarks:2 µx:6 soliton:4 considered:2 axx:2 kh:3 flow:9 physica:1 kr:7 kp:3 ku:1 velocity:8 ky:1 kx:3 vries:1 quantity:5 show:4 ki:13 relation:7 solutions:11 keywords:1 substituting:1 kx2:1 find:1 slow:2 ratio:6 parameters:4 situations:1 distributed:2 only:4 bases:1 subsection:1 integrable:1 his:1 goes:4 means:5 dependent:2 de:1 fluid:9 feels:1 cannot:3 dx:2 new:3 uy:2 dr:1 ds:5 becomes:2 evolution:1 kadomtsev:1 qy:1 qx:1 arxiv:1 acknowledgments:1 investigate:1 though:3 through:3 fixed:2 traverse:2 set:3 hξ:1 exists:2 ωt:3 observed:1 see:2 result:2 existence:1 discussions:2 recently:1 points:1 µy:6 2kr:2 pictures:1 away:1 irrotational:1 state:1 various:4 envelopes:1 between:10 drawn:1 boundary:7 αj:2 conditions:5 across:4 preserve:1 terms:2 takeshi:1 vertical:1 jp:2 solv:2 iki:1 both:3 pempinelli:1 many:2 taking:2 against:4 distinguished:1 ln:2 figures:1 variance:1 disappears:1 fokas:2 comes:1 conclude:1 reasons:1 asymptotically:1 leon:1 height:11 dimensional:2 directions:1 moreover:1 writing:2 considering:1 described:2 analogies:1 2kh:1 due:4 been:2 defined:2 much:1 slowly:1 basic:1 expected:1 choose:3 direction:7 deeper:1 quantities:2 miki:1 external:1 those:4 applied:1 k2:1 exponential:1 tanh:3 straight:3 nishinari:4 value:6 will:7 while:2 passes:2 identical:1 larger:1 played:1 sincere:1 surface:7 iv:1 ii:1 ih:1 ij:2 vt:1 owes:1 vx:2 disappear:1 different:2 φt:1 assure:1 φx:2 φy:2 φz:2 cross:1 same:2 complex:1 runge:2 modification:1 φj:1 gets:1 infer:1 higher:1 kutta:2 independent:1 investigated:2 peaks:1 cubic:1 numerical:11 effect:13 hand:3 kz:3 purpose:1 potentials:1 ablowitz:3 expand:2 yy:1 mech:1 schr:2 changes:2 analysis:2 observations:1 teukolsky:1 model:1 dimension:1 usual:1 less:2 generally:1 valuable:1 thanks:1 immediately:1 hongo:1 localize:2 reality:1 scattering:1 stewartson:3 previous:5 density:1 wei:1 point:2 simple:1 εn:3 attractive:3 yonezawa:1 mod:1 plasma:2 real:2 ripples:2 around:2 disappearance:1 five:2 press:2 using:2 part:3 αf:1 apart:1 necessary:2 like:2 semi:1 follows:2 velocities:4 korteweg:1 either:1 stationary:1 right:1 phenomena:1 calculated:1 b0:1 b1:1 b2:1 table:3 ourselves:1 df:1 dimensions:10 bottom:9 dgw:1 affects:1 opposite:1 integration:2 comments:1 behave:1 analyzed:1 gratitude:1 process:1 problems:2 2c:1 expansion:2 step:12 viewpoints:1 although:1 yamagata:3 analyses:5 2µv:1 properties:2 discussed:5 generated:1 o:2 simulation:1 addition:1 2ck:1 introduced:2 contours:1 perturbed:3 cambridge:1 into:6 numerically:3 ηj:1 three:2 phase:1 appropriate:1 because:3 proportional:4 spline:1 flannery:1 log:3 area:1 assumed:1 there:5 transform:1 long:1 dispersion:1 width:3 encouragements:1 low:1 lot:1 malomed:1 analyze:1 function:2 hx:1 hy:1 form:1 constantly:1 dips:1 but:3 lowered:1 line:5 highest:3 faster:1 inverse:3 applying:1 places:2 corroborate:1 characteristic:2 ωr:2 up:2 us:2 ωi:2 problem:1 laplace:1 detailed:3 ac:2 constant:2 int:2 certain:1 aj:1 conserved:1 simulations:2 physical:2 satsuma:2 functions:2 compared:3 qη:5 no:1 when:11 vanishes:1 qξ:1 other:7 role:1 spatial:4 department:1 deviation:2 briefly:2 kinds:1 exp:11 hirota:1 asterisk:1 variation:1 a1:4 a0:2 meaning:1 important:2 peak:7 hietarinta:1 variable:1 structure:5 longer:1 assume:2 physics:1 depth:1 time:9 vetterling:1 lett:3
|
solv-int9508005.txt |@word partial:1 consider:1 sci:1 dimentional:1 inverse:1 const:1 paris:1 th:3 under:2 urel:1 condition:10 look:1 sklyanin:2 list:1 solution:1 large:1 solved:1 vector:1 anal:2 unexpected:1 consistent:3 direct:2 integrability:8 uk:1 pass:1 even:1 established:3 what:2 nonlinear:2 stands:1 sum:2 3v:2 version:1 above:2 new:2 consisting:2 contrast:1 here:1 sine:6 equations:9 obtained:3 institute:1 studied:5 allows:1 classification:1 replace:1 apply:1 linearly:1 derivatives:2 usc:1 prove:1 call:2 type:5 more:1 nauka:1 nkc:1 becomes:2 correspondingly:1 particular:1 known:2 cases:1 equation:25 work:1 corrigan:1 following:4 zametki:1 weaker:1 cited:1 effectively:1 exclude:1 evidently:1 axis:1 rather:2 verify:1 acts:1 occur:1 criterion:2 sin:3 gordon:6 mat:2 algebra:3 replacing:1 earlier:2 applications:3 data:2 compatibility:3 stress:1 dynamical:1 third:1 computations:1 explicit:2 su:1 fundamental:1 order:5 holds:1 help:2 uτ:10 its:3 group:1 chosen:1 affine:2 forms:1 systems:1 researches:1 mail:1 dan:1 acklund:1 processes:1 introduce:1 framework:1 identically:1 discuss:1 2u:1 teoret:1 found:4 side:1 mean:1 homogeneous:1 differential:3 formulate:1 series:1 toda:5 investigated:1 quantum:1 our:1 really:1 ru:1 shown:1 matrix:3 admissible:1 looking:1 investigation:1 rk:1 foundation:2 after:1 theory:5 admits:1 completely:3 dirichlet:1 geometry:1 isn:1 ism:3 teor:1 first:1 initial:3 symmetry:20 question:1 variables:4 number:1 long:1 another:1 given:2 requirement:1 hyperbolic:1 introduction:1 system:2 least:1 their:1 statement:2 uki:1 academy:1 exactly:1 differentiate:1 than:1 kind:2 effective:1 painlev:1 uk1:2 classes:1 str:1 were:2 russia:1 symmetries:11 modern:1 turned:1 matem:1 say:1 any:3 uξξ:2 lie:1 latter:1 note:2 instance:3 k1:2 take:1 finding:1 unless:1 satisfying:1 nothing:2 workshop:1 don:1 consequences:1 considered:1 zamolodchikov:2 clear:1 coincides:1 exp:5 physics:1 particularly:1 supported:1 attempts:1 solutions:1 fifth:1 based:2 explain:1 should:2 only:2 integrable:7 means:2 famous:1 international:1 evolution:1 approach:4 arxiv:1 method:1 common:1 analytical:1 declared:1 set:4 exists:1 sep:1 imposing:1 turbulent:1 notice:1 connections:1 see:4 recently:1 subject:1 surfaces:1 uξ:2 uη:1 urses:1 state:1 simplest:1 invariant:1 boundary:38 conditions:17 ends:1 terms:1 shabat:4 attention:1 however:1 js:1 efficiency:1 solv:2 dependance:2 both:2 essentially:1 according:1 fiz:1 admit:2 passing:1 point:2 simple:1 connection:1 dimensional:2 mkdv:1 prilozh:1 article:1 respect:4 described:1 basis:1 been:3 much:1 algebras:2 vtt:2 describe:1 commutes:1 cos:3 else:2 func:1 derivative:1 c3:3 c2:7 c1:7 former:1 case:1 splits:1 unlike:1 value:10 will:1 suppose:1 property:2 mistake:1 vol:1 uxx:3 iv:1 vt:4 uxxx:2 grant:2 recursion:1 problems:6 vut:1 same:1 φi:1 finite:2 higher:11 independent:1 used:1 singapore:1 hand:1 infinite:2 prescribed:1 reflection:2 sssr:1 nevertheless:1 well:2 analysis:1 burgers:3 consistency:1 undertaken:1 possesses:1 usual:1 rietdijk:1 proposed:1 less:1 half:1 immediately:1 differentiation:1 scattering:1 vτ:2 sciences:1 zakharov:1 lattice:4 lett:2 theorem:4 transformation:1 aspects:1 press:1 imposed:1 saleur:1 necessary:1 follows:1 reduces:1 loses:1 either:1 arbitrary:2 acad:1 classical:1 some:1 examples:1 kdv:2 lead:1 subclass:1 proc:1 demonstrated:1 scientific:1 ufa:2 equivalent:1 tm1:1 constraint:3 discussed:1 o:2 compatible:19 involving:2 warner:1 dorey:1 presence:1 into:1 within:1 references:1 operator:1 nowadays:1 hep:3 there:2 u1:11 u3:1 u2:8 cauchy:1 ghoshal:1 ed:1 m1:1 was:7 complete:1 form:8 but:5 construction:1 russian:2 line:1 adler:1 partially:1 tarasov:2 ux:5 whether:1 ut:5 us:4 um:1 below:1 un:2 ui:3 utt:2 uj:1 problem:13 similar:1 proved:1 worthwhile:1 int:3 flow:1 abstract:1 received:1 general:1 sasaki:1 field:3 other:1 test:2 mathematics:1 out:1 june:1 variable:2 gap:1 kiev:1 implies:1 time:2
|
solv-int9509001.txt |@word partial:2 consider:3 gp:2 global:1 results:3 leads:1 mni:1 proposition:15 montr:2 computation:1 c2:1 row:1 inverse:2 calculate:1 send:1 former:1 petersburg:2 di2:2 degeneration:2 applied:1 straightforward:3 very:1 trigonometric:2 corollary:2 wishes:1 putting:1 jack:2 entries:2 difference:2 dil:3 3h1:7 din:2 3h3:6 solves:1 dik:3 turns:1 notes:2 sklyanin:2 solution:2 leave:1 involution:4 commute:6 elsewhere:1 announced:1 indices:3 m212:1 equation:1 ville:1 heckman:2 h13:18 h14:5 lyngby:1 h15:2 generalisations:1 integrability:5 theory:1 spectral:8 dissertation:1 sub:4 euclidean:2 section:3 m33:5 m32:9 expressed:1 new:3 3g:3 acknowledgments:1 satisfy:2 respectively:3 even:1 here:4 separation:4 address:1 concluding:1 quite:3 change:3 obtained:1 sending:1 remark:1 institute:2 studied:1 leaving:1 poisson:1 permutation:5 action:3 hospitality:1 involves:1 see:2 mij2:1 jm1:5 1st:1 use:2 dunkl:7 working:1 prove:1 give:2 dnj:1 m1:33 m3:43 ψm:11 em1:2 associated:3 type:5 theoretical:1 sort:1 discriminant:1 higher:1 operators:73 known:3 iii:1 keeping:1 tokyo:1 deformed:2 recall:5 h12:20 mn:1 mi:11 modified:1 superstructure:2 publications:1 following:19 trans:1 root:3 mx:3 proof:9 wojciechowski:1 stated:1 calculation:1 relativistic:1 permutations:3 autumn:1 numbers:1 sense:1 δil:3 needs:1 s3:1 verify:2 s1:26 acts:1 how:1 get:3 instead:1 explains:1 r2n:1 algebra:24 after:1 applications:1 succ:1 multiplication:1 parameter:2 author:2 explicit:2 mji:2 pdos:5 st:2 sk:1 sj:2 si:10 so:5 sn:10 sl:16 9h2:1 representation:1 2m22:1 order:14 restriction:4 s0:31 interpretation:1 help:1 over:1 a01:3 paper:3 through:4 letters:1 still:1 its:1 s2:26 supplemented:1 derive:6 group:4 symmetry:5 chosen:1 fix:1 coxeter:1 d32:1 coordinates:2 actually:1 kuznetsov:2 absence:1 systems:5 jacobi:2 hidden:5 djl:1 pjm:2 pjl:3 them:4 pji:1 pjk:3 rotations:1 3h2:6 introduce:6 a0j:4 hamilton:2 they:2 now:6 2s1:1 ebec:1 gets:1 hereafter:1 xli:1 always:1 university:7 hamiltonian:4 professorship:1 2z:1 2g:18 each:5 universit:1 x13:9 2k:1 schneider:1 arxiv:1 solved:1 related:1 constitute:1 elementary:1 quantum:16 operation:2 out:2 canada:1 shown:1 space:6 res:28 since:1 crucial:1 research:1 aji:1 acting:2 hill:1 rational:4 formula:3 rn:7 induction:1 math:3 shows:1 earlier:1 linear:4 2h1:2 frank:1 2h3:12 2h2:6 standard:1 small:1 york:1 j32:1 ask:1 iai:1 ruijsenaars:1 finite:1 definition:5 geometry:1 could:2 m21:17 m22:13 m23:18 motion:9 ordering:1 symmetrised:1 δij:9 δik:3 hence:2 oscillator:1 2m21:1 think:1 2m23:1 first:10 xj:13 xk:8 xi:23 xn:3 xl:2 nhl:2 variables:6 restrict:1 clear:1 done:5 construct:2 another:1 sutherland:2 given:1 bracket:1 guest:1 jeu:1 introduction:2 xij:8 system:19 relations:15 anyone:1 superintegrable:2 statement:4 final:1 6g2:3 gives:1 commutativity:2 4b1:3 4b2:1 proving:1 x2:78 diminish:1 x1:81 kind:3 showed:1 sections:1 second:2 kth:3 were:2 distinguished:1 published:2 supplement:1 mind:1 disjoint:1 mjk:2 orders:3 eal:2 lie:6 mik:1 mij:22 mil:1 calogero:17 h22:10 k2:6 k1:6 potential:2 take:1 lectures:2 unless:1 centre:2 algebraic:6 position:1 remarks:1 commutation:2 acknowledges:1 considered:1 ki:1 m231:1 hi:7 exp:3 physics:3 sum:1 fact:3 superintegrability:5 phenomenon:1 show:1 supported:2 notations:1 purely:3 relation:1 m31:12 x3:41 find:3 pkl:3 contruction:1 parameters:2 commutators:1 should:1 monomial:1 only:7 explicitly:1 generators:5 transcendental:1 jai:1 integrable:5 moser:15 ematiques:1 hope:1 do:3 dm:3 dj:7 dk:10 notation:1 means:4 de:3 ones:4 valuable:1 progress:2 combinations:2 qu:1 denmark:3 differential:11 2b2:7 2b1:18 common:2 contain:1 fixed:2 9b2:1 set:5 sep:1 δjk:3 δjl:3 j3:2 depends:1 result:1 existence:1 discussions:1 x12:14 dk1:1 dlj:1 symmetric:17 various:1 closed:4 between:2 invariant:2 luminy:1 x21:5 x23:14 notice:3 terms:1 rims:1 comp:1 jm:45 djr:1 solv:3 amer:1 thank:1 restrictions:1 last:1 2n:3 4h3:4 3j7:1 russia:1 pdo:1 σx:6 casimir:2 dkl:1 whole:1 dki:1 generalisation:3 groups:2 supply:2 simple:3 cf:4 dimensional:2 m13:4 m12:7 polynomial:2 table:17 described:1 commutative:1 basis:1 ai:7 treat:1 define:3 aj:4 corresponding:2 commutes:1 quantities:1 propositions:1 modelling:1 observe:1 kalnins:1 x2i:1 general:2 djk:2 present:2 case:9 multi:3 look:2 exponential:1 laplace:1 mlj:1 mli:3 mln:1 deformation:5 will:8 technical:2 while:2 aii:1 aij:21 situation:1 di:16 property:1 h3c:1 played:1 non:4 ii:9 ik:14 ij:10 il:1 limit:2 ig:1 verified:1 d12:1 grant:2 identities:1 make:1 same:7 any:1 parts:1 constructed:1 erdelyi:1 difficult:1 independent:9 used:1 yi:1 nil:1 i1:2 mkl:2 i2:4 identity:1 lower:1 reflection:2 well:6 analysis:1 obviously:1 coordinate:1 entry:2 model:5 otherwise:1 latter:1 spherical:1 being:2 when:1 rest:1 underlying:1 gdi:1 functionally:1 previous:1 doctoral:1 preprint:1 instance:3 m223:1 lett:1 easy:4 theorem:12 apart:1 transformation:1 real:1 iν:2 eigenfunction:4 easily:1 big:1 possible:2 harmonic:1 helpful:1 like:4 particle:2 m42:2 follows:11 m41:2 specific:1 12b2:2 integrals:13 m43:2 become:1 mathematical:2 because:1 school:2 classical:5 2h12:2 some:6 algebraically:7 understood:1 trends:1 b1:99 b2:62 moreover:2 bessel:5 demonstrated:1 refer:1 3b2:6 3b1:2 run:1 european:1 kyoto:1 bn:7 bj:18 bk:1 br:4 mcgraw:1 super:5 properties:2 pli:2 stage:1 x32:5 about:1 x31:10 a0:3 column:3 nijhoff:1 discussed:1 mutually:4 plus:1 introduced:3 soc:1 computational:1 statements:1 h2:86 h3:28 into:1 h1:78 integral:3 square:2 references:1 sov:6 operator:10 amsterdam:1 additional:12 there:4 question:1 mki:4 quadratic:6 way:1 was:3 function:5 hypergeometric:1 complete:3 form:9 leiden:1 m2:79 but:4 hj:7 hk:21 construction:2 hn:17 hl:2 partially:1 october:1 applying:1 whether:1 inside:1 us:7 below:2 those:2 problem:9 called:1 examples:1 mechanics:1 separated:1 pij:43 pik:5 pil:1 pim:1 int:3 abstract:1 describe:1 denote:2 together:2 work:5 commuting:7 defines:2 functions:14 no:1 open:1 fixing:1 nai:1 generally:1 vanishes:1 other:2 role:1 details:1 department:1 explaining:1 repeat:1 models:1 miscellaneous:1 polynomials:4 commutator:1 a2:2 variable:3 structure:1 opdam:1 vadim:1 coulomb:1 assume:1 d22:1 rather:1 rule:1 6b2:1 6b1:2 4j:1 2j3:1 recherches:1 4g:3 nxi:1 having:1
|
solv-int9509002.txt |@word sector:2 positions:1 concept:1 remarkable:1 represent:1 caused:2 results:2 leads:1 consists:1 inverse:9 depend:1 technique:2 preserved:2 divergent:1 applied:1 orthogonal:2 very:2 wave:13 difference:10 exact:1 annihilated:1 level:3 turns:1 hψn:1 involution:1 vector:1 annihilates:1 small:2 eigenvalues:1 work:1 go:1 integrability:3 dynamics:2 section:1 birk:1 en:5 above:1 new:1 consisting:1 coefficient:1 led:1 here:1 quite:1 equations:3 change:2 obtained:2 sending:2 dividing:1 shift:2 studied:2 products:2 permutation:5 gambardella:2 composed:1 projection:1 hermite:1 viz:1 readily:1 additive:1 dunkl:4 commun:2 positive:1 next:1 few:1 going:1 ψn:6 taken:1 until:1 more:5 lowering:1 hahn:1 becomes:1 operators:6 hψ0:1 known:2 poles:1 must:1 tokyo:2 science:1 equation:1 mn:17 oscillator:1 modified:1 following:1 trans:1 proof:1 division:1 relativistic:9 permutations:1 states:3 dxn:3 numbers:1 rescaling:1 occur:1 information:1 needs:1 end:1 rather:2 discussion:1 nontrivial:1 symposium:1 ordinary:2 parameter:3 product:4 may:3 reps:1 oscillators:6 after:6 dx1:3 4th:1 lax:1 date:1 ryj:1 dynamical:2 light:1 schneider:2 explicit:1 element:1 sj:5 so:4 representation:1 order:2 wigner:1 indeed:2 over:2 satisfied:1 years:2 course:1 through:1 guadalajara:1 y1:2 japan:2 y2:2 its:6 before:1 boson:3 actually:1 parts:1 degrees:1 systems:1 derivative:5 deformation:2 combination:1 yn:2 finitedimensional:1 solubility:1 now:3 discuss:1 developments:1 eigenvalue:3 term:1 university:1 hamiltonian:14 labeling:1 iff:3 l2:2 each:3 found:1 monomials:6 hinges:1 characterized:2 differential:1 financial:1 weight:2 energy:2 gaussian:1 society:1 combining:1 quantum:9 eq:6 out:1 shown:2 matrix:3 solved:2 restricted:1 furthermore:1 since:1 crucial:1 denotes:2 particles:6 acting:3 rational:2 rn:3 integrated:1 interchanging:1 provide:1 linear:1 diagonal:1 standard:3 ruijsenaars:9 e0:4 definition:1 interaction:3 nonnegative:1 motion:4 βg:1 hence:2 promotion:1 onto:1 eqs:3 first:1 xj:33 xk:13 already:1 xn:4 symmetry:2 relate:1 number:1 precisely:1 sutherland:2 size:3 given:7 introduction:1 leading:1 interact:1 sep:1 system:14 relations:1 2ωa:1 continuous:1 2aj:1 immediate:1 part:1 probably:1 x1:5 than:1 coefficients:1 sections:1 suslov:1 second:1 submitted:1 annihilation:4 determined:4 pairwise:1 were:2 gives:2 minus:1 ann:1 spectrum:9 generalization:1 conjugate:1 seen:1 recover:1 clearly:1 viewed:1 symmetrized:6 lie:1 zero:3 convenient:1 latter:1 sciences:1 intends:1 potential:1 triangularity:2 switching:1 olshanetsky:2 denominator:1 involving:1 pair:1 unorthodox:1 commutation:1 observation:1 clear:2 coincides:2 inferred:1 proceedings:1 exp:4 fact:4 precise:1 incorporate:1 discovered:1 relation:1 substituting:1 analogue:3 brink:1 ground:8 parameters:3 basel:1 enough:1 should:2 only:2 explicitly:3 surveyed:1 factor:1 integrable:5 do:1 dj:3 means:3 simplest:1 overall:1 feels:1 despite:1 boils:1 meguro:1 interpreted:1 gen:3 regarding:2 transposition:1 arxiv:1 acknowledgments:1 multiplying:1 computed:1 achieved:1 observed:1 see:2 terms:1 interacting:3 infers:1 below:1 symmetric:4 state:8 closed:1 between:4 invariant:3 conditions:2 available:1 recently:5 august:1 nature:1 however:1 key:1 solv:1 amer:1 originates:1 askey:1 both:2 essentially:1 diejen:3 x2j:3 many:1 quantization:1 contribution:1 expression:1 detailed:1 cn:1 nonrelativistic:4 simple:1 overview:1 corresponds:1 except:1 dimensional:1 conjugation:1 polynomial:4 ordered:2 throughout:1 math:10 basis:2 been:3 much:2 asymptotics:3 algebras:1 pn:12 komaba:1 describe:2 corresponding:7 subspace:1 hmn:4 confinement:1 external:7 stems:1 irrelevant:1 present:2 case:3 replaces:1 expanded:1 remaining:1 will:2 harmonic:8 aid:1 property:1 iz:5 coupled:2 vol:1 vj:14 thus:2 ii:2 reads:2 eigenfunction:3 author:2 same:1 poincar:1 complex:2 resulting:1 difficult:1 independent:4 literature:2 infinity:2 numerical:1 nj:5 nk:1 uses:1 introduce:3 invariance:2 recent:1 well:3 without:3 solve:1 model:24 arising:1 calogero:16 usual:1 just:1 monomial:3 obtain:1 integer:1 speed:1 auser:1 point:1 had:2 emphasis:1 setting:2 transformed:3 lett:1 easy:1 theorem:1 guarantees:1 excited:3 real:1 rescaled:1 around:1 replaced:1 iβ:1 possible:3 spanned:1 cf:1 matters:1 using:3 apart:1 appearing:1 particle:4 interestingly:1 δj:1 integrals:1 essential:1 mathematical:1 destroying:1 classical:6 creation:5 some:1 back:1 cancel:1 deduce:1 respect:3 nonzero:1 describing:1 does:1 yields:2 eigenfunctions:11 expansion:3 step:3 reduces:1 freedom:1 discussed:1 factors:1 o:2 regular:1 introduced:3 gamma:2 xnn:1 perelomov:5 soc:1 rev:1 statements:1 presence:1 down:1 hermitian:1 square:8 references:1 operator:9 proportional:1 ixj:2 van:3 comparing:1 assumed:1 support:1 there:1 specifically:2 jsps:1 inner:2 way:2 exico:1 was:3 function:12 form:3 hr:2 denoting:1 triangular:1 encodes:1 construction:2 observes:1 hc:3 line:1 considerable:1 partially:2 absent:1 made:1 up:1 abstract:1 liouville:1 limit:2 ωn:1 problem:1 similar:1 called:1 mechanics:2 ab:1 constant:5 computing:2 int:1 certain:2 ak:2 aj:2 denote:1 check:1 constructed:2 again:1 functions:10 compared:2 nn:4 whereas:2 when:1 detail:1 field:7 other:2 hpn:2 papers:1 department:1 theor:1 picture:1 elements:2 ku:1 separate:1 polynomials:7 bounded:1 atakishiyev:1 structure:1 ago:2 coupling:7 space:1 mass:1 n1:5 n2:2 having:2
|
solv-int9509003.txt |@word partial:1 results:3 gy:8 proposition:4 edu:2 follow:3 whose:2 weierstrass:1 b386:1 b388:1 equivalence:1 finally:4 present:1 under:4 izt:1 norm:3 hill:1 activities:1 notations:1 far:1 choice:1 surprise:1 difference:3 exact:2 condition:1 entire:8 obvious:2 presented:1 solution:2 try:1 solved:1 differential:3 interchanging:1 succession:1 small:3 upper:1 periodicity:2 foundation:1 za:1 zb:1 cosh:17 approximation:3 second:11 dynamics:1 theory:2 index:3 what:2 nonlinear:4 appear:1 invertible:1 sum:2 weren:1 expressed:2 reminiscent:1 en:1 above:4 sup:1 expresses:1 subtracting:1 method:1 exercise:1 satisfy:6 full:1 led:1 lee:1 equals:4 here:8 desired:3 cylindrical:1 ansatz:5 sinh:7 address:2 equations:14 logarithmic:1 remark:1 institute:1 items:1 larger:1 allows:1 completely:1 contradiction:1 example:1 periodic:2 surely:1 fourier:7 york:1 boundedness:1 b342:1 summation:1 apply:2 derivatives:2 use:13 usa:2 prove:8 remains:1 positive:3 give:5 next:5 nucl:6 call:1 therefore:1 taken:1 associated:1 type:1 theoretical:1 more:3 hahn:1 formally:1 operators:1 aware:1 appendix:5 eθ:18 particular:2 known:2 cases:1 hold:7 iii:6 must:4 valued:1 ma:1 integrating:1 recall:5 equation:2 work:4 theories:3 values:8 rewritten:1 pioneering:1 proof:11 stated:5 relativistic:3 cited:1 yξ:3 want:1 sense:1 conversely:2 yang:5 θ2m:4 end:1 lemma:25 verify:1 holds:9 write:5 how:1 instead:1 mccoy:2 absolute:1 parameter:1 gordon:1 cecotti:3 product:1 fs:1 may:11 thermodynamic:5 earlier:1 hence:5 plane:1 multiplication:1 representations:3 constants:1 fo:1 third:2 λ2m:2 lemmas:10 explicit:1 korepin:1 so:23 fundamental:1 correlation:1 representation:9 sa:2 integrand:1 order:2 dx:2 itd:1 displayed:1 satisfied:2 course:2 wiener:1 already:2 through:4 banach:2 mentioned:1 satisfies:5 still:1 its:10 before:4 derive:3 thank:1 energies:1 solving:1 actually:1 continuations:4 parts:2 systems:2 lp:1 mail:2 main:2 defining:2 supersymmetry:1 combination:3 intriligator:1 repulsive:1 they:8 half:1 thms:1 sπ:34 4πr:1 2u:7 inversion:3 university:2 e2θ:2 factorizable:1 sufficiently:2 inequality:4 l2:10 l1:9 found:1 side:5 subset:1 square:1 series:9 energy:3 hard:1 r2m:1 related:2 extended:1 combining:1 eu:1 our:9 special:2 conjectures:4 large:1 shown:1 matrix:3 3rd:1 space:5 restricted:1 since:11 crucial:2 denotes:1 acting:1 dominated:3 socalled:1 conjectured:4 formula:8 rn:7 suffices:3 math:6 shows:1 sinh2:3 harold:1 linear:5 ucdavis:1 parseval:2 free:1 assures:1 reason:1 necessarily:1 california:2 term:1 e2:3 definition:3 interaction:2 could:3 turn:2 exponentially:2 incorporated:1 davis:1 first:16 elucidating:1 reversing:1 simplifies:1 rudin:1 done:1 construct:1 another:2 precisely:2 given:8 perturbation:2 temperature:1 introduction:1 leading:1 πi:2 system:7 relations:4 their:3 assumption:4 statement:4 potts:1 gives:9 continuous:5 part:8 riesz:1 authors:2 sign:2 than:2 kind:1 showed:1 sections:1 painlev:5 limiting:3 matter:1 fˆ:11 were:2 powers:1 minus:1 perturbative:1 motivation:1 conjectural:1 craig:1 zamolodchikov:3 argument:6 dθ1:2 say:1 apparently:1 clearly:2 lie:1 zero:1 min:2 convenient:1 latter:1 converges:6 take:4 φab:2 εa:2 εb:1 formulas:2 begin:1 exactly:1 shall:8 most:1 involving:1 definitions:1 pair:3 tracy:6 acknowledgements:1 class:2 laurent:1 kf:11 ke:3 clear:2 later:1 kn:5 kq:2 kp:2 combinations:2 left:1 physics:1 section:1 fact:15 quantity:1 precise:1 particularly:1 show:13 supported:1 converge:2 discovered:1 purely:1 spaces:1 relation:2 solutions:2 find:6 ground:2 q2:8 just:1 dividing:1 written:2 topological:2 should:3 analytic:10 only:1 factor:14 preliminaries:1 continuity:1 do:2 over:1 establishes:1 notation:2 means:1 express:2 words:2 new:2 tba:6 closure:2 4πv:5 determinants:3 widom:5 arxiv:1 4πe:1 including:1 fixed:3 4πi:1 kernel:16 set:5 exists:1 sep:1 national:1 signs:1 λk:1 see:13 result:3 dµ:3 mth:1 techniques:1 said:1 b367:1 liouville:2 tend:2 state:5 dms:2 various:1 between:1 boundary:7 conditions:1 terms:9 wu:1 hypothesis:1 solv:2 bose:1 both:2 circumference:1 last:5 signed:1 limits:1 similar:3 taking:2 equal:6 quantites:1 expression:3 among:2 widen:1 nonrelativistic:1 δt2:2 ca:2 period:4 dimensional:2 mkdv:1 grants:1 anti:1 polynomial:1 proved:1 throughout:1 kernels:2 slavnov:1 described:1 addition:1 locally:1 three:4 been:2 int:3 change:1 interest:1 basic:2 ak:2 define:1 supersymmetric:5 klassen:1 quantities:1 sufficient:1 body:1 observe:1 derivative:8 general:8 former:1 those:1 case:3 look:1 value:1 will:7 near:1 replaced:4 applies:1 conformal:1 iy:7 satisfying:2 thus:9 iv:1 ii:1 reads:1 converts:1 claimed:1 c0:4 different:2 preparatory:1 belong:12 same:4 any:8 complex:2 hierarchies:1 finite:4 status:1 independent:1 used:5 imply:4 numerical:1 infinite:3 identity:14 scaling:2 lower:1 specialize:1 no:2 fusion:1 analysis:3 lim:1 model:1 arising:1 usual:2 cosh2:1 alluded:1 less:2 identically:1 obtain:4 transforms:1 immediately:1 facts:3 paul:1 melzer:1 scattering:1 yet:1 previous:4 adv:1 adding:3 now:8 lebesgue:1 conclusions:1 conclude:2 had:1 except:1 thermodynamics:2 belongs:6 extends:8 easy:2 theorem:8 iπ:111 fendley:3 details:1 real:15 increased:1 iξ:1 exponentiating:2 boundedly:4 matters:1 cruz:1 using:8 saleur:1 mod:1 like:3 follows:21 δt:2 unnecessary:1 steps:1 either:2 postponed:1 mcgraw:1 δe:1 polymers:2 right:7 methods:1 sequence:1 some:6 deduce:11 choosing:1 proofs:3 2d:2 dense:2 integration:1 everything:1 ucsc:1 does:3 provides:1 tends:3 subtracted:1 tk:1 demonstrated:1 ba:2 bc:1 equivalent:3 each:7 step:1 negatives:1 santa:1 2m:1 relating:2 properties:3 science:1 about:2 pointwise:5 would:4 extension:1 b350:1 commun:3 o:7 2i:3 range:2 fredholm:2 introduced:1 statements:1 decreased:1 into:2 integral:12 bound:2 because:5 references:1 strip:13 operator:10 substitutions:1 neumann:1 log:13 elastic:1 vafa:2 strictly:1 there:8 transform:4 long:1 bosons:1 way:1 ed:1 resolvent:3 was:3 function:30 complete:1 form:6 enough:2 converse:1 but:6 construction:1 delta:2 convergence:3 line:1 true:3 he:2 applying:4 versions:1 2πi:4 wish:1 bounds:2 us:1 bethe:5 below:4 un:10 limit:2 continuously:3 b432:1 ua:2 ab:2 constant:3 defined:7 certain:6 abstract:1 measure:1 denote:7 dξ:4 quantum:1 dθ:17 corresponding:2 identities:8 again:5 functions:35 analyticity:2 eventual:1 ingredients:2 retrace:1 when:4 vanishes:1 arctan:3 other:4 make:1 department:2 mathematics:2 izergin:1 conclusion:1 excitation:1 expressible:3 models:3 gas:1 preceding:1 uniformly:13 variation:1 bounded:20 ising:1 variable:2 sides:2 sech:6 implies:4 assume:10 established:2 factors:1 together:1 equivalently:2 came:1 once:1
|
solv-int9509004.txt |@word q2m:4 surrounded:1 partial:1 consider:10 funct:4 iassns:1 pseudodifferential:1 results:11 four:1 eds:1 scalar:5 commute:2 grateful:1 consists:4 u2k:1 dα:9 pril:1 compact:2 inverse:9 depend:3 calculate:5 nonlocal:4 γk:6 dijkgraaf:1 tk:8 elliptic:3 marks:1 tf:1 γg:17 case:15 g3:9 g2:8 very:10 conditions:4 dokl:2 geometrical:2 corollary:3 formula:7 matrices:1 deformations:5 condition:3 identity:1 notations:2 dubrovin:10 riemann:63 hamiltonian:4 did:2 t4:3 t5:14 t2:3 t3:10 ri:1 try:1 involution:1 convenience:1 vector:21 lv:6 small:10 anal:4 glued:1 lapse:1 surface:21 β2n:1 too:1 periodicity:1 zk:4 l2i:1 lecture:1 consistent:1 zg:4 τ2n:10 direct:8 sign:2 jump:2 surrounding:3 integrability:1 σkα:4 value:1 nonhomogeneous:1 chen:2 dynamics:1 odd:3 substitute:2 linear:6 spectral:4 t2k:5 nonlinear:8 plays:1 t2n:6 section:9 expressed:7 3t:2 sheeted:3 infinitesimal:1 poles:5 fuchssteiner:3 above:1 new:9 3g:3 method:3 contrast:2 satisfy:6 full:7 lee:2 respectively:7 even:4 component:1 here:7 agreement:1 objects:4 b2k:1 galilean:1 nonsingular:5 consideration:1 along:1 equations:36 z1:4 change:2 tn:2 obtained:4 remark:2 ǫx:2 divisor:1 ot:1 institute:1 shift:4 study:1 studied:3 allows:1 periodic:9 products:2 published:1 action:14 symmetrical:3 fourier:1 york:1 uniquely:5 emerge:2 via:15 useful:1 projection:2 family:5 extra:1 explained:1 plenum:2 marked:9 coinciding:1 modulated:2 santini:2 pp:16 rkl:1 rkm:2 virasoro:6 derivatives:2 use:7 superpositions:2 usa:1 analytic:1 positive:2 contains:2 negative:2 cauchy:4 properties:15 comparing:3 handles:1 bases:3 call:2 ibragimov:2 expanding:1 associated:6 mckean:2 type:8 theoretical:1 more:7 fokas:2 operators:2 factor:2 normalized:3 why:1 known:6 potential:5 e2n:6 mg:1 valued:5 world:1 deformed:1 recall:10 equation:15 averaged:24 det:1 χk:1 mk:3 mj:1 kiev:1 paragraph:9 values:1 marshakov:1 following:43 im:7 wsf:6 example:6 proof:10 es:14 dedicated:2 want:1 links:1 give:2 calculation:3 correctness:2 choice:1 lψ:4 morozov:1 sphere:1 tβ:3 numbers:1 degenerate:1 sense:3 verlinde:2 david:1 formulas:2 string:1 hodograph:2 needs:1 s2:4 holds:1 regions:1 maps:2 nontrivial:2 e2g:22 forest:5 pure:3 answer:2 instead:2 ordinary:6 parameter:14 modulations:1 e2k:2 map:9 product:5 mironov:1 description:1 singular:4 may:8 algebro:1 after:1 singularities:4 containing:1 residues:3 bkk:1 applications:1 independent:1 plane:13 lax:7 ω2n:5 waves:4 representations:2 wave:2 data:12 compatibility:2 constants:3 ωkα:4 introduced:1 natural:2 dynamical:1 lemmas:1 explicit:1 correspond:5 parameterized:1 bloch:1 so:13 doklady:1 pay:1 definitions:3 order:2 fα:5 torino:1 interpretation:3 words:1 hierarchy:7 developed:2 pointed:2 move:1 vary:2 soc:1 course:1 paper:5 including:2 counterclockwise:1 cuts:1 existence:3 its:6 roots:1 before:1 τn:1 write:3 ginzburg:1 derive:1 group:5 qkm:3 located:3 ln:3 interesting:1 lj:1 vicinity:1 coordinates:2 li:4 late:1 parts:1 systems:8 derivative:2 ωki:7 main:5 variables:4 serre:1 them:6 combination:1 spencer:1 ya:1 introduce:2 landau:2 scaling:3 sssr:2 they:24 singularity:3 now:2 yu:13 discuss:2 easily:3 term:1 dikii:1 invariants:4 presented:1 2z:1 sufficiently:1 2g:8 found:2 2n:9 higher:8 side:5 characterized:1 2k:5 multiphase:1 differential:14 ek:32 ej:1 τnm:1 series:5 energy:1 related:1 solution:7 operator:7 qjk:1 dence:1 connect:1 changed:1 quantum:2 our:10 t1:6 special:2 out:2 shown:1 matrix:12 space:15 res:8 algebra:11 rev:1 denotes:8 looking:1 re:1 nauk:4 grinevich:3 kωn:1 kosygina:1 nontrivially:1 integrated:2 math:13 shows:1 wiley:1 theory:28 derived:2 diagonal:4 standard:1 expansion:1 reason:1 complicated:3 bkj:1 e5:2 e4:3 e7:1 e6:1 e1:23 generate:1 e3:5 e2:9 definition:1 unique:3 fixed:1 asymptotical:2 r1:9 r2:9 r3:8 argument:1 rule:1 omit:1 xux:1 used:1 times:7 motion:1 manakov:1 ω2k:1 place:1 δij:5 consequence:1 first:6 v1:2 xn:1 symmetry:3 qkl:3 klimyk:1 possessing:1 number:12 2u2:1 construct:4 another:1 open:1 dispersive:1 given:3 law:1 sheet:1 introduction:3 vωi:1 tata:1 system:7 least:2 their:3 appl:5 manifolds:1 a2n:3 uki:1 realization:1 zeros:4 scheme:2 structures:5 hyperelliptic:24 gives:2 shifted:1 holomorphic:13 e0:5 tu3:2 calculations:4 prescribed:1 soviet:1 moscow:1 exactly:1 σki:7 stress:1 formulate:1 whitham:12 part:6 qlk:1 x2:4 gluing:4 l2n:1 below:2 coefficients:7 mclaughlin:5 determines:1 princeton:2 double:1 cim:1 zero:2 normalizing:1 determined:8 amplitude:1 were:10 treated:6 fand:1 plus:1 symmetries:47 boston:1 topics:1 modern:1 spectrum:6 generalization:1 summing:1 progr:1 multivalued:3 increment:1 conjugate:2 need:4 any:4 lie:2 wilson:1 constructions:1 petviashvili:2 depending:2 convenient:5 lin:2 gravity:1 indexes:5 maison:2 generalized:3 kawamoto:1 canonical:4 analogs:2 bilinear:2 play:2 akad:2 uyy:1 sl:4 birkh:1 z2:4 algebraic:2 88a:1 connected:1 plan:1 representation:5 phase:2 tsuchiya:1 µn:1 class:2 uk:7 tensor:4 soliton:6 mumford:1 takes:1 orlov:13 considered:2 ckl:4 calculated:5 partition:1 coincides:7 vertices:3 physica:1 possesses:2 proceedings:1 kp:25 exp:14 nuclear:1 physics:1 sum:4 fact:5 laws:1 oevel:2 akhiezer:7 text:1 gerasimov:1 functionals:1 discovered:1 russian:2 relation:5 solutions:20 x3:1 guaranties:2 d2:2 d3:2 d1:2 slow:4 based:2 parameters:2 2πiδ:1 commutators:1 ies:1 basel:1 outside:2 topological:6 completes:2 lemma:29 only:16 explicitly:2 inherited:1 quasimomentum:3 integrable:8 circle:1 local:12 over:5 dn:1 do:3 goes:1 notation:1 means:1 genera:1 de:5 aα:3 ones:4 dz:2 reading:1 dx:11 combinations:1 dp:6 gel:1 evolution:3 kadomtsev:2 eψ:1 covering:2 upper:2 fields:7 arxiv:1 expansions:2 consisting:1 intervals:1 hydrodynamic:1 grassmannians:1 analytical:2 wesley:1 cycles:10 preserve:1 moduli:7 set:15 constructing:2 exists:8 sep:1 differentials:22 facts:1 see:28 gaps:2 result:8 japan:1 discussions:1 close:2 contour:11 analog:4 shabat:2 surfaces:31 ωi:12 phases:3 quasiperiodic:4 tsarev:8 αv:6 nondegenerate:2 αx:1 review:1 definite:2 ωk:24 λn:4 vki:1 written:10 classes:2 correctly:2 regge:2 theta:7 boundary:2 σni:1 approach:3 deformation:2 meromorphic:9 αt:1 accord:1 matveev:2 terms:11 uux:6 wk:2 attention:1 points:36 trubowitz:1 vanishing:2 punctured:2 ws:2 answers:1 key:1 solv:1 jetp:1 suggested:4 both:2 last:2 σn:1 limits:1 always:3 many:2 infinitely:4 belavin:1 equal:11 stuttgart:1 connection:4 l2k:1 genus:8 whole:1 jersey:1 γn:1 point:35 simple:8 tori:4 cg:1 corresponds:3 pupt:1 dimensional:12 pole:4 taylor:2 bα:4 sing:1 wider:2 constant:2 pr:10 forms:3 most:3 ωf:1 described:7 commutative:1 second:2 basis:6 moerbeke:1 locally:1 three:1 been:1 mark:1 ai:25 much:4 slowly:1 treat:1 basic:3 empty:1 choose:1 addison:1 determinant:2 relations:3 corresponding:3 going:1 formed:1 gap:20 noncommutative:3 weierstrass:1 present:1 quotation:1 applied:1 splits:1 ǫu1:1 choices:1 will:27 while:1 ǫt:2 property:7 conformal:3 procedure:3 periods:1 real:2 vectors:1 kernel:4 averaging:5 wkb:1 thus:2 non:2 uxx:2 reads:3 flaschka:5 vt:1 ia:2 nuov:1 uxxx:6 id:1 around:1 different:2 formalism:1 inc:1 author:3 recursion:3 lett:4 same:3 check:1 shifts:1 complex:21 hierarchies:1 finite:25 subalgebra:4 degasperis:2 qji:1 extended:1 infinity:4 qjm:1 solved:1 πip:1 akl:4 upon:3 flows:9 hand:6 v0:2 usually:1 v2:2 v3:2 moving:3 purpose:1 potentials:4 infinite:14 normalization:5 gsp:1 lower:1 correspondent:4 well:5 object:1 without:2 solve:3 ωni:1 components:1 coordinate:1 position:1 model:1 parametric:2 calogero:2 left:2 unified:1 surveys:1 manifold:1 less:1 λx:3 residue:2 obtain:2 uuxxx:1 using:2 λk:3 λi:1 converges:1 scattering:10 brackets:1 λm:2 reduced:1 segal:1 vσ:1 preprint:5 field:16 zakharov:3 vω:2 auser:1 characterization:1 self:1 wes:1 lattice:1 e0l:2 valid:5 transformed:1 e0k:7 theorem:4 plasma:1 transformation:2 details:1 identical:1 bij:17 bik:1 depends:2 2u:3 posed:1 possible:1 9d:1 qj:3 press:1 integer:1 intersection:2 correcting:1 formal:2 necessary:4 sakharov:1 workshop:1 velocities:3 ωn:1 schwarz:2 integrals:13 arbitrary:4 topologically:2 ragnisco:1 therein:1 because:7 functional:3 classical:1 discrete:1 some:11 λ2n:2 algebraically:1 polynomial:3 mat:1 examples:1 uspekhi:1 apply:1 kdv:50 peter:1 diagonalizing:1 scale:1 congress:1 avoid:1 integration:2 disk:1 everything:1 defined:17 does:3 hep:1 esn:3 mined:1 minimal:1 ωij:1 bg:2 scientific:1 izvestiya:1 equivalent:4 q2k:1 bi:22 bj:9 bk:3 how:1 step:1 variation:2 2m:4 yamada:1 imaginary:1 between:2 schulman:7 integers:1 prove:2 central:3 extension:2 constraint:1 novikov:7 bgk:1 o:6 essential:2 compatible:1 mutually:4 carries:3 kj:1 const:1 act:2 ti:1 mean:1 slightly:2 book:2 exponents:1 massachusetts:1 iπp:1 kσn:1 statements:1 publishing:1 isomorphic:4 bji:2 pair:5 appropriate:3 ussr:2 references:3 novosibirsk:2 sov:1 isospectral:6 abel:4 physical:1 van:1 additional:5 vˆ:2 u5:2 springer:3 there:8 u1:1 transform:12 long:1 u2:1 conservation:1 way:2 ed:2 m1:1 was:16 function:32 complete:1 form:17 memory:1 but:15 zamolodchikov:1 construction:3 hn:1 convergence:1 lectures:1 vω1:2 he:1 commun:5 ψa:2 applying:2 ux:3 consist:1 2πi:17 ut:4 inside:1 uv:1 variations:3 us:21 krichever:12 liouville:1 ωj:9 limit:3 ωl:14 levermore:3 uj:1 problem:18 define:2 similar:4 called:14 ωg:1 b1:3 detailed:1 later:1 proved:6 ag:2 qij:1 int:2 cover:1 ak:3 aj:10 am:2 eigenfunction:1 general:7 single:5 proves:1 right:4 dλ:13 families:4 tα:2 commuting:5 simplest:2 constructed:10 functions:11 polygon:3 no:21 when:2 pitaevsky:1 dispersionless:1 ny:1 other:4 role:3 neighbourhood:11 branch:19 papers:2 theor:1 hydrodynamical:3 company:1 nice:1 picture:1 elements:4 denote:9 calculating:1 models:5 sided:1 problems:1 bundle:1 prepared:1 a1:2 a0:2 generated:5 important:7 bounded:2 log:1 variable:1 belinskii:2 sides:3 structure:4 xu1:2 auxiliary:3 assume:7 vries:3 baker:7 rs:2 curve:2 b1k:1 together:1 strings:1 situations:1 time:2 4g:1 starting:1 original:7
|
solv-int9509005.txt |@word ψ1x:7 consider:3 chinese:2 funct:1 crucial:1 results:1 leads:3 ψ1j:27 ψ1k:3 ψ1n:1 follow:1 expressions:2 preserves:1 inverse:2 depend:4 tu:4 tr:1 tn:2 finally:1 th:2 under:6 semenov:1 tg:4 ingredient:1 applied:1 straightforward:1 far:2 rise:5 rm:5 matrices:12 condition:1 hamiltonian:10 turns:1 sklyanin:2 involution:3 convenience:1 vector:4 shanskii:1 anal:1 solutions:1 2k0:4 takhtajan:1 direct:5 lpthe:1 elegant:1 integrability:4 further:2 q1x:1 linear:1 spectral:7 established:1 what:2 nonlinear:1 developed:1 brackets:1 diag:1 section:1 celebrated:1 expressed:1 maillet:1 kij:3 3n:1 above:3 new:5 consisting:1 contrast:1 satisfy:3 ichikawa:4 respectively:1 here:4 b2n:1 b2m:10 china:1 illustration:1 address:1 along:1 standard:2 equations:7 deduced:1 obtained:8 search:1 studied:2 allows:1 mx:1 p2:8 poisson:18 permutation:2 suitable:1 wojciechowski:1 useful:2 extra:2 namely:1 talon:1 q22:3 derivatives:1 use:1 would:2 distinct:1 contains:1 next:2 few:1 call:1 therefore:2 m2:1 associated:7 type:1 qcm:1 more:1 introducing:3 elliptic:1 becomes:1 curvature:1 berlin:1 particular:1 known:2 cases:3 hold:1 must:3 springer:2 hamiltonians:1 science:2 equation:14 work:1 reads:3 ij:26 three:1 following:5 example:4 f0:3 beijing:1 f2:4 calculation:4 expanding:1 sense:1 conversely:1 yang:10 information:1 g1:2 verify:1 holds:1 write:1 how:1 acta:1 ordinary:1 yangbaxter:1 product:1 may:2 derived:2 tsiganov:1 produce:1 lax:11 representations:1 compatibility:1 types:2 λ2j:13 λ2n:5 dynamical:25 λ2m:3 yielding:1 so:8 allow:1 representation:15 order:8 restriction:1 hierarchy:17 indeed:1 pointed:1 satisfied:4 years:1 paper:4 through:1 p1x:1 satisfies:6 still:1 before:1 derive:2 interesting:1 coordinates:2 permanent:1 systems:9 jacobi:8 main:1 fin:1 into:1 them:2 tsinghua:1 they:1 now:3 discuss:1 possess:1 eigenvalue:6 february:1 dikii:1 hereafter:1 university:2 presented:6 2g:9 found:2 2j:2 constraints:1 baxter:10 financial:1 series:1 µb:2 related:3 isospectral:1 used:2 obtains:1 our:1 eq:1 special:1 out:2 shown:3 superscripts:1 matrix:21 space:1 restricted:1 furthermore:1 since:1 rx:3 research:1 m2l:1 contained:1 denoted:1 nontrivially:1 rn:1 math:3 shows:1 theory:3 2h1:1 kaup:5 possibility:2 quite:1 tian:1 ψ2n:1 york:1 ψ2k:3 ψ2j:29 ask:1 finite:6 v1:2 sinica:1 could:1 finland:2 konno:4 m21:1 m22:2 motion:2 4p1:1 consequence:1 adjoint:3 first:8 features:1 variables:6 meng:1 xx:2 relations:2 f1:2 illustrate:2 given:9 bracket:4 needed:1 introduction:1 eqs:1 system:17 construct:3 their:1 c2n:1 too:1 siam:2 variational:1 structures:2 gives:6 academy:1 newell:6 immediate:1 segur:1 than:1 βαi:2 1j:1 see:3 project:1 were:1 sec:3 powers:1 correction:1 ram:1 need:1 constrained:16 any:2 zero:1 depending:2 self:1 note:1 sciences:1 k0:23 take:2 canonical:3 trace:1 index:2 most:2 class:2 soliton:5 laurent:1 kj:2 later:1 flow:9 kn:2 physica:1 h2m:1 h2n:1 physics:1 bulletin:1 fact:4 supported:1 λq:2 ψ2x:7 relation:1 akns:5 µa:2 find:4 q1:21 partially:1 q2:16 depended:1 parameters:7 should:1 avan:1 only:8 explicitly:1 rich:1 factor:1 integrable:10 enolskii:1 moser:2 do:2 his:1 notation:1 means:1 express:1 straightforwardly:1 probably:1 evolution:1 qr:2 babelon:1 qx:3 arxiv:1 method:8 qi:1 fixed:1 2p1:1 requirement:1 2p2:1 sep:1 national:1 observed:1 depends:3 p21:1 terms:7 turku:2 liouville:1 λn:1 written:6 permutes:1 αi:16 invariant:2 αj:14 approach:2 µc:2 c2m:5 recently:1 however:1 ji:1 jk:3 solv:1 coadjoint:1 both:1 σi:1 last:1 σn:2 many:3 according:1 admit:1 expression:1 finds:2 cm:4 had:2 others:3 dimensional:10 m12:2 respect:2 considering:1 ensures:2 second:1 δλj:1 copies:1 been:8 defined:2 basic:1 pi:1 define:2 describe:2 corresponding:2 quantities:1 m1k:1 c3:1 viallet:1 c1:1 general:3 present:9 case:7 p1:13 arnold:1 will:6 rbm:1 property:1 wki:3 generate:1 jpn:1 almost:1 vi:1 ik:4 itself:1 rij:1 vx:2 spaces:3 different:1 verified:1 recursion:2 make:1 belong:1 same:1 antisymmetry:1 pauli:1 qam:1 hierarchies:2 physical:1 higher:1 independent:1 literature:1 flows:16 constraining:2 v2:2 v3:1 purpose:1 infinite:1 ablowitz:1 a2m:4 identity:5 recent:1 lower:1 nevertheless:1 well:5 solve:1 consistency:2 model:1 calogero:2 usual:1 eilbeck:1 λr:2 gelfand:1 just:2 obtain:2 λc:2 λb:2 underlying:1 immediately:1 λk:9 λj:33 ostrogradsky:2 scattering:1 yet:1 functionally:1 preprint:1 conclusions:1 seems:1 except:1 add:1 transformed:1 lett:4 easy:1 guarantees:2 transformation:1 identical:1 eigenfunction:1 read:1 term:2 possibly:1 know:1 using:7 m11:1 necessary:2 like:1 follows:4 δu:4 steps:1 integrals:2 essential:1 mathematical:1 parity:1 methods:1 classical:25 some:9 deduce:1 examples:10 b3:1 kdv:5 ijk:12 lead:2 extensively:1 refer:1 gratitude:1 faddeev:1 obey:2 bm:6 expansion:1 although:1 2m:14 properties:1 constraint:10 discussed:2 generated:1 o:1 important:2 act:1 introduced:1 soc:1 h2:7 h0:5 h1:5 due:3 δui:1 references:1 qrx:1 hep:1 additional:1 support:1 there:2 philadelphia:2 start:1 appl:2 inner:1 way:3 m1:1 was:3 q12:5 lowest:2 form:9 but:4 construction:4 rauch:1 truncation:1 ut:1 uv:1 utn:1 up:1 us:5 below:2 ui:1 problem:7 called:2 b1:1 mechanics:1 sometimes:1 constant:2 int:1 certain:2 abstract:1 contribute:1 am:5 zeng:5 denote:2 pix:1 conserved:1 qix:1 relates:1 gradients:1 identities:2 constructed:1 no:1 acknowledgments:1 when:3 application:1 other:4 details:1 solitons:2 department:2 mathematics:2 briefly:1 kinds:1 problems:2 a0:1 wadati:4 a2:1 a4:1 gets:3 structure:13 implies:3 auxiliary:1 proposed:1 time:2 original:1
|
solv-int9509006.txt |@word partial:3 consider:2 results:1 four:1 scalar:1 proposition:9 preserves:1 depend:2 equivalence:2 th:1 under:1 straightforward:1 very:1 induce:1 wishes:1 condition:2 try:1 vector:1 math:1 indices:1 noted:3 substitutions:22 second:1 street:1 further:1 index:2 nonlinear:1 appear:2 invertible:2 incompatible:1 expressed:4 above:3 acknowledgments:1 coefficient:1 respectively:3 here:2 consideration:1 equations:12 obtained:3 institute:1 study:4 ψu1:1 montreal:1 technique:2 useful:1 classification:3 apply:1 total:5 derivatives:7 ψx:1 prove:4 ψv:2 next:3 therefore:3 more:4 nkc:1 iu:1 auv:2 virtue:3 known:3 cases:2 must:2 account:1 equation:36 work:2 kamran:1 following:6 example:3 proof:4 give:2 calculation:1 preserving:1 sokolov:5 dxn:1 dxm:1 dxk:1 dxi:7 conversely:1 e2u:2 darboux:3 verify:3 how:1 nontrivial:6 ϕv:6 fu:1 algebra:1 relates:1 dx3:1 dx2:3 plane:1 correspond:3 su:1 doklady:1 order:1 september:1 satisfied:1 paper:1 mentioned:1 existence:2 satisfies:3 its:1 thank:1 deriva:1 interesting:1 mail:1 main:1 ya:2 now:1 easily:2 university:1 side:4 differential:38 reduce:1 idea:3 eu:8 our:5 pu1:1 shown:1 research:1 contained:2 formula:1 symme:1 shows:1 admits:3 complicated:1 definition:5 starts:1 nonnegative:2 u21:1 u22:1 hence:1 βm:1 βi:2 symmetry:6 miura:2 variables:4 another:3 given:1 checked:1 hyperbolic:6 system:14 assumption:3 statement:1 variational:1 relationship:1 academy:1 wide:1 see:5 determined:1 pairwise:2 bicomplex:1 russia:1 w2:2 symmetries:4 rewrite:1 ran:2 argument:1 need:2 any:15 depending:1 convenient:2 latter:2 recommended:1 contact:2 generalized:2 formulas:1 shall:1 who:1 surv:1 class:1 especially:1 considered:1 ki:2 phis:1 fact:3 show:1 solutions:2 trivial:1 based:1 should:4 only:6 integrable:2 do:1 ϕx:5 ϕu:1 express:1 ones:1 dyi:5 dx:44 dy:17 report:1 evolution:6 arxiv:1 method:1 thanks:1 satisfy:4 set:2 exists:2 sep:1 finiteness:2 w3:2 result:2 w1:8 discussions:1 said:2 αi:6 invariant:28 αk:2 conditions:4 preserve:2 terms:1 wi:11 solv:1 both:1 essentially:1 many:2 taking:1 laplace:5 admit:1 ci:2 point:4 simple:1 dimensional:1 sequences:1 respect:4 described:4 transformations:10 pu:2 corresponding:2 commutes:1 sufficient:2 maps:6 observe:1 understand:1 derivative:1 present:2 case:2 fux:1 remaining:1 aim:1 technical:1 au:1 property:3 vi:4 avv:2 thus:3 vn:1 uxy:3 2ux:1 vt:2 vu:1 vy:3 different:2 φs:2 author:4 same:3 proved:1 used:1 hand:4 v1:2 infinite:3 2u1:1 center:1 well:2 without:1 λv:2 λx:2 obtain:1 transforms:1 integer:2 preprint:1 belongs:1 transformed:1 lett:1 easy:2 theorem:6 transformation:7 2u:2 admitting:3 using:3 remind:1 either:1 evolutions:1 reduced:2 mathematical:1 right:4 examples:3 moreover:1 eliminate:2 ufa:2 equivalent:7 substitution:20 relating:1 about:1 quasilinear:1 nonequivalent:4 into:10 ηv:3 references:1 operator:8 ψu:2 ηx:2 there:7 u1:14 u3:1 u2:13 anderson:2 way:1 was:2 function:21 complete:1 form:18 converse:1 but:1 russian:4 2vx:1 true:1 uy:3 ux:22 ut:4 uv:1 up:1 us:3 un:1 ui:12 demonstrate:1 problem:4 similar:1 called:3 detailed:1 constant:1 int:1 abstract:2 general:2 exist:4 av:5 constructed:1 tedious:1 again:1 functions:5 integrability:1 no:1 cmr:1 field:1 other:1 offered:1 conclusion:1 ξx:2 june:1 ξv:2 important:1 implies:1 assume:2
|
solv-int9509007.txt |@word proposition:1 consider:5 similarity:1 rev:1 equalities:1 results:15 leads:2 scalar:7 commute:2 computation:3 edu:2 follow:1 expressions:4 trickier:1 row:8 compact:1 whose:7 inverse:3 wish:1 fellowship:1 tr:3 acting:2 factoring:4 finally:3 rg:1 chaps:1 present:3 under:1 analogous:7 must:3 norm:6 p2:1 belonging:1 supported:3 consequently:1 orthogonal:7 very:2 nonselfadjoint:1 focus:2 putting:1 interpreting:1 entries:6 difference:3 matrices:11 condition:2 χd:32 entire:1 indicate:1 gue:4 level:5 did:2 yin:1 notes:1 solution:5 vε:9 integrated:1 leave:1 solved:2 differential:14 subscript:1 small:1 eigenvalues:9 anal:1 rk:13 solutions:2 smaller:1 says:1 lecture:1 estimates:2 painlev:11 evaluated:1 substituting:2 rigorous:1 manipulating:1 dynamics:1 odd:8 primes:1 substitute:2 theory:1 even:7 established:4 what:5 appear:4 invertible:2 xσ:2 sum:4 analogously:1 expressed:3 suspect:1 above:16 boundary:2 new:5 consisting:1 exercise:1 satisfy:1 justification:6 respectively:11 spacing:3 equals:25 here:9 met:1 groups:1 address:2 represented:2 appropriate:1 standard:3 equations:22 appears:2 change:2 q4:7 obtained:3 sobolev:1 institute:1 larger:2 allows:1 completely:1 suggests:1 products:11 action:1 complicated:2 specialize:1 changes:1 sup:1 york:2 det2:3 useful:1 santa:1 family:1 scales:2 discontinuous:1 hermite:2 belongs:2 vii:3 engineering:1 lτ:1 replace:3 scaled:14 limn:4 roles:1 sgn:2 apply:4 establish:1 research:1 manipulate:1 derivatives:2 use:18 takes:2 usa:2 tn2:2 probabilities:2 beginning:1 contains:2 physics:1 next:6 comparing:1 explicitly:1 therefore:2 endowed:1 taken:2 compactly:1 theoretical:1 more:8 chapter:1 gohberg:1 h1:11 operators:18 award:1 berlin:1 particular:4 known:4 cases:4 hold:2 iii:6 eβ:7 springer:1 valued:1 integrating:2 recall:8 equation:8 work:4 det:14 four:2 infinitesimal:1 obvious:1 rewritten:1 following:3 root:3 example:1 proof:5 point:1 f1:2 f2:3 f4:2 want:1 figure:1 give:8 cited:1 permutations:1 purposes:1 ratios:1 indicates:1 degenerate:1 arise:4 r21:1 yang:1 basor:1 quaternions:1 respective:1 end:3 goal:1 awkward:1 turn:3 fortunately:1 discussion:1 holds:5 enlarge:1 write:16 how:3 mehta:1 pure:1 answer:1 instead:2 ordinary:1 sin:3 either:2 map:2 product:12 algebra:1 replacing:4 suppose:2 earlier:1 derived:2 mapping:1 factored:2 hence:6 multiplication:3 representations:3 evaluations:1 choice:3 arch:1 heidelberg:1 fn:11 λ2i:2 interscience:1 asymptotics:4 succeeded:1 lemmas:2 quoted:1 explicit:1 correspond:1 rather:2 so:39 correlation:1 definitions:1 βk:4 order:3 sd:2 operations:4 fβ:6 wigner:2 words:1 schwartz:1 itd:1 move:1 displayed:2 choose:1 interpreted:1 course:4 paper:3 through:2 signs:1 satisfies:1 integrands:2 its:8 before:7 derive:5 thank:1 maps:2 solving:1 sε:8 writing:1 better:1 absence:2 systems:5 mail:2 might:3 into:5 outside:1 freeman:1 them:5 good:1 introduce:2 bound:1 scaling:11 mention:2 they:4 eµ:4 bar:1 now:20 sχ:5 widom:7 eigenvalue:11 term:9 several:2 2p:2 2q:1 2r:1 always:2 university:2 drop:1 wε:8 ensemble:10 applied:3 l2:54 each:6 found:4 2n:22 sato:1 side:19 integrand:1 r1:28 domain:2 square:3 just:5 weight:1 ed:1 reduce:1 gaussian:16 obtains:1 measure:1 quantum:1 our:28 approximated:1 differ:4 special:2 out:9 rt:6 shown:3 jimbo:1 matrix:26 factors:6 goe:13 since:19 xσn:2 denotes:7 may:3 contained:2 investigation:1 convergent:1 reader:5 formula:11 get:1 evaluation:1 correct:1 math:7 densities:1 foundation:1 harold:1 after:1 turning:1 linear:5 ucdavis:1 variant:1 diagonal:2 quite:3 difficulty:2 reason:4 california:2 imperial:2 e4:6 chen:1 e1:6 e2:18 r4:9 definition:3 perform:1 derivation:6 r2:5 interpretation:1 dunford:1 route:2 insert:1 times:5 xσ2:2 thing:1 xσ1:2 derivations:1 incorporated:1 davis:1 qn:10 onto:1 think:4 first:23 xj:5 xk:1 xi:5 xn:8 probability:15 laguerre:2 variables:1 number:1 rank:4 restrict:1 multiplying:2 done:2 another:3 precisely:4 size:1 defined:2 interchange:1 given:15 temperature:1 similarly:6 introduction:6 deift:1 top:1 notational:1 πn:1 system:12 relations:3 their:7 transcendent:2 constants:2 justified:1 normalization:1 airy:9 πx:2 behaved:2 final:3 gives:10 exactly:4 immediate:1 part:4 differentiate:1 manipulation:1 x2:1 x3:1 x1:8 than:5 coefficients:3 clarkson:1 kind:2 third:2 showed:3 cyclic:1 was:5 piii:1 see:23 limiting:8 matter:1 determined:2 doubly:1 represents:2 were:2 college:2 treated:1 minus:1 vector:2 san:1 rewrite:2 craig:1 ann:1 pass:1 argument:2 generalization:1 already:2 rat:1 need:2 seen:3 recover:2 any:3 lie:2 lim:9 self:1 1d:1 able:3 εs:17 converges:12 note:3 potential:2 take:1 εk:16 εj:13 gse:13 formulas:12 play:2 continuous:2 trace:19 though:1 sets:1 most:4 involving:5 representation:4 multiply:2 tracy:7 qp1:1 class:18 tensor:2 χs:13 treats:1 χq:2 χp:2 considered:1 professor:1 kn:10 physica:1 sf:1 lχ:1 χf:1 points:1 principle:1 exp:1 left:12 χk:1 section:14 fact:19 quantity:2 science:2 show:13 random:5 functionals:1 discovered:1 bring:2 miwa:1 spaces:5 relation:1 cψ:6 constituent:1 corner:1 analogue:9 find:25 fifth:2 subtracting:1 q1:12 based:1 ensembles:26 explain:1 assertion:2 should:1 lemma:7 only:7 smallest:1 factor:12 integrable:1 over:6 do:4 sense:1 establishes:1 notation:8 means:1 df:1 simplified:1 express:4 aα:1 ϕn:2 ϕi:3 dx:42 dy:16 compute:2 dt:9 dr:1 ds:17 differentiating:1 prime:1 resolve:1 determinants:23 heaviside:1 nicely:2 arxiv:1 comprising:1 remove:1 underlying:1 common:2 contain:2 fixed:3 krein:1 view:1 kernel:42 set:12 computed:1 exists:1 sep:1 national:1 correlations:1 vol:1 depends:2 sec:2 result:5 triples:2 λi:1 concern:1 hilbert:3 exponent:1 visiting:1 uε:13 olver:1 consequence:1 tend:3 symmetric:2 enough:2 unable:1 various:1 between:3 invariant:1 αk:2 αj:2 conditions:2 2pq:1 multiplied:2 notice:5 terms:16 interchangeably:1 extend:1 oddness:1 transpose:1 analogues:4 however:2 js:4 council:1 comm:4 multiplies:1 solv:1 bose:1 amer:1 come:1 jc:1 both:8 interpretations:1 accident:1 last:18 σn:1 limits:20 desired:1 many:1 taking:2 equal:9 attributed:1 etc:1 connection:1 symplectic:7 σs:1 variance:1 contribution:1 expression:1 uniformity:2 cn:2 space:15 conclude:2 simple:2 ca:2 bai:1 corresponds:2 grants:1 simply:1 constant:8 actually:1 speak:1 kernels:8 pp:2 sine:1 second:15 union:4 stages:1 providence:1 been:1 quickly:1 int:1 much:1 evenness:2 interest:2 basic:1 pn:6 ak:15 fig:1 determinant:63 arises:1 corresponding:3 quantities:12 sufficient:1 subscripts:1 gas:1 spectrum:4 bulk:5 observe:4 monogr:1 derivative:1 denote:13 those:3 case:12 p1:24 p4:16 defining:1 empirical:1 value:3 easier:1 will:9 while:3 replaced:7 viii:2 shall:14 evaluates:1 di:1 0x:1 graphed:1 unitary:4 necessary:1 geometric:1 almost:2 vi:3 thus:14 iv:6 ii:11 cluster:1 itself:2 dual:2 aspects:1 vanish:3 different:1 handled:1 author:1 perhaps:2 identities:2 make:4 belong:1 same:31 antisymmetry:1 parts:3 arguments:2 largest:10 resulting:3 proved:3 finite:30 higher:1 independent:2 used:6 infinity:1 diego:1 numerical:1 upon:1 asymptotic:1 moment:1 delicate:1 hospitality:1 infinite:4 changing:2 a2k:2 identity:6 lower:1 mech:1 off:1 proceed:1 idempotent:1 well:7 roughly:1 deal:1 without:1 thought:3 academic:2 edge:8 solve:2 greatest:1 εt:11 authors:1 position:2 arising:3 latter:1 usual:1 isometry:2 interpret:1 alluded:1 being:6 obtain:13 vanishes:3 intervals:9 thanks:1 immediately:1 facts:2 rn2:2 alternative:1 yet:3 convolution:2 letting:1 adding:2 rs:27 density:4 nilpotent:1 extra:1 had:2 except:1 exclusively:1 appeared:1 add:1 interested:1 combine:1 treatment:1 easy:3 norms:2 sτ:32 solvable:1 transformation:1 real:1 2p2:1 around:2 easily:2 evaluate:5 possible:1 early:1 cruz:1 know:3 εd:1 press:2 using:17 claims:1 appearing:2 helpful:1 semi:4 follows:23 δt:6 substitution:2 remind:1 δj:3 δk:25 integrals:11 arbitrary:1 become:2 pointwise:3 reduces:2 terminology:1 parity:1 right:27 methods:1 classical:1 sequence:1 absolutely:1 some:4 begin:2 regularized:2 deduce:5 sure:1 equivalent:1 respect:1 nonzero:1 mcleod:1 scale:3 proceeding:2 zhou:1 affects:1 separate:2 integration:3 comments:1 manipulations:3 conditionally:1 everything:2 ucsc:1 does:1 summand:1 tends:2 χr:2 bessel:2 prob:1 cϕ:20 refer:2 inserting:1 eigenfunctions:1 ba:2 notations:2 l1:2 quaternion:3 although:3 2m:10 subtract:2 properties:1 simpler:1 pβ:2 integers:1 about:1 adjoining:1 would:3 impenetrable:1 pε:14 column:7 commun:1 o:4 recalling:2 range:1 a2:2 fredholm:11 act:3 discard:1 introduced:1 slightly:3 qτ:2 dz:10 soc:1 letters:1 ηn:5 dyson:3 within:3 integral:14 jα:1 down:3 retaining:1 hermitian:2 because:15 references:1 determine:2 operator:77 refined:1 letts:1 acknowledgements:1 log:2 strictly:1 there:11 approximate:1 long:2 why:1 cats:1 inner:15 way:4 resolvent:8 sections:3 treat:3 function:36 complete:1 form:9 denoting:2 but:17 hoped:1 convergence:2 don:1 line:1 removed:1 true:3 observation:1 made:1 applying:2 characteristic:1 smooth:4 us:4 below:8 dms:2 limit:19 uk:1 gaudin:1 distribution:7 define:2 similar:3 called:4 expect:1 pii:3 ab:2 associated:5 ai:10 certain:1 abstract:1 general:9 transl:1 single:1 exist:3 simulations:1 dε:1 distributions:6 piv:1 again:3 functions:18 qε:48 entirely:1 no:2 amounts:1 whereas:1 when:16 detail:1 other:7 role:1 details:2 department:3 mathematics:3 really:1 shows:5 deviation:2 elements:2 connect:1 completes:2 expressible:3 models:3 remains:1 uniformly:5 polynomials:2 stay:1 a1:11 commutator:1 important:2 bounded:8 a4:7 variable:4 sides:2 careful:1 independently:1 implies:2 values:8 dτ:17 interval:10 together:3 χj:10 time:1 appl:1 requires:2 once:1
|
solv-int9509008.txt |@word partial:3 results:2 roy:1 scalar:1 perturbations:1 whose:1 calculate:1 technique:1 recurrence:1 summarised:1 program:1 δhk:2 th:2 under:1 worth:1 straightforward:2 far:1 rise:1 intriguing:1 exact:1 condition:4 tri:1 hamiltonian:17 turns:1 solution:2 δh1:2 δh0:1 large:1 involution:1 dealt:1 mulvey:2 noted:1 application:1 direct:1 generalisations:1 imply:1 further:1 theory:1 subscripts:1 will:3 invertible:1 expressed:2 current:4 abs:1 above:1 supplies:1 construction:2 bdx:1 satisfy:1 degree:3 arik:1 here:3 behaviour:2 xξ:1 groups:1 standard:3 equations:16 implicit:1 change:2 study:1 vectors:1 allows:2 mx:1 poisson:3 linearised:2 suitable:1 useful:1 family:1 durham:3 derivatives:5 ψx:3 infinitum:1 would:1 prove:1 charge:1 ψt:3 hilbert:1 few:1 nucl:1 noting:1 criteria:2 3le:1 type:4 more:2 flat:1 becomes:1 particular:1 known:2 cases:1 must:1 nutku:7 springer:1 valued:1 equation:22 work:1 values:1 following:2 example:4 indicated:1 give:1 process:1 assumptions:1 yη:1 verlag:1 end:1 protect:2 write:2 how:1 parameter:1 fr:2 continues:1 singular:1 may:2 advice:1 earlier:1 derived:1 demanding:1 lax:2 φ2t:4 verified:1 law:2 compatibility:3 constants:1 attempt:1 third:2 perform:1 so:5 representation:2 first:8 order:3 september:1 satisfied:1 paper:1 london:1 mentioned:2 existence:1 satisfies:1 its:2 rapidly:1 thank:1 thence:1 interesting:1 solving:1 forms:1 lt:1 systems:1 h3:1 jacobi:3 olver:5 h0:1 generalised:2 them:1 combination:2 kumei:2 framework:1 hamilton:2 they:1 now:2 discuss:2 possess:1 easily:2 2q:2 always:2 university:1 b373:1 each:1 2l:6 found:4 difficult:1 2k:3 homogeneous:5 el:2 arxiv:2 ed:1 reduce:1 δh2:1 our:3 out:1 w2:1 matrix:4 admissible:1 lagrangian:9 denotes:1 math:7 after:1 linear:2 ascertain:1 divergence:2 free:1 quite:1 admits:4 complicated:1 york:2 members:1 org:1 impose:2 david:1 motion:3 turn:1 repeats:2 south:1 hydrodynamics:1 already:2 features:1 symmetry:2 bluman:2 variables:5 number:4 least:1 given:2 φ2x:5 rewritten:1 introduction:1 adjoint:3 system:4 construct:1 echet:2 assumption:1 expand:1 postulate:1 structures:2 morozov:1 than:1 a125:1 accordance:1 require:1 second:6 matter:1 dtp:1 result:1 mind:1 argument:1 extremals:1 need:1 seen:2 any:3 lie:1 zero:2 convenient:2 able:1 note:1 sciences:1 take:1 canonical:1 magri:2 most:3 pleasure:1 pair:3 acknowledgements:1 inserted:1 class:3 observation:1 calculated:1 phil:1 uε:2 bracket:2 principle:1 camb:1 physics:1 bateman:13 fact:1 laws:3 show:1 vrule:1 supported:1 analyis:1 find:7 govaerts:4 northern:1 should:2 hierarchy:2 only:1 his:1 legendre:1 dk:1 means:1 dependent:2 hopefully:1 dx:14 new:3 dw:3 dt:4 closure:2 evolution:5 conditions:1 differential:5 method:1 common:1 mapped:1 set:1 reference:1 sep:1 j1:9 j2:11 namely:2 descriptions:1 inequivalent:1 techniques:1 ways:1 subsequent:2 siam:1 various:2 simplest:1 simplifying:1 approach:1 email:1 notice:1 terms:1 nature:1 subject:1 reproduces:3 solv:1 suggested:1 restrictions:2 collaborators:1 many:1 region:1 vk3:1 according:1 context:1 expression:1 relevant:1 point:1 lagrangians:3 2nd:1 simply:1 lagrange:2 respect:1 considering:1 fairlie:5 skew:3 due:1 been:1 appears:1 defined:1 much:1 ireland:1 basic:1 abstract:1 dots:1 relations:1 corresponding:1 quantities:3 essentially:2 derivative:2 denote:1 present:2 case:4 multi:1 aim:1 while:1 suppose:1 property:1 vk2:1 studied:2 non:1 ii:1 lbi:1 itself:1 vt:2 vx:3 different:1 dε:1 φt:24 author:1 φx:21 recursion:4 formulations:4 same:1 tells:1 parts:1 hierarchies:1 finite:1 higher:1 independent:1 used:3 http:1 see:1 interscience:1 hand:1 v2:1 arose:1 infinite:4 invariance:1 identity:3 courant:1 task:1 charges:2 adapted:1 analysis:2 arising:1 dh1:1 φtt:2 homogeneity:1 infeld:4 financially:1 preprint:2 candidate:2 density:1 education:1 adx:2 smoothness:2 grigore:1 lett:1 theorem:3 guarantees:1 euler:3 real:1 depends:1 possible:1 know:2 using:6 unique:1 formal:2 generated:1 like:1 follows:1 δp:1 href:1 steps:1 δh:1 arbitrary:2 become:2 works:1 mathematical:2 methods:1 classical:1 sequence:3 some:2 born:4 deduce:2 choosing:1 provided:2 dimensions:1 integration:1 comments:1 whole:1 expressing:1 assuming:1 proc:2 demonstrated:1 equivalent:4 continuing:1 use:2 references:1 substitution:2 properties:3 about:3 quasilinear:1 discussed:1 dependence:3 compatible:3 ensure:1 consequently:1 road:1 soc:2 φxx:2 h2:2 φxt:2 into:2 h1:4 functional:2 ut:4 down:1 bihamiltonian:7 operator:7 width0pt:1 hep:2 stucture:1 support:1 there:8 transform:1 start:1 conservation:5 terminates:1 was:1 function:2 complete:1 form:10 but:2 volume:1 hk:1 properly:1 larger:1 he:1 whether:1 characteristic:2 uv:1 smooth:2 up:1 us:2 limit:1 uk:2 uf:1 similar:1 called:1 bearing:1 ac:1 associated:6 ad:1 int:1 certain:1 universal:3 pseudodifferential:1 general:6 conserved:12 proves:1 formalism:1 functions:3 ideally:1 integrability:2 no:2 when:3 nx:1 field:4 other:1 papers:2 department:2 nice:1 expressible:1 meaning:1 structure:15 dψ:1 dφ:1 appl:1 quantity:1 requires:1
|
solv-int9509009.txt |@word ψ1x:2 consider:2 chinese:1 funct:1 skii:1 ψ1j:17 ψ1k:1 ψ1n:1 consists:1 u2k:2 content:1 inverse:1 depend:1 tn:1 δhn:1 elliptic:1 under:1 semenov:1 case:1 r12:7 straightforward:1 far:1 rise:1 formula:1 matrices:3 dij:2 presented:2 turns:1 enol:1 large:1 involution:3 shanskii:1 anal:1 takhtajan:1 hk0:2 direct:1 integrability:2 iσ2:1 canonical:3 spectral:2 nonlinear:1 diag:1 section:1 celebrated:1 maillet:1 above:1 bm:7 new:6 acknowledgments:1 satisfy:3 respectively:1 here:2 understanding:1 china:1 q13:2 address:1 along:1 equations:9 deduced:2 obtained:4 study:1 studied:1 example:2 poisson:9 permutation:1 action:1 hospitality:1 via:1 ψ2k:1 extra:1 talon:1 establish:1 research:1 derivatives:1 use:2 would:1 distinct:1 contains:1 2bm:1 comparing:1 m1:4 m2:4 taken:1 type:3 more:2 separated:2 introducing:2 multiplying:1 γm:1 becomes:2 berlin:2 origin:1 ramani:1 springer:2 science:1 equation:11 work:1 following:6 mx:1 proof:1 wojciechowski:1 beijing:1 calculation:2 permutations:2 bk0:2 sense:1 r21:2 guarantee:1 information:1 provide:3 s0:3 how:2 sij:1 product:1 may:2 after:2 hence:1 lax:7 constants:2 λ2j:2 natural:6 dynamical:15 third:1 author:1 sk:3 so:4 representation:9 order:2 restriction:1 holds:1 hierarchy:8 developed:1 paper:2 d32:2 coordinates:7 li:1 kuznetsov:1 permanent:1 systems:5 jacobi:14 fin:1 h0:3 introduce:1 p12:1 p13:1 hamilton:11 tsinghua:1 now:1 possess:1 eigenvalue:2 term:1 gets:3 equality:1 2q:1 university:2 hamiltonian:13 applied:1 theory:1 2g:1 each:2 found:3 side:1 baxter:7 financial:1 obtains:1 our:2 out:1 shown:2 matrix:10 rx:2 denotes:1 m2l:1 rm:3 rn:1 math:2 shows:1 ψ2x:2 standard:2 tian:1 ψ2n:1 members:1 ψ2j:11 tsiganov:1 finland:2 m21:1 m22:2 motion:3 consequence:1 βi:1 first:3 separable:4 neccesary:1 variables:4 2p2:5 construct:1 illustrate:2 given:1 cartesian:1 introduction:1 adjoint:2 system:9 relations:1 ukn:5 zeros:3 miller:1 1j:2 gives:1 centered:1 academy:1 exactly:1 newell:1 immediate:1 than:1 coefficients:1 kind:1 variational:1 cyclic:2 painlev:1 project:1 determined:1 were:1 constrained:4 any:1 complete:2 calogero:1 sciences:1 k0:21 generalized:2 play:1 shall:1 constructed:1 considered:1 professor:1 flow:1 physica:2 bracket:2 hietarinta:1 qbm:2 eilbeck:1 show:5 supported:1 solutions:4 substituting:1 find:1 q1:30 q2:13 parameters:3 separability:7 avan:1 only:5 rich:1 parabolic:1 integrable:3 circle:1 moser:1 his:1 notation:1 means:1 express:3 ones:1 prime:1 bas:1 babelon:1 qx:4 arxiv:1 method:1 contain:1 qi:1 fixed:1 qn:1 2p1:3 coefficient:1 set:3 constructing:1 sep:1 national:1 differentiation:1 depends:3 radius:1 p23:1 p22:3 discussions:1 terms:4 λi:2 turku:2 liouville:1 written:4 λm:2 αi:7 invariant:1 notice:2 recently:1 p2i:1 however:1 jr:1 jm:2 solv:1 σk:5 both:5 viallet:1 vk2:1 equal:1 expression:2 separation:2 cm:2 q12:7 tabor:1 dimensional:2 m12:2 rauch:1 respect:2 throughout:1 gratitude:1 δλj:1 due:1 been:2 int:1 offers:1 4q2:2 basic:1 pi:1 define:1 quantities:1 concerning:1 dji:1 c1:7 c0:1 present:1 p2:8 p1:4 arnold:1 rbm:1 property:1 dλ:3 residuum:1 2uk:1 vj:4 vk:16 thus:3 reads:1 ij:1 rij:2 containing:1 d12:6 d13:6 same:1 pauli:1 finite:2 independent:1 extended:1 infinity:1 see:1 flows:4 identity:1 s23:1 consistency:2 model:2 usual:1 spherical:1 λq:1 obtain:3 valuable:1 using:4 λk:1 λj:24 ostrogradsky:2 λn:6 functionally:1 except:1 other:1 transformed:1 lett:6 easy:1 read:1 february:1 admitting:1 immediately:1 hereafter:1 m11:1 like:1 follows:4 δu:4 either:1 integrals:3 mathematical:1 methods:1 classical:14 some:3 q22:4 q23:1 b0:1 examples:2 b2:1 b3:1 lead:2 sufficiently:1 replicas:1 8p1:2 faddeev:1 2q2:1 obey:2 2q1:3 s13:1 s12:1 bn:2 expansion:1 comparison:1 constraint:1 o:2 important:1 plus:1 introduced:2 h2:11 into:1 h1:4 integral:2 references:1 additional:1 support:1 u1:4 appl:1 inner:1 way:2 was:1 function:1 interest:1 form:11 δkj:2 but:3 hn:2 hm:4 partially:1 2πi:1 us:2 um:2 ul:9 below:1 un:5 ui:2 uk:79 uj:19 problem:1 similar:1 called:1 b1:7 mechanics:1 associated:5 defined:2 abstract:1 describe:1 am:4 zeng:5 denote:3 pix:1 conserved:1 qix:1 physical:1 when:2 yang:7 role:1 solitons:1 department:2 mathematics:1 m1k:1 polar:1 completes:1 separate:1 problems:2 ragnisco:1 a1:9 a0:1 a2:1 variable:1 structure:8 implies:1 d23:2 together:1 n0:2 having:2
|
solv-int9509010.txt |@word consider:10 funct:3 global:2 y2:2 grateful:2 sung:1 compact:1 inverse:7 const:1 calculate:1 technique:1 nonlocal:1 finally:1 program:1 stable:1 norm:10 hill:1 p2:3 orthogonal:3 very:2 dokl:1 wave:3 putting:1 affect:1 difference:1 condition:8 cmn:17 obvious:1 riemann:1 level:1 bn:1 solution:16 md:1 large:5 vector:2 small:6 anal:3 correct:1 zn:2 says:1 eλx:4 coefficient:1 direct:14 located:1 rate:2 pmn:2 estimated:1 substitute:1 linear:3 spectral:9 aim:1 dmn:3 section:9 above:1 new:3 ground:1 method:2 satisfy:4 degree:8 component:1 here:1 eλ0:3 path:1 auxiliary:1 equations:5 z2:5 dk:9 remark:5 institute:1 study:5 studied:2 contradiction:1 periodic:3 usually:1 hospitality:1 studies:1 uniquely:8 via:2 sgn:4 use:3 dpdq:3 would:1 lemma:14 contains:1 visit:2 negative:2 properties:8 comparing:1 call:1 associated:3 volterra:1 type:1 theoretical:1 more:5 zeroes:6 fokas:4 operators:3 odinger:5 bogdanov:1 cases:2 reλ:1 ma:1 integrating:4 recall:2 equation:44 mn:18 regularity:1 values:1 following:24 nonsingular:9 example:7 stimulating:1 proof:14 give:1 expanding:1 lψ:1 assumptions:1 degenerate:1 sense:1 weaken:1 δm0:1 information:1 needs:2 decaying:17 fortunately:1 means:1 orthogonality:5 how:2 parameter:2 fredholm:3 singular:2 may:4 kosygina:1 earlier:1 singularities:3 collection:7 plane:1 coming:3 data:10 grow:1 constants:8 λ2i:1 third:1 grant:3 rather:4 green:5 eµx:1 fundamental:1 imλ:1 order:3 schwartz:4 developed:1 course:1 paper:8 including:1 y1:2 y0:9 satisfies:4 still:1 decay:8 parts:3 fig:1 2λr:1 mail:1 main:2 2λy:2 correspondence:1 non:2 greater:1 introduce:3 landau:2 they:4 eµ:1 now:8 discuss:1 easily:1 term:2 φk:15 always:1 university:1 2y:2 teoret:1 possibilities:1 sufficiently:4 l0:14 each:1 found:4 monomials:3 side:3 2j:1 mean:1 homogeneous:14 ei:3 series:11 energy:3 elementary:1 extended:1 our:8 approximated:1 special:1 aˆ3:1 ru:1 shown:1 space:1 iλi:3 denotes:2 ψmn:6 grinevich:2 dxdy:11 stud:2 max:11 induction:1 integrated:1 math:5 shows:1 foundation:2 theory:13 surveys:1 standard:2 c00:1 complicated:1 put:1 estimate:1 generate:1 definition:4 ist:1 introduction:1 exponentially:7 leading:2 hence:11 first:7 origin:1 pgg:1 symmetry:1 xm:2 variables:3 number:4 approximate:2 construct:2 another:1 impossible:1 open:2 given:1 perturbation:3 likely:1 manakov:2 unknown:1 adjoint:7 zk:1 least:11 assumption:5 too:1 statement:2 scheme:2 exponents:1 gives:1 calculations:1 ratio:1 tool:1 continuous:1 part:5 x2:11 july:1 representing:1 than:5 coefficients:6 distance:1 unfortunately:1 pansion:1 second:1 limiting:1 classes:1 were:1 russia:1 lowest:1 generality:3 conjugate:1 need:1 any:18 petviashvili:2 convenient:2 converges:2 potential:15 generalized:1 so:3 coincide:2 moscow:1 shall:1 uyy:1 simplify:1 regular:4 connected:1 plan:2 preliminary:1 class:3 µx:2 prove:3 laurent:1 δn0:1 considered:1 clear:3 physica:1 points:3 physics:2 technical:2 applied:1 show:5 text:1 supported:1 converge:1 norms:1 spaces:1 solutions:22 substituting:2 d2:2 d3:3 d0:1 d1:3 based:1 state:1 completes:3 analytic:2 only:8 circle:2 do:3 dj:10 µk:2 notation:1 get:12 rudin:1 arcwise:1 obtain:1 dx:6 dy:1 combinations:1 during:1 differentiating:1 kadomtsev:2 bar:2 qy:3 approach:3 arxiv:1 contain:1 analytical:1 fixed:3 explanations:1 view:1 kernel:2 set:4 constructing:1 exists:2 sep:1 6uux:1 ξmn:3 see:7 result:2 existence:1 discussions:1 λi:8 satisfying:1 eigenfunctions:1 review:1 diverge:2 boundaries:1 outside:1 determined:1 cooperation:1 between:2 boundary:5 conditions:7 terms:12 shabat:2 2m:2 solv:1 jetp:1 suggested:3 essentially:3 pempinelli:2 last:1 2n:1 irregular:6 equal:3 fulfilled:5 coefficents:1 whole:1 otherwise:1 ck:2 point:10 simple:1 asymptotically:1 corresponds:1 dimensional:4 cy:1 taylor:1 proved:9 simpler:1 described:1 aˆ:6 px:3 locally:1 int:1 asymptotics:5 ak:4 empty:2 define:2 obtained:1 direction:3 corresponding:5 lecce:2 sufficient:4 formed:2 gap:1 zero:1 derivative:1 general:2 case:1 look:1 exponential:1 will:1 ǫr:1 suppose:1 situation:2 property:5 procedure:1 iq:2 boiti:3 thus:9 ii:12 reads:7 ready:1 uxxx:1 different:2 italy:1 author:5 same:2 intersecting:2 complex:2 finite:4 used:1 infinity:23 hand:3 domains:5 potentials:7 ablowitz:3 recent:1 schr:5 well:4 analysis:4 without:8 components:1 position:1 λr:19 neighborhood:1 less:1 λx:1 solvability:5 2dx:1 formulated:1 aspect:1 differentiation:1 alternative:1 scattering:28 previous:1 adding:2 intersection:2 zakharov:2 belongs:2 easy:2 theorem:16 solvable:1 details:2 real:25 read:1 big:1 spatial:1 results:2 know:1 using:1 unique:6 formal:10 loss:3 modifications:1 necessary:1 like:1 follows:8 unstable:1 either:1 integrals:2 arbitrary:9 mcgraw:1 essential:2 right:4 absolutely:3 some:15 b0:1 examples:2 nonzero:10 nonsingularity:1 does:1 assuming:1 scientific:1 june:1 equivalent:1 pose:1 agreement:1 expansion:13 bk:4 step:2 kpi:1 hilbert:1 asymptotic:9 constraint:1 novikov:3 basis:3 discussed:1 o:16 nonvanishing:2 konopelchenko:1 book:1 letters:1 orders:2 unbounded:1 integral:19 functional:1 appropriate:1 because:1 references:1 strip:1 operator:18 next:1 additional:3 assumed:3 strictly:1 there:7 question:1 transform:20 fast:2 yaacov:1 appl:4 way:1 yaakov:1 resolvent:1 was:12 function:31 complete:1 form:2 but:9 heat:10 russian:3 line:1 partially:1 commun:1 applying:1 2πi:1 ut:1 smooth:10 up:2 us:6 historically:1 krichever:3 below:2 decays:5 problem:10 2πz:1 similar:2 called:3 detailed:1 ac:1 ab:1 constant:3 defined:20 abstract:1 denote:3 exist:3 pis:1 check:2 fizika:1 constructed:2 functions:13 analyticity:1 no:8 vanishes:5 reality:1 kp:18 aˆ2:1 solitons:1 department:1 out:1 company:1 draw:1 zhou:2 problems:4 polynomials:1 a0:1 important:2 bounded:2 serious:1 faster:11 assume:12 χk:1 equivalently:1 international:1
|
solv-int9509011.txt |@word concept:1 consider:1 consolidated:2 global:2 splitting:1 existing:1 leads:1 computation:5 denotes:1 displaying:1 paris:1 tn:1 finally:2 those:1 stable:12 divergent:9 applied:7 fax:1 far:1 risc:1 sons:1 trouble:1 exact:2 condition:5 impressive:1 solver:7 solution:10 t0:1 occurs:4 large:1 discrete:7 detected:4 tel:1 dealing:1 nonautonomous:1 approximation:1 second:10 displays:3 further:1 dynamics:9 ode:2 quite:3 linear:3 even:2 will:1 nel:1 nonlinear:21 essence:1 appear:1 section:1 selected:5 version:11 above:4 fractional:3 new:2 method:6 here:3 behaviour:8 cise:4 explore:1 studio:1 concluding:1 strong:1 equations:5 implicit:2 involved:1 study:1 allows:1 typically:1 periodic:1 generale:1 domains:1 suitable:1 plotted:3 via:1 followed:1 griffiths:1 namely:1 apply:2 total:1 tools:1 linearly:2 use:1 asymptotic:5 conservation:1 type:3 diagrams:7 more:5 thompson:1 transient:1 particular:1 known:2 cases:2 effort:1 states:1 account:1 ibm:1 mb:1 equation:6 work:3 del:1 growing:1 example:1 control:4 compare:2 figure:10 high:1 performed:1 axis:1 provide:1 feature:1 regions:1 maps:2 methodology:2 fourth:12 ordinary:3 parameter:3 map:4 wiley:1 collection:1 stefano:1 diagram:5 applications:1 produce:2 designed:1 coming:1 verified:1 stiff:1 dynamical:7 third:1 following:2 explicit:4 cascade:1 algorithms:7 allow:1 stewart:1 order:23 typical:1 produces:1 developed:1 pointed:1 insight:2 stability:13 course:3 paper:1 through:3 innovative:2 y1:1 y0:3 y2:1 its:4 integrators:2 chosen:1 troubles:1 better:2 absence:3 systems:8 mail:1 parametric:5 non:2 combination:2 they:1 documented:1 hall:1 hamiltonian:1 loosely:1 capability:2 sufficiently:1 each:3 found:3 development:1 domain:2 schemes:5 successively:1 related:5 literature:2 beyond:9 out:4 space:4 chaos:1 research:1 increase:1 evaluation:3 integrated:1 sma:1 shows:3 theory:2 possibility:1 standard:2 interaction:1 starts:2 iterative:1 linearized:5 reggio:1 first:2 initial:11 features:5 render:1 explored:2 solvers:3 precisely:1 size:1 given:4 necessarily:1 introduction:1 system:1 relations:1 their:3 station:1 eqn:4 scheme:3 gives:2 explanation:1 continuous:6 complesso:1 than:4 plausible:1 john:1 holland:1 require:2 richer:1 computations:3 exhibit:1 comput:1 need:1 numerics:3 lie:1 zero:1 depending:2 efficient:1 note:8 jacobian:2 coincide:1 techniques:3 tool:1 accuracy:3 multiple:2 trace:1 successive:1 retaining:2 analytically:1 class:1 especially:4 considered:1 performances:2 steady:2 points:6 physics:2 show:2 solutions:26 stepping:3 bernouilli:1 trivial:2 find:1 impact:1 just:1 dividing:1 implementation:1 true:1 window:1 only:5 indeed:2 engrg:1 employed:1 handle:1 means:1 spurious:12 familiar:1 quantified:1 fluid:1 degradation:1 despite:1 report:1 produced:1 resolve:1 covering:2 conditions:1 differential:6 intervals:1 logistic:3 analytical:1 fixed:6 set:1 computed:7 exists:1 catastrophic:1 unpublished:1 achieves:1 see:7 result:3 recently:1 subject:2 state:1 trapezoidal:1 between:2 limit:9 prentice:1 approach:5 available:1 terms:1 nature:1 efficiency:1 both:2 last:1 limits:1 many:2 hours:2 according:1 involve:1 figures:1 whole:1 point:8 sixth:1 period:2 iterations:1 expensive:2 conference:1 create:1 three:1 been:2 interest:1 basic:1 abstract:1 pm:1 generating:1 concerning:1 present:2 bifurcations:1 case:6 exception:1 look:1 value:13 lesser:1 while:2 procedure:3 chaotic:1 thus:1 equal:1 sas:1 different:2 italy:1 journal:1 complex:1 runge:4 inc:1 higher:1 kutta:4 extended:2 numerical:28 counterparts:1 hand:1 steps:2 purpose:1 recent:3 mech:1 campo:1 nevertheless:1 unconditionally:1 well:5 analysis:9 severe:1 bifurcation:12 solve:3 very:2 model:2 arising:4 proposed:3 being:1 accurate:8 yee:1 valuable:1 underlying:1 world:1 useful:1 simo:1 previous:2 onset:1 capabilities:1 extensive:3 remaining:1 euler:1 secondorder:2 advances:2 possible:1 using:1 unique:1 like:1 semi:1 discarded:1 indication:1 either:1 because:3 often:1 classical:6 some:3 proceeding:1 avoid:1 recorded:1 integration:2 conservative:3 conditionally:1 critical:2 assuming:1 unstable:5 varying:1 problems:8 equivalent:2 how:1 step:3 analyses:2 properties:6 comparison:1 about:3 extension:2 practical:2 range:1 emilia:1 discretization:2 computational:3 tecnologie:1 presence:3 into:3 numerically:1 implications:1 due:1 nonperiodic:2 references:1 determine:1 methods:6 deal:2 area:1 there:4 fast:1 quadratic:1 way:2 analyze:1 was:3 north:1 offer:1 differences:1 but:1 crank:5 convergence:1 dissipative:1 applying:1 evident:1 inside:1 us:1 discretized:3 below:7 exploration:1 problem:4 display:1 interval:2 constant:1 milano:1 universal:1 engineering:1 reliability:1 periods:1 file:1 regime:1 mutual:1 compared:1 no:2 whereas:3 when:9 application:1 other:1 remarks:1 test:3 mathematics:2 picture:2 models:1 uniformly:2 stay:2 generated:1 important:1 dekker:1 structure:1 algorithm:4 nicolson:5 required:2 pseudo:1 rule:1 time:11 appl:1 backward:2 cpu:2
|
solv-int9509012.txt |@word secondly:1 partial:1 consider:2 remarkable:2 funct:4 induces:1 results:4 invent:1 eds:2 proposition:1 llm:3 follow:1 gl:5 localized:2 alk:2 devoted:1 whose:4 inverse:3 finally:1 investigation:1 tk:2 elliptic:1 under:3 semenov:1 ingredient:1 r12:5 advantage:1 very:1 choice:3 entries:2 tridiagonal:1 difference:1 matrices:2 trl:4 variable:1 hamiltonian:18 did:1 turns:1 july:1 applicable:1 involution:2 interpolating:1 eigenvalues:2 anal:4 upper:2 sapienza:1 discover:1 sign:8 past:1 elegant:1 integrability:7 further:4 dynamics:5 canonical:3 even:1 established:1 nonlinear:3 stands:1 section:3 symes:1 en:1 fuchssteiner:2 above:5 new:5 equivalent:1 led:1 αkj:2 l1:4 here:2 water:1 sinh:4 concluding:1 standard:2 equations:6 interpret:1 ekj:3 remarks:1 allows:2 suggests:1 periodic:1 characterizing:1 poisson:4 suitable:1 makes:1 montreal:1 uniquely:1 shorthand:1 family:3 9a:1 merely:2 9b:1 rki:1 readily:4 would:2 prove:1 sake:1 linear:2 moro:1 centre:2 mckean:1 type:1 preserving:1 becomes:1 hereby:1 holm:5 basically:1 particular:5 known:2 cases:2 iii:1 must:1 account:1 amaldi:1 recall:2 equation:4 work:2 novikov:1 following:9 stimulating:1 proof:1 wojciechowski:1 give:2 relativistic:1 sense:1 νx:1 assumptions:1 14b:1 something:1 14a:2 conversely:1 r21:2 guarantee:1 needs:1 boussinesq:1 straightforward:1 turn:1 rather:2 holds:2 write:5 far:1 pure:3 e2j:5 map:1 algebra:2 replacing:1 after:1 derived:4 containing:1 independent:1 lax:10 waves:1 summarize:1 types:1 natural:6 dynamical:7 whenever:2 explicit:1 yielding:2 mjk:1 so:6 discretisation:7 fundamental:1 representation:7 looking:2 talk:1 superscript:1 restriction:1 hierarchy:2 indeed:1 spectral:1 years:1 course:1 paper:3 through:3 denotes:2 signs:1 existence:1 still:2 its:6 suffix:1 revived:2 le:1 la:1 ln:4 interesting:1 lm:4 lj:2 lk:4 coordinates:3 fruitful:1 degrees:1 systems:9 jacobi:2 main:1 might:1 possessing:1 non:1 crucial:1 outlined:1 delivered:1 introduce:2 number:1 framework:2 hamilton:2 they:1 now:2 yu:2 possess:1 easily:1 term:1 several:1 nonperiodic:3 invariants:1 university:2 good:1 l2:4 2a:1 2b:2 2c:2 found:1 universit:2 characterized:2 arxiv:1 ei:5 ek:2 ej:5 hard:1 inverted:1 toda:16 investigated:3 computable:1 our:3 eq:2 special:10 out:2 ejl:1 shown:3 rp:5 matrix:31 ejj:1 space:2 hyman:1 lagrangian:1 research:1 particles:1 may:1 ajk:1 istituto:1 denoted:5 formula:3 get:2 ref:1 integrated:1 math:6 unifying:1 theory:1 8b:1 8a:1 fisica:3 quite:2 completely:1 complicated:1 e0:1 care:1 derivation:1 levi:1 pang:1 keep:2 motion:3 introduction:1 hence:1 crm:2 exhibited:1 first:5 initial:2 features:2 render:1 striking:1 miura:1 variables:3 geodesic:1 rank:1 restrict:1 construct:1 open:2 given:3 ordering:5 dipartimento:2 achieved:1 system:20 least:1 1a:3 their:2 1c:1 1b:3 scheme:2 structures:1 final:1 paved:1 tool:2 continuous:1 took:1 part:2 authors:1 translation:1 cosh:2 peculiar:1 coefficients:1 finitely:1 kind:1 see:2 submitted:1 winternitz:1 classes:1 7c:2 7b:3 generality:1 rewrite:1 argument:1 already:3 say:4 αlj:1 αlk:1 ans:1 element:2 any:1 solitons:1 lie:3 pursued:1 calogero:5 able:1 note:1 instance:1 take:1 finding:2 formulas:2 trace:1 shall:1 ujk:2 most:2 exploited:2 pair:1 appear:1 soliton:1 constructed:1 consequences:1 considered:1 flow:4 physica:2 bracket:3 exp:23 physics:1 fact:4 ambiguities:1 oevel:1 characterisation:1 manipulation:1 anyway:1 notations:2 solutions:5 carefully:1 d4:1 trivial:1 find:1 q1:1 q2:1 parameters:2 than:1 only:2 explicitly:4 integrable:14 constant:3 moser:3 do:1 legendre:1 therefore:1 notation:1 di:6 df:1 dg:1 overall:1 aim:1 suris:2 symmetries:1 interpreted:1 gen:1 prime:2 qr:1 held:1 babelon:1 conditions:1 transposition:1 differential:1 investigate:1 activity:1 uncover:2 qk:32 qj:37 qn:2 set:1 exists:1 sep:1 physically:1 δjm:1 δjl:2 connections:1 lnl:1 namely:4 result:2 recently:2 alternative:2 encouraged:1 closer:1 evaluation:3 tensor:1 factorisation:3 label:1 symmetric:2 written:3 determined:1 various:1 between:1 invariant:2 enjoys:2 approach:3 available:1 adv:1 notice:1 terms:3 nature:3 however:2 ln0:2 derive:2 comm:2 jk:7 solv:1 relying:1 behaviour:2 essentially:3 viallet:1 many:1 taking:2 equal:2 fulfilled:1 connection:3 succeed:1 symplectic:1 context:2 expression:5 finds:1 cj:1 relevant:1 groups:1 simple:3 corresponds:2 coincidence:1 moreover:2 peakons:8 li:2 camassa:5 kp:1 conference:1 perspectives:1 basis:2 simplification:1 locally:1 been:11 int:1 interest:2 basic:4 pj:22 pk:13 pl:17 pm:2 6a:2 6b:1 aj:1 corresponding:3 both:1 quantities:2 modelling:1 scrutiny:2 coherent:1 observe:3 understand:1 7a:2 denote:1 present:1 case:22 intriguing:1 look:1 endomorphism:2 will:6 while:1 neat:1 property:3 procedure:1 played:1 endowed:2 metric:1 thus:4 according:2 ii:1 reads:2 flaschka:1 rik:2 dual:4 cjk:1 different:5 perhaps:1 cross:1 same:3 clearly:1 complex:2 finite:5 evolve:2 used:3 rmatrix:1 trivially:1 upon:1 flows:6 hand:1 jkl:1 moment:1 identity:2 recent:1 lower:1 task:2 off:1 nucleare:1 edinburg:1 whole:1 simplicity:1 well:3 roma:4 model:3 αjk:4 manifold:1 just:4 being:1 scotland:1 guided:1 newton:2 identify:2 thanks:2 questions:1 immediately:1 differentiation:2 momenta:1 previous:1 elj:1 visualization:2 preprint:2 elm:2 lattice:12 belongs:1 conjugated:1 lett:4 skl:1 transformation:5 identical:1 casting:1 rev:1 read:2 papers:1 possible:3 usefully:1 using:1 occurring:1 ljk:4 like:2 lost:1 follows:1 reduces:3 yields:2 gjk:1 sezione:1 essential:1 pertaining:3 trl2:1 methods:1 classical:1 discrete:6 phenomena:1 b1:1 b2:1 respect:2 proper:1 bruschi:1 provided:3 describing:2 though:1 everything:1 francoise:1 assuming:1 biology:1 11a:2 l0:1 11b:1 rescale:1 bn:1 each:1 bi:1 bj:1 qˆ:1 refers:1 super:1 comparison:1 rederived:1 freedom:1 nijhoff:2 discussed:1 o:5 alber:1 compatible:1 whence:1 a2:1 extensions:1 consequently:1 considerations:1 discretization:1 own:2 into:1 down:3 phase:1 weyl:1 references:1 isospectral:1 assumed:1 strictly:2 there:2 transform:1 noticed:2 appl:6 italia:1 way:3 naturally:1 function:5 complete:5 form:7 some:2 δkl:1 δkm:2 triangular:2 but:3 transformed:1 construction:2 rauch:2 rjk:2 marsden:1 instructive:2 up:2 us:1 krichever:3 harnad:1 backlund:1 problem:2 similar:1 called:1 strongly:1 associated:4 worthwhile:1 defined:3 abstract:1 describe:1 generating:1 proven:3 general:8 conserved:1 6c:2 formulation:2 nazionale:1 commuting:5 check:1 physical:1 again:2 functions:6 no:3 when:1 bremen:2 other:2 role:1 fokas:2 picture:3 generates:1 separate:1 setting:1 ragnisco:3 a1:2 generated:2 important:1 previato:1 included:1 structure:3 algebraic:1 algorithm:1 assume:3 vinet:1 ejk:11 time:12 starting:2
|
solv-int9510001.txt |@word represent:1 is0:1 partial:2 consider:3 magnetic:1 global:6 results:1 2c1:3 four:2 known:5 grateful:1 parameterization:1 consists:1 expressions:3 contributions:1 row:1 copernicus:1 preserves:1 inverse:1 depend:2 tx:2 uz0:8 tu:2 editors:1 tx2:2 vigier:1 must:1 investigation:1 those:1 under:7 include:1 xe:1 returning:3 implicitly:9 rise:2 springer:1 choice:4 ovsiannikov:1 putting:1 manifolds:1 2rx:6 specific:1 associated:1 linearizability:1 exact:7 condition:5 states:1 leads:2 17th:1 positions:1 z12:4 solution:38 damped:1 leave:2 solved:1 differential:9 math:9 dealt:1 relation:6 linearizing:2 work:1 consistent:1 direct:2 literature:1 sign:1 second:11 traveling:8 further:1 dynamics:1 linear:18 even:1 established:2 what:3 nonlinear:32 const:1 sub:9 invertible:1 sum:1 dr2:1 analogously:1 current:1 above:10 new:3 3a:1 method:3 publications:1 clausthal:7 respectively:2 loose:1 certainly:1 here:3 desired:1 free:6 sinh:2 represented:1 tz:1 corrections:1 equations:49 implicit:8 change:8 obtained:8 remark:2 technical:2 involved:2 study:6 larger:1 example:2 resulting:1 published:1 involves:1 zhdanov:2 via:1 useful:1 diffeomorphisms:1 extra:1 logarithmic:1 texts:1 linearization:1 mizrahi:1 apply:3 readily:1 derivatives:4 ψx:5 takes:1 would:1 prove:2 positive:2 ca1:1 contains:1 finally:1 next:1 approach:1 therefore:2 ϕt:2 december:1 taken:1 means:3 type:3 theoretical:3 more:5 4at:8 definition:1 becomes:2 odinger:10 surprisingly:1 correspondingly:2 basically:1 particular:13 iim:1 foundations:1 cases:5 iii:6 uz1:5 r1:1 topic:1 account:1 valued:2 integrating:5 deformed:1 recall:2 equation:66 constraint:1 oscillator:14 ere:3 infinitesimal:1 nine:1 eikonal:2 following:17 vt:2 arrive:7 institute:3 decoupled:2 f1:11 f2:7 xz1:5 indicated:2 give:5 relativistic:4 preserving:1 organized:1 involve:1 numbers:1 sense:1 ciemat:1 tan:3 linearized:2 evidently:1 νj:1 hodograph:2 needs:1 provide:1 get:11 utilize:1 significance:1 ensure:2 ordinary:2 verlag:1 parameter:1 sin:3 classifying:1 product:1 sommerfeld:1 algebra:4 may:3 schro:7 after:2 derived:1 containing:4 consequence:3 plane:5 value:4 representations:3 wave:11 compatibility:1 constants:2 sx:14 natural:1 third:2 explicit:15 correspond:1 st:22 diffeomorphism:3 so:6 specifying:2 representation:1 order:13 fα:1 least:2 interpretation:2 indeed:2 uvt:2 choose:3 interpreted:1 principles:1 paper:7 2sx:1 mentioned:3 existence:2 satisfies:1 kibble:1 its:8 before:3 solitary:2 group:15 symmetry:18 fit:1 ln:17 interesting:2 solving:3 actually:1 toru:2 annales:1 according:1 humboldt:1 systems:5 jacobi:1 mail:2 main:1 maximal:2 non:18 motivated:2 parabola:1 irreversible:1 hamilton:1 they:5 instead:1 multidimensional:1 now:3 s0:4 possess:1 2t:10 easily:4 always:1 university:3 arrows:1 alembert:1 sufficiently:6 2f:1 magnitude:1 2a:3 2z1:2 2z0:7 2m:1 characterized:2 scherer:3 homogeneous:2 domain:3 square:15 ei:1 directly:1 t2:15 reduce:2 gaussian:2 prolonged:1 operator:1 used:3 measure:1 quantum:17 our:2 special:2 out:2 rt:10 shown:1 sabatier:2 kiev:1 space:5 gradient:1 furthermore:4 since:7 rx:3 rz:5 particles:1 bertolami:1 contained:4 vector:1 at2:5 formula:10 rn:3 integrated:5 rj:5 shows:1 classification:1 turning:1 theory:4 found:1 singularities:1 fisica:1 possibility:2 admits:3 applications:2 complicated:1 york:2 besides:1 consequences:1 asi:3 r4:1 r5:1 r0:2 derivation:2 r2:4 r3:1 utilization:1 stiftung:1 times:1 turn:2 exponentially:1 linearizations:1 castle:1 support:1 atx:3 first:20 initial:13 features:1 probability:2 variables:18 cj:2 number:4 dinger:7 restrict:3 will:1 relations:2 another:1 ψxx:3 between:3 given:11 rewritten:3 their:9 introduction:1 top:1 system:37 construct:5 indicate:1 zeros:1 calculations:2 ehrenfest:5 speaking:2 gives:2 statement:1 relationship:1 academy:1 2at:7 part:1 authors:1 x2:9 july:1 cosh:4 separability:1 coefficients:1 diffusion:3 determines:1 unfortunately:1 was:2 cim:1 see:5 tangency:2 stt:1 symposium:2 determined:15 contrary:1 str:1 were:3 enables:1 stx:2 ia2:2 suggestions:1 symmetries:9 derivative:1 generality:1 rewrite:3 appreciate:1 linearizable:1 turned:1 generalization:1 summing:1 seen:1 cumbersome:2 any:3 lie:11 academic:2 convenient:1 latter:2 courant:1 gravity:1 contact:4 note:2 sciences:1 potential:23 generalized:3 coincide:1 rediscovered:2 broglie:1 serov:1 ukrainian:3 twodimensional:1 object:1 2ia:1 germany:2 formulae:8 pair:2 future:1 why:1 appear:3 cke:2 workshop:1 reduces:1 tpa:3 considered:4 typeset:1 proceedings:4 construction:1 principle:1 exp:39 physics:7 notion:2 fact:2 quantity:1 german:1 labels:1 converge:1 gauge:7 solutions:61 substituting:4 guerra:1 find:1 principal:2 henceforth:1 parameters:12 pdes:17 specified:1 should:2 only:7 summarizing:2 ambiguity:1 developed:1 integrate:3 integrable:20 local:22 oct:1 centrally:1 abelian:1 ϕx:2 notation:2 exceptional:2 dependent:8 dg:33 de:4 ones:2 dx:2 progress:2 iceberg:1 dt:1 du:1 ds:1 coth:2 alexander:1 evolution:2 ushveridze:3 fields:1 arxiv:1 yield:2 acknowledgments:1 twice:2 dodonov:1 contain:2 analytical:1 grad:1 inside:1 l47:1 satisfy:2 set:2 dobrev:1 constructing:1 physically:2 carrying:1 hα:1 j2:1 depends:1 result:5 arg:1 discussions:1 inequivalent:2 particle:1 winternitz:1 hilbert:1 doebner:22 olver:1 functionals:2 enough:2 classes:5 µj:1 invariant:6 conditions:1 hence:3 publishers:1 terms:1 inertia:1 continuously:2 vanishing:5 concentrate:1 comm:1 solv:1 problem:5 thank:1 suggested:1 cos:5 last:2 goldin:20 limits:3 xλ:2 treated:1 taking:1 linearizes:1 quantization:1 enabling:1 chosen:1 connection:1 figures:1 context:2 section:6 pde:3 expression:2 schroedinger:1 otherwise:2 unitarily:1 among:3 groups:1 conclude:3 harmonic:13 dimensional:10 distinguish:4 anti:7 lagrange:1 nonlinearity:1 respect:4 considering:1 ensures:1 transformations:15 pt:2 addition:1 z0:33 invert:2 locally:3 due:2 been:8 z1:96 defined:7 describes:1 galilei:3 basic:1 ph:3 algebras:5 xz:1 fig:4 nuovo:1 ukraine:2 nattermann:9 families:5 arcsin:1 gen:2 coherent:1 systematic:1 c12:7 c2:15 c1:37 extensive:1 present:3 cot:2 case:25 globally:1 exception:1 p1:1 splits:2 tanh:1 arnold:1 transformation:21 trick:1 euclidean:1 suppose:1 studied:2 coupled:1 vol:1 von:1 thus:12 them:3 uxx:4 iv:2 ii:7 dζ:5 reads:5 im:11 ax:8 vx:3 ic:3 currents:1 different:2 l53:1 salamanca:1 suggest:1 make:2 admit:1 clearly:1 complex:2 quant:3 emphasize:1 s2x:3 finite:4 difficult:1 tz1:4 independent:5 extended:2 singapore:2 cubic:2 interscience:1 sym:10 purpose:1 necessity:1 potentials:9 infinite:9 invariance:2 recent:1 linearize:1 schr:10 nevertheless:2 whole:4 well:7 analysis:3 double:1 burgers:1 without:3 solve:2 lim:3 position:1 model:2 arising:1 dimension:3 unified:1 world:2 proposed:1 less:1 being:1 when:3 resp:1 half:1 obtain:8 homogeneity:2 press:2 shape:2 transforms:1 amp:2 polish:1 nicolas:1 unique:1 preprint:1 family:16 kluwer:1 density:2 regarded:1 z02:3 guaranteed:1 quadratures:2 attractive:1 theorem:1 input:1 consideration:1 remaining:1 euler:3 take:1 real:15 iγ:2 measurement:1 possible:2 admitting:2 possibly:3 five:1 lett:8 reobtained:1 confined:1 using:9 subfamily:3 mod:2 loss:1 like:2 semi:1 follows:3 xsx:1 performing:1 admitted:1 separately:1 yields:4 either:2 integrals:1 arbitrary:39 stationary:2 reduced:1 mathematical:5 galilean:1 because:1 methods:4 madrid:1 some:7 sym3:4 sym2:2 sym1:1 sym0:2 examples:1 choosing:1 sym4:1 fushchych:6 ourselves:1 provided:6 describing:1 dimensions:2 bottom:1 broad:1 integration:16 dz1:3 dz0:3 does:2 decomposition:1 inserting:3 conference:1 syma:1 bold:1 zα:1 rep:1 lu:2 use:3 revtex:1 although:1 substitution:2 possesses:1 properties:6 carried:1 extension:1 getting:1 discussed:1 o:1 deserves:1 a2:12 nothing:1 connected:1 vz1:2 vz0:4 consequently:5 presence:1 into:12 integral:2 three:1 remarks:2 references:1 iψt:3 determine:2 frames:1 financial:1 additional:3 strictly:3 there:2 question:1 transform:1 class:5 quadratic:5 way:3 forward:2 scientific:2 analyze:1 sections:2 function:30 form:10 ea:1 smolin:1 but:8 idea:1 volume:1 heat:6 properly:1 iµ1:1 line:1 dissipative:2 applying:2 ux:8 uz:1 fulfilling:1 ut:5 metries:1 smooth:14 up:1 us:8 international:1 dordrecht:1 below:1 ix2:2 fluctuations:1 distribution:1 xxvi:1 similar:1 called:5 mechanics:9 constant:9 heidelberg:1 int:3 certain:1 abstract:1 combining:1 linearity:1 general:33 dξ:11 examine:1 invertibility:1 exist:3 sxx:21 corresponding:5 physical:6 tedious:1 again:3 functions:19 differentiable:2 integrability:2 no:3 generally:2 detail:2 graduate:1 rewriting:2 field:2 other:2 spatial:3 mathematics:2 really:1 conclusion:2 polar:1 briefly:1 elements:1 models:2 preceding:1 problems:1 z13:1 important:3 variable:4 structure:3 correlated:1 algorithm:1 dτ:12 interval:3 implied:1 volumes:1 time:6 observables:2 backward:2 having:1
|
solv-int9510002.txt |@word partial:1 consider:7 funct:5 lagrangian:3 llp:1 results:4 eds:1 ferreira:1 proposition:4 computation:1 consists:1 sci:1 expressions:2 chaundy:1 lptens:1 gh:1 whose:1 inverse:2 dickey:5 tr:2 γj:1 finally:1 dijkgraaf:2 elliptic:1 under:2 analogous:2 indicating:1 degeneration:1 proved:1 string:2 wave:13 witten:3 manin:3 deformations:1 condition:1 common:1 dubrovin:3 riemann:1 hamiltonian:10 notes:1 list:1 solution:2 integro:1 commute:6 universal:1 indices:1 eigenvalues:1 bxb:1 abbreviated:1 wronskian:1 grateful:1 approximation:1 go:1 zero:2 further:1 spectral:1 established:1 what:2 nonlinear:3 appear:1 invertible:2 section:2 expressed:2 poles:7 expresses:1 consisting:1 coefficient:1 degree:1 respectively:6 here:3 tangent:2 governing:1 address:1 consideration:1 xα:1 equations:22 deduced:1 obtained:3 remark:2 gln:2 remarks:1 institute:1 lomi:1 inspired:1 studied:2 kontsevich:1 resulting:2 poisson:14 action:6 resonance:1 studies:1 φkl:2 family:1 bonora:1 isomonodromic:1 replace:1 apply:1 invitations:1 virasoro:1 use:1 takes:1 would:3 prove:2 remains:1 played:1 visit:1 quasi:2 memorial:1 ψj:16 classically:1 nucl:1 ψi:49 call:1 eϕ:2 type:5 theoretical:1 distinct:1 pavlov:1 µi:6 th:3 ecole:1 operators:9 stable:1 ematiques:1 curvature:2 eν:1 eλ:2 particular:1 known:2 eα:2 logarithm:1 valued:1 defines:2 deformed:1 recall:2 equation:5 mn:1 theories:3 following:6 example:2 proof:6 impose:1 give:2 generically:1 lϕ:1 aratyn:1 dxi:1 sense:1 verlinde:3 provide:1 s1:2 s0:4 takebe:2 maps:5 ordinary:1 parameter:1 map:12 product:2 algebra:1 may:1 zimmerman:1 singularities:1 orbits:1 lax:10 waves:3 representations:1 wronskians:1 compatibility:1 realized:2 short:1 natural:2 third:2 chern:3 packets:1 isf:1 so:12 writing:1 media:1 representation:2 talk:4 e2ϕ:1 holds:2 dx:2 hierarchy:10 over:2 dy:1 satisfied:1 rubtsov:3 paper:2 lattices:1 satisfies:2 its:5 itp:1 write:1 group:3 thank:1 how:1 ln:9 ll:1 lj:10 lk:8 li:25 xb:3 lt:1 permanent:1 systems:22 lp:1 lq:1 defining:1 13c:2 13b:2 them:3 return:1 enriquez:3 they:8 βkl:2 now:7 yu:3 βki:2 term:1 finite:7 classified:1 wdvv:3 hepth:1 2d:3 each:2 found:1 2n:1 higher:1 constraints:2 subset:2 arxiv:1 series:2 energy:2 idea:1 connect:2 quantum:2 our:2 operation:1 conjectures:1 mas:1 shown:1 benney:10 matrix:4 involution:2 res:1 since:2 induces:1 denotes:2 vector:9 rational:4 formula:3 rn:1 induced:1 induction:1 math:10 shows:1 theory:5 interactions:1 free:6 mapping:4 admits:1 ramos:1 iop:4 log:4 r3:2 geometry:2 could:1 similarly:1 takasaki:2 times:1 motion:1 turn:1 int:1 δij:10 δik:1 hence:1 βi:4 βj:3 first:12 xk:2 xi:8 xn:1 βlk:3 bijection:1 miura:3 variables:1 xa:1 cj:1 primary:1 bershadsky:1 rosly:1 dega:1 degb:2 construct:2 directly:2 xp:1 open:2 zap:1 ser:1 given:6 degenerations:1 introduction:1 leading:2 hydrodynamics:1 cheremushkinskaya:1 system:15 relations:4 insitute:1 their:5 conservation:1 observations:1 convention:1 1i:4 1j:1 structures:8 fermions:1 holomorphic:1 moscou:2 moscow:1 kupershmidt:4 nauch:1 part:7 authors:1 tft:2 x1:2 coefficients:2 distance:7 showed:1 accordance:1 imply:2 classes:2 pairwise:2 were:8 powers:1 fashion:1 symmetries:1 7b:3 7a:3 generalization:2 need:1 constrained:3 any:5 viewed:1 lie:5 wilson:2 λl1:1 petviashvili:1 depending:1 latter:1 gravity:2 inv:1 note:2 take:1 finding:1 cnrs:2 multiple:1 opposite:2 who:1 satisfy:1 paid:1 birkh:1 surv:1 most:1 connected:5 formulae:3 phase:8 acknowledgements:1 class:1 soliton:1 constructed:1 ura:1 orlov:2 considered:1 clear:2 later:1 coincides:2 points:3 verdier:1 exp:4 dop:3 physics:2 fact:4 laws:1 lebedev:2 show:8 βjk:2 supported:2 spaces:3 relation:3 solutions:9 analogue:3 find:3 ratio:1 aψ:1 written:4 topological:4 should:3 lemma:2 going:1 pairing:1 integrable:6 hamiltonians:1 oct:1 hope:1 his:3 dj:2 means:1 de:1 da:1 aα:4 ones:1 ϕi:45 closely:2 ϕj:11 during:1 du:1 evolution:1 kadomtsev:1 babelon:1 fields:6 differential:11 expansions:1 method:2 hydrodynamic:2 fixed:1 ql:1 view:1 kernel:3 set:4 computed:1 attached:5 δjk:1 hα:1 j1:1 plausible:1 λk:1 namely:1 result:1 discussions:1 terms:3 sem:1 surfaces:1 shirshov:1 commutation:1 liouville:3 µl:12 enough:1 various:1 between:2 αi:5 limit:1 boundary:2 αj:3 conditions:2 preserve:1 recently:1 extend:1 analogues:5 flow:3 manakov:1 ji:1 δab:1 solv:1 jetp:2 both:1 last:5 limits:2 treated:1 0x:5 equal:2 fulfilled:1 etc:1 connection:3 symplectic:2 context:1 expression:1 generalisation:1 point:3 simple:2 cf:1 semiclassical:2 pole:3 grants:1 lagrange:1 cancel:1 fibres:1 cp:1 diff:4 conference:4 ps:2 commutative:1 second:9 addition:2 informed:1 due:1 sl2:1 ai:11 pk:4 algebras:4 pn:1 abstract:1 define:11 generating:2 covector:1 corresponding:4 mcj:1 cotangent:2 quantities:2 formed:2 x2i:2 xiong:1 case:5 divisions:1 multi:2 itep:2 subsets:1 ada:1 expanded:1 will:4 euclidean:1 near:2 replaced:3 aij:1 situation:1 study:2 correspondence:1 simons:3 endowed:6 non:2 ii:2 ij:2 aspects:1 different:1 formalism:1 author:2 commuting:1 make:2 same:1 palaiseau:1 parts:1 φi:1 hierarchies:4 several:1 composition:1 difficult:1 extended:1 infinity:3 yi:2 i1:4 i0:2 flows:12 hand:2 viewing:1 auser:1 landau:1 identity:3 weakly:1 δϕi:3 dispersionless:4 solve:1 model:1 arising:1 preprints:1 usual:6 λs:1 gelfand:4 among:1 being:4 resp:1 obtain:1 λa:2 δψi:3 facts:1 scattering:1 λl:21 adv:1 preprint:2 classification:1 zakharov:2 seems:1 add:1 other:4 lett:3 theorem:1 solvable:1 euler:1 generalized:1 burchnall:1 sytems:1 iα:7 posed:1 possible:1 lychagin:1 know:1 using:3 ams:1 vλ:3 moreover:2 formal:4 dimensional:2 appearing:1 like:2 follows:6 losev:1 δp:2 δl:1 δj:1 polytechnique:1 translated:1 leaves:2 stationary:2 because:1 methods:1 classical:5 sequence:1 some:8 identified:1 understood:2 equivalent:1 b1:4 b2:1 specified:1 kdv:2 δbb:1 provided:1 centre:1 integration:2 comments:1 prop:1 prog:1 proc:1 gratitude:1 obey:1 bn:2 bi:4 βij:5 βik:3 properties:2 about:2 pα:8 central:1 algebraic:1 novikov:2 o:1 compatible:2 union:1 extensions:1 cartier:1 act:1 introduced:5 soc:1 contains:1 letters:1 bundles:1 into:1 successive:1 functional:1 modifying:1 pair:2 gomes:1 references:1 sov:1 operator:16 france:1 hep:2 additional:3 whom:1 there:1 question:2 lond:1 long:6 appl:6 way:2 ed:1 was:3 gij:1 function:10 elsewhere:1 form:7 but:3 volume:1 construction:2 russian:1 rffi:1 true:1 adler:3 he:2 applying:1 wish:1 smooth:4 us:12 krichever:15 ul:1 below:1 ui:3 uk:2 russ:1 problem:5 eigenvector:1 interplay:1 bearing:1 ab:4 associated:2 defined:6 certain:1 ak:1 pseudodifferential:1 proven:1 denote:1 transl:1 conserved:2 13a:2 khoroshkin:1 work:1 identities:1 βji:1 bracket:2 again:2 functions:14 no:1 index:1 whereas:1 field:9 definitions:1 kp:13 role:1 papers:1 cp1:2 models:3 symbol:1 radul:2 problems:1 bundle:1 a3:1 structure:7 implies:1 assume:4 space:12 curve:2 equivalently:1 kera:1 time:1 ls:5 starting:2
|
solv-int9510003.txt |@word consider:3 rev:11 particular:3 datum:1 amplifies:1 leads:2 cooperative:1 consists:4 forget:1 compact:2 whose:1 inverse:3 terms:3 zone:1 everything:2 created:1 finally:6 present:1 th:1 case:10 g0:7 rise:1 results:4 every:1 summarized:1 exact:1 plemelj:1 common:1 entire:2 riemann:6 solves:1 level:2 transmission:2 t2:3 solution:24 large:8 solved:5 anal:1 optics:2 solutions:3 upper:4 computation:3 f21:2 discover:1 pulse:2 approximation:1 zero:1 value:8 nonhomogeneous:1 dynamics:2 choices:1 linear:2 spectral:15 nonlinear:7 appear:3 section:1 dephasing:2 expressed:2 νt:3 version:1 poles:3 wenzel:2 goes:2 new:3 principal:1 method:8 coefficient:7 discontinuity:2 notions:1 respectively:1 here:9 relaxation:2 represented:1 19d:1 equations:16 appears:1 interpret:1 obtained:8 arrive:1 study:1 vectors:1 allows:3 amount:1 resulting:1 resonance:1 studies:1 uniquely:1 montpellier:3 scales:1 discontinuous:1 explicitely:1 replace:1 select:1 readily:1 use:5 feb:1 would:1 prove:3 france:1 comparing:5 therefore:1 spike:6 taken:2 volterra:1 zeroes:1 incident:1 becomes:3 envelope:4 emission:1 transient:1 walmsley:2 sharply:1 varying:1 iv:26 iii:47 states:5 account:1 valued:2 integrating:1 rν:1 equation:12 work:2 det:1 reads:3 renders:1 transparency:1 following:15 closing:1 equilibrium:1 proof:1 f1:9 f2:9 give:4 process:1 choice:1 νx:2 high:1 effectively:1 performed:2 times:1 occur:1 overbar:1 axis:6 information:1 end:1 sit:1 verify:1 discussion:1 get:2 strikingly:1 instead:1 parameter:1 fredholm:1 description:1 fx:1 max:1 oscillators:2 wiley:1 residues:2 consequence:2 plane:5 lax:6 waves:2 requirements:1 wave:6 data:8 compatibility:1 realized:1 short:3 physical:5 remember:1 third:1 light:4 explicit:1 correspond:1 so:3 allow:2 definitions:2 order:5 2ikx:20 holds:1 indeed:2 entries:1 soon:1 furnishes:3 experiments:3 pulses:1 ηc:3 still:1 its:3 before:1 derive:2 thank:1 ln:5 interesting:1 solving:3 conjugation:1 actually:6 systems:1 lq:1 defining:2 non:1 matches:1 uhl:3 material:3 runs:1 they:3 half:5 now:5 possess:2 easily:2 νe:1 l2:1 mode:1 l1:1 simplified:1 2i:2 constraints:1 homogeneous:1 mikhailov:2 differential:7 ei:5 generation:1 reduce:1 related:2 frequency:2 quantum:5 our:1 redwood:1 shown:1 matrix:4 discrete:2 res:5 iλi:1 since:2 vectorial:1 denotes:2 stud:1 formula:5 electronics:1 induced:1 occurs:1 math:6 matrices:2 theory:3 written:4 kaup:4 diagonal:4 free:1 standard:1 reason:1 york:1 dλf:2 definition:1 interaction:2 applications:1 determining:1 ist:3 unitarity:1 length:1 dλr:1 hence:7 first:11 informations:1 there:4 variables:1 number:3 transform:7 clear:1 done:4 relations:6 directly:1 precisely:2 equating:1 city:1 given:10 law:1 introduction:1 system:7 construct:1 their:2 siam:1 especially:1 gives:8 shifted:1 relationship:1 continuous:1 proving:2 newell:2 immediate:1 optical:1 manifestation:2 off:2 coefficients:2 population:2 distance:1 require:3 imply:1 submitted:1 preformed:1 amplitude:1 were:2 f12:2 f11:6 behaviors:4 raman:9 reduction:6 spectrum:1 already:1 say:2 seed:1 20d:1 ans:1 need:2 seen:1 turn:1 any:1 convenient:2 self:1 scott:1 physique:1 polarization:2 instance:1 potential:1 green:4 accuracy:1 cnrs:1 exactly:1 fundamental:1 shall:2 pleasure:1 pair:5 stands:1 soliton:2 laurent:1 ura:1 macpherson:1 ki:2 later:1 coincides:1 kn:22 physica:4 kl:2 ks:2 kr:3 part:1 kv:2 exp:18 velocity:1 physics:1 fact:1 quantity:2 nls:3 selection:1 relation:8 inconsistent:1 ground:1 just:1 claude:2 situations:1 distributed:1 pump:9 analytic:10 only:1 going:1 integrate:1 integrable:2 polarizability:2 do:1 above:8 notation:2 means:6 express:1 dx:16 dr:3 segur:1 evolution:21 determinants:1 qt:3 approach:1 arxiv:1 predicted:1 analytical:3 through:2 view:1 requirement:3 set:1 alsing:1 physically:1 see:6 sec:1 result:3 discussions:1 close:2 contour:1 chose:1 hilbert:6 bowden:1 phonons:1 scattering:3 f22:6 state:2 envelopes:3 between:3 boundary:21 conditions:1 meromorphic:1 recently:1 shabat:1 nature:1 initially:3 however:3 js:16 jl:14 vanishing:4 ikf:1 demonstrate:2 solv:1 distribution:1 both:3 pempinelli:3 many:1 ill:1 according:1 context:2 passing:1 comes:1 relevant:1 cn:13 point:1 simple:3 continuation:2 ca:1 period:1 leon:7 simply:2 polynomial:1 moreover:1 li:1 ensures:1 second:2 addition:1 due:1 been:13 acheived:1 defined:5 detuning:1 cauchy:6 initiation:1 ensured:1 interest:1 basic:3 substraction:1 dk:1 pm:1 addison:1 corresponding:1 coherence:1 gas:1 coherent:1 2im:1 2ik:7 denote:1 aknowledgements:1 those:2 applied:1 laser:4 profiles:2 spontaneously:1 will:7 while:2 evaluating:2 applies:2 property:5 coupled:1 vi:15 boiti:3 ir:1 surface:1 equal:1 ii:49 ik:1 itself:2 im:23 il:2 vx:1 vanish:4 interacts:1 different:1 recover:1 verified:1 qas:2 same:5 stimulated:2 complex:2 dimensionless:4 finite:14 grows:1 four:1 used:4 infinity:1 i0:13 parametrized:1 purpose:1 potentials:2 infinite:4 ablowitz:1 identity:1 prescribed:1 lower:2 schr:1 reflection:4 well:2 englund:1 solve:8 experimental:1 components:2 lim:3 dimension:1 usual:1 λr:2 nonanalytic:4 proposed:3 being:1 resp:2 identically:1 obtain:2 rest:2 λi:1 macroscopic:1 adding:1 preprint:3 density:3 zakharov:2 guaranteed:2 except:1 iω:5 interested:1 lett:7 theorem:4 iρ:1 input:3 solvable:4 remaining:1 real:8 rescaled:2 around:1 rules:1 posed:2 corresponds:1 eorique:1 swanson:1 vacuum:1 using:7 moloney:1 necessary:2 like:1 semi:6 reduces:1 menyuk:2 steps:1 integrals:1 arbitrary:5 evolutions:4 output:7 essential:3 because:3 methods:1 namely:1 creation:1 some:1 calculated:2 growth:2 extended:1 electromagnetic:2 integration:2 comments:1 depletion:1 does:4 prog:1 yariv:1 refer:1 run:1 obey:1 rescale:1 expansion:1 constructive:1 wesley:1 step:5 although:1 become:2 properties:3 raymer:2 stokes:9 constraint:2 dependence:3 o:3 compatible:1 srs:12 obeys:2 introduced:1 consequently:6 2iπ:12 letters:1 into:2 within:2 integral:14 bound:5 down:1 phase:4 operator:1 successively:1 next:1 assumed:1 support:3 initial:11 approximate:1 long:1 dispersion:6 appl:1 way:1 slowly:1 chu:1 function:8 medium:13 form:1 denoting:1 but:4 cedex:1 construction:1 line:8 true:3 observation:1 compute:4 ut:1 ωs:9 ωt:14 ωv:4 note:3 ωl:8 fluctuations:4 problem:24 define:1 called:1 interval:9 proved:5 conserves:1 computing:1 int:1 general:6 single:1 eigenfrequency:1 dλ:27 6d:2 distributions:1 constructed:2 functions:9 analyticity:2 ematique:1 no:3 when:8 vanishes:3 field:3 other:2 fokas:2 eiθ:1 theor:1 briefly:1 elements:1 star:1 excitation:3 problems:1 odinger:1 important:1 bounded:3 kz:3 goursat:1 implies:1 auxiliary:1 assume:2 values:17 required:2 usefull:2 appendix:1 mass:1 time:10
|
solv-int9510004.txt |@word angles:2 illustrates:1 squared:1 results:2 leads:1 eds:1 rebbi:1 ruback:2 localized:5 seemed:1 inverse:3 depend:1 concerned:1 tr:1 belavin:1 stable:1 tf:1 analogous:1 include:1 interchange:1 norm:1 stud:1 srivastava:1 choice:2 monopoles:1 matrices:2 condition:10 arrange:1 induction:1 rosenzweig:1 solution:26 large:3 vector:1 anal:1 strachan:1 force:1 integrability:2 10r:1 dynamics:2 decelerating:1 even:2 factorizes:2 what:4 nonlinear:2 appear:1 d2:1 section:6 axes:1 near:1 version:2 poles:3 goes:1 new:1 row:2 method:1 contrast:2 here:3 understanding:1 pioneered:1 directions:1 along:5 equations:5 obtained:1 shift:1 vectors:2 approaches:2 example:7 resulting:2 usually:1 myers:1 spacetime:1 emerge:3 family:2 kudryavtsev:1 unitarity:4 ask:1 durham:2 total:1 standing:1 asymptotic:2 would:1 commun:1 distinct:1 positive:3 negative:1 next:2 comparing:1 nucl:2 therefore:1 centre:1 taken:1 3le:1 type:2 more:3 introducing:1 leese:2 solitons:28 under:1 everywhere:1 particular:3 known:1 ward:5 must:2 rotational:1 equation:12 det:1 mk:3 values:1 exceptions:1 making:1 scatter:1 proof:1 f1:2 f2:2 figure:2 do:1 4t2:2 sense:2 collision:5 lorentz:2 allowed:1 axis:7 turn:1 rather:1 holds:1 feature:1 write:1 how:3 nontrivial:6 parameter:2 belongs:1 product:1 nonconstant:1 description:1 may:6 variant:1 lump:2 uhlenbeck:1 plane:4 coming:1 fk:2 revealed:2 higgs:2 consequently:1 explicit:2 su:6 so:8 order:4 davey:1 words:3 produces:1 indeed:1 move:1 expects:1 stability:1 course:1 paper:7 through:1 satisfies:5 still:1 its:5 located:2 interesting:2 undermined:1 coordinates:1 strange:1 degrees:1 systems:6 travelling:1 might:3 them:1 collide:2 they:7 smoothness:1 easily:1 term:1 2p:2 2q:1 2r:2 university:1 identified:1 merge:1 each:3 higher:4 referred:1 differential:1 energy:6 idea:2 related:1 static:4 expect:1 our:1 out:1 matrix:5 space:3 since:1 crucial:1 denotes:2 looking:1 geom:1 rational:4 nontrivially:1 get:2 forth:1 math:6 linear:3 interactions:1 standard:2 admits:1 completely:2 put:1 generate:1 8t:2 interaction:1 chiral:8 r2:4 geometry:1 could:1 impose:1 motion:3 thing:1 consequence:1 undergo:1 speeds:1 first:3 origin:3 features:1 symmetry:3 variables:1 number:1 xy:2 another:1 ring:2 size:1 passes:1 given:3 necessarily:1 likely:1 their:3 introduction:1 interact:3 system:13 approximately:1 indicate:2 eqn:3 speaking:1 gives:2 exactly:2 x2:3 moriarty:1 representing:3 than:1 coefficients:1 peaked:1 distance:1 was:5 painlev:1 classes:1 kth:2 were:1 e2iφ:1 exhibit:1 boston:1 wiesbaden:1 conjugate:1 close:1 seen:1 seem:1 any:2 angle:1 zero:1 depending:2 latter:2 mills:2 note:3 sciences:1 internal:2 take:5 finding:1 begin:1 towards:1 shall:1 quote:1 birkh:1 algebraic:1 multisoliton:1 phase:1 analytically:1 class:1 involving:1 soliton:10 nonlinearity:4 examining:1 inferred:1 yang:2 exp:2 velocity:1 physics:1 fact:4 quantity:1 phenomenon:1 show:1 radii:1 solutions:13 carefully:1 tempted:1 trivial:5 find:3 d1:1 impact:1 parameters:1 piette:2 enough:1 topological:3 only:4 wood:1 integrable:10 nonzero:1 oct:1 abelian:1 cube:1 above:1 di:3 dependent:2 simplest:1 satisfied:1 closely:1 dy:1 peyrard:1 kadomtsev:1 approach:1 arxiv:1 taubes:1 rotationally:1 though:1 double:3 requirement:2 constructing:2 exists:1 j0:3 j1:2 maximum:1 observed:1 depends:2 bordag:1 jx:3 subject:1 satisfying:1 interacting:1 speed:1 definite:1 symmetric:2 written:1 determined:1 various:2 µk:3 between:1 invariant:1 boundary:4 conditions:1 meromorphic:2 matveev:1 terms:3 jy:4 jt:5 emitted:1 transpose:1 however:3 manakov:2 sutcliffe:4 solv:1 topology:1 both:1 many:3 taking:1 etc:1 admit:1 whole:1 shabat:1 relevant:1 fields:3 conclude:1 simple:3 corresponds:1 height:1 dimensional:7 concluding:1 pole:6 associated:1 points:1 described:3 addition:1 three:2 been:1 int:2 reduction:1 describes:2 expected:1 lett:6 direction:1 arises:1 corresponding:5 maps:1 systematic:1 2ig:2 general:1 hidden:1 those:1 case:5 multi:1 strictest:1 single:1 value:3 will:2 dept:1 while:2 replaced:1 irrespective:1 procedure:1 iy:2 unitary:3 orientation:1 coupled:1 non:1 dual:1 confirmed:1 things:1 zakrzewski:4 radiation:2 connection:1 same:5 vieweg:1 complex:4 finite:1 difficult:2 independent:5 used:1 infinity:1 see:4 trivially:2 numerical:4 functions:3 driven:1 moving:1 auser:1 identity:1 petviashvili:1 uniton:4 roughly:1 without:1 consistency:1 coordinate:1 model:2 self:1 dh1:1 less:1 being:2 rotated:1 obtain:2 inelasticity:1 shape:1 scattering:14 stewartson:1 previous:3 density:4 zakharov:5 seems:2 except:1 5r:2 other:8 extends:1 attractive:1 reason:1 role:1 mod:1 εh:2 iθ:1 possible:2 admitting:2 harmonic:1 appearing:1 highly:1 apart:1 modifications:1 rotate:1 necessary:2 like:1 sizes:1 follows:3 accelerating:1 imposes:1 yields:1 either:1 arbitrary:1 stationary:1 mathematical:1 grouped:1 because:1 namely:2 vortices:2 some:4 somehow:1 understood:1 accelerate:1 diff:1 happens:4 proceeding:1 dimensions:1 opposite:1 overlap:1 does:2 provides:1 elucidate:1 nowhere:1 fordy:1 takes:2 freedom:1 discussed:1 o:2 r1:1 ensure:2 2iφ:1 introduced:2 slightly:1 rev:2 letters:1 previously:1 into:2 integral:1 functional:1 shellard:1 pair:2 right:2 references:1 proportional:3 elastic:2 there:12 long:2 spread:1 appl:2 way:4 exceptional:1 dx:1 naturally:1 function:1 head:3 form:8 but:5 volume:1 construction:2 true:1 suspect:1 jaffe:1 whether:1 smooth:4 up:1 us:1 below:1 limit:4 uk:1 constant:4 defined:2 abstract:1 evidence:1 conserved:1 simulations:1 check:1 constructed:1 again:1 mutual:1 no:3 when:2 detail:1 field:2 setting:1 remarks:1 spatial:2 test:1 picture:4 apparent:1 separate:1 models:2 a1:3 commutator:1 a2:3 variable:3 needed:2 implies:1 assume:1 sigma:1 factors:1 having:2 departs:1 mass:1 time:8 func:1 original:2 once:1
|
solv-int9510005.txt |@word secondly:1 partial:1 crucial:1 global:6 results:1 four:1 go:1 expressions:1 ward:4 localized:1 certainly:1 inverse:3 technique:1 tr:4 nonlocal:11 finally:1 preserved:1 currents:2 under:2 analogous:4 divergent:3 federation:1 very:1 translations:1 multi:1 choice:2 putting:1 fall:1 matrices:1 condition:10 entire:2 solution:5 deals:1 involution:1 vector:4 indices:1 eigenvalues:1 noted:1 consistent:2 direct:1 sign:1 painlev:2 further:1 odd:1 theory:1 even:2 established:1 appear:1 diag:1 section:3 expressed:1 version:2 above:3 new:3 contrast:1 satisfy:1 full:1 respectively:2 component:1 equals:1 here:2 situation:1 concluding:1 sine:1 equations:17 obtained:1 remark:1 allows:1 suggests:1 resulting:1 action:2 makes:1 involves:3 via:1 useful:1 family:1 ϕ2t:2 durham:2 apply:1 unit:3 derivatives:1 use:1 takes:1 would:1 prove:1 sake:1 positive:3 next:1 few:1 ψn:1 therefore:1 3le:1 refs:1 more:4 flat:1 leese:1 formally:1 solitons:1 operators:1 aware:1 particular:3 known:6 cases:1 valued:2 equation:22 det:1 obvious:4 ρt:3 following:2 ρx:1 ρz:2 example:3 initial:1 compare:1 wang:1 give:1 relativistic:1 sense:1 involve:1 arise:2 needs:1 rather:1 discussion:3 ϕz:2 feature:1 write:2 maps:1 antiholomorphic:1 acta:1 parameter:1 simplicity:2 description:3 algebra:2 may:2 singularities:3 lump:1 consequence:1 explored:1 law:1 data:1 constants:1 natural:1 third:1 sets:1 sech:1 explicit:2 correspond:1 su:7 think:1 so:16 sl:1 breaking:1 dx:7 pointed:1 equally:1 paper:1 including:1 mentioned:2 existence:4 satisfies:2 still:1 its:2 before:1 leznov:3 tending:1 group:5 located:1 chosen:1 coordinates:1 absence:1 parts:1 defining:1 them:2 motivated:1 they:5 rotation:1 now:2 discuss:1 represents:1 several:1 2p:4 fully:1 university:1 sufficiently:1 2f:2 each:4 soc:1 referred:1 differential:1 financial:1 energy:9 reduce:1 related:3 sinha:1 owing:1 static:4 our:3 really:1 matrix:6 space:5 since:6 lagrangian:7 acting:1 geom:1 rational:2 rn:2 issue:1 occurs:1 math:8 linear:2 localization:1 derived:1 possibility:1 approaches:1 generate:1 xuv:1 chiral:17 r2:2 geometry:1 could:1 impose:2 times:2 motion:1 manakov:1 gordon:1 hence:3 exhibited:2 first:5 already:1 symmetry:9 relate:1 variables:2 number:1 lond:1 xx:2 specifically:3 another:2 xv:2 angular:1 given:6 necessarily:1 rewritten:1 indicate:1 introduction:1 πk:1 system:2 relations:1 their:3 appl:1 eqn:2 gives:2 holomorphic:1 part:1 somewhat:1 than:2 require:3 zero:1 determined:1 were:2 stricter:1 exhibit:1 symmetries:5 argument:1 say:1 acknowledgment:1 conjugate:1 need:1 iχ:1 seem:1 any:3 lie:2 angle:1 self:3 mills:3 converges:1 note:6 sciences:1 potential:1 take:5 timelike:1 shall:2 decreasing:1 most:1 involving:2 connected:1 pair:1 xµ:3 soliton:8 pohlmeyer:2 parametrize:1 nonlinearity:1 clear:1 later:1 yang:3 exp:2 physics:1 fact:1 laws:5 precise:1 particularly:1 show:1 jµ:4 gauge:6 solutions:9 find:1 q1:1 enough:1 stud:1 only:5 integrable:13 local:6 oct:1 do:7 ϕx:1 means:1 cannot:2 dz:1 words:2 dy:8 dt:1 positivedefinite:1 densities:12 arxiv:1 yield:3 investigate:1 mαβ:1 fixed:1 qn:11 set:5 exists:1 j0:3 j1:2 depends:2 jx:7 tensor:1 µz:1 speed:2 positivity:1 complementary:1 definite:1 diverge:4 written:1 between:1 invariant:3 boundary:8 conditions:4 meromorphic:1 multiplied:1 terms:1 jy:2 jz:4 nature:1 jt:9 ju:7 jv:2 however:5 sutcliffe:3 concentrate:2 key:1 solv:1 both:2 essentially:1 many:3 among:1 relevant:2 characterization:1 simple:2 ca:1 cf:2 dimensional:6 anti:1 lagrange:1 polynomial:1 diff:1 prasad:2 light:1 described:1 west:1 skew:1 locally:1 three:1 been:1 int:1 reduction:2 much:1 ensured:1 define:2 direction:1 arises:1 corresponding:7 quantities:20 xxx:1 search:1 observe:1 denote:1 present:1 case:8 p0:1 novel:1 bρ:1 straight:1 conserved:40 value:1 dept:1 euler:1 applies:1 irrespective:1 property:1 iy:2 real:2 unitary:1 spacelike:1 applic:1 metric:1 dual:3 claimed:1 ie:1 examine:1 different:3 author:1 make:1 same:2 member:1 complex:2 avoids:1 sinegordon:1 finite:2 independent:4 used:1 infinity:3 see:4 effect:1 moving:1 infinite:7 totally:1 identity:1 mentioning:1 off:1 charges:8 well:12 analysis:1 components:2 consistency:1 model:1 arising:1 latter:2 dh1:1 being:3 sdym:5 thanks:1 harrison:1 alternative:1 scattering:2 yet:1 previous:1 bullough:1 density:6 zakharov:1 point:2 parametrization:2 appeared:1 extends:1 lett:5 easy:1 theorem:2 dqn:1 momentum:10 noether:3 iθ:1 harmonic:1 vα:10 increases:1 using:2 appearing:1 like:1 follows:3 yields:1 either:1 integrals:4 arbitrary:2 reduced:3 mathematical:1 because:2 old:1 deal:1 sequence:5 sequences:7 some:1 nonzero:1 dimensions:5 lead:1 integration:2 does:1 proc:1 prob:1 saveliev:1 aαβ:2 equivalent:4 how:1 although:4 properties:1 comparison:1 about:1 2cy:2 algebraic:1 commun:2 o:5 uhlenbeck:1 germany:1 consequently:1 automatically:1 jν:1 raised:1 rev:1 letters:1 previously:3 into:1 integral:4 functional:2 locus:1 phase:1 hermitian:2 references:1 operator:1 reducing:1 classical:1 support:1 there:12 question:1 transform:1 fast:1 thirdly:1 conservation:7 way:4 was:4 function:6 complete:2 form:9 regard:1 but:9 repeated:1 lowered:1 convergence:2 line:1 true:1 he:1 made:1 evident:1 whether:1 welldefined:1 up:4 us:6 liouville:2 uk:1 demonstrate:1 problem:2 called:1 ac:2 constant:7 defined:11 abstract:1 contribute:1 general:3 single:1 exist:2 moves:1 sasaki:1 constructed:1 again:1 functions:2 integrability:2 no:2 whereas:2 vanishes:1 reality:3 field:1 other:4 remarks:2 spatial:5 out:1 conclude:1 bounded:1 sides:1 nonintegrable:1 independently:2 implies:3 values:1 together:1 time:6 quantity:1 original:1 once:1
|
solv-int9510006.txt |@word consider:3 depend:1 equivalence:1 tn:12 finally:1 does:1 tj:2 th:1 under:2 p2:1 conjecture:1 far:1 mδm:1 wave:2 difference:2 condition:5 solves:2 list:1 solution:8 zz:4 further:2 theory:3 bilinear:3 stands:2 t2n:3 expressed:1 above:2 kyoto:2 coefficient:1 here:2 sinh:3 equations:7 obtained:1 remark:1 algebra:1 study:3 periodic:6 mulase:2 makes:2 formulated:1 9a:2 9c:2 9b:1 univ:2 clifford:1 dpdq:1 would:1 negative:2 next:1 nucl:2 type:4 more:1 becomes:1 operators:6 appendix:1 fermionic:2 tokyo:3 equation:4 det:4 modified:1 infinitesimal:1 following:3 example:3 proof:1 give:1 expanding:2 sense:1 14b:1 14a:1 uker:1 end:1 viewpoint:3 rather:2 takebe:1 pure:2 fredholm:8 fs:2 npj:1 lax:1 choice:1 compatibility:1 ueno:3 element:1 so:1 acknowledges:1 hierarchy:11 through:2 japan:1 satisfies:3 τn:7 group:1 manuscript:1 ln:1 affine:1 boson:1 systems:1 remarked:1 mail:1 pjm:3 13b:1 them:1 pjn:2 continuum:6 finite:2 2p:1 university:1 identified:1 2d:2 2n:1 referred:1 domain:3 arxiv:1 ej:2 reduce:1 toda:5 our:2 eq:15 special:1 jimbo:1 matrix:2 since:1 denotes:1 contained:1 ajm:1 stud:2 conjectured:2 ref:4 integrated:2 math:4 linear:1 8b:1 8a:1 quite:1 mmm:1 ntn:2 impose:1 takasaki:4 gordon:2 xj:1 xi:3 symmetry:1 another:1 given:1 similarly:1 eqs:4 relations:1 their:2 recovered:1 authors:1 than:1 showed:1 powers:1 7b:1 7a:1 zamolodchikov:5 kajiwara:1 any:2 lie:2 latter:1 note:1 sciences:1 take:3 coincide:1 even:1 trace:1 though:1 algebraic:1 automorphism:1 nothing:2 tracy:2 class:1 soliton:6 professor:1 kp:1 ku:1 fact:1 quantity:6 12a:1 12b:1 show:3 miwa:1 relation:3 substituting:3 based:1 should:1 bernard:2 explicitly:1 integrable:2 oct:1 hope:1 dn:7 his:4 dj:2 notation:1 get:4 expectation:1 meguro:1 dp:1 determinants:1 widom:2 differential:1 shg:5 qj:6 kernel:1 set:3 imposing:1 δjk:1 j1:2 see:2 recently:1 between:1 reading:1 conditions:3 terms:2 shabat:3 rims:2 p2n:1 jp:1 jl:4 solv:3 come:1 both:1 taking:2 expression:2 cj:2 cn:7 cm:2 corresponds:3 16b:1 16c:1 mkdv:5 addition:1 suppressed:1 been:1 int:3 reduction:3 cauchy:1 pj:16 pk:1 komaba:1 pl:1 define:1 6a:1 determinant:6 understand:1 c1:2 c0:9 former:1 those:1 case:2 value:1 will:1 yi:1 cylinder:1 refs:1 non:1 obeying:1 yj:5 fermion:2 author:1 member:1 hierarchies:1 several:1 used:1 qjm:2 qjn:2 publ:2 infinite:1 identity:2 recent:1 acknowledgement:1 well:1 cj1:2 λs:2 λw:1 resp:1 λk:2 λj:4 λn:1 adv:2 preprint:2 zakharov:3 lattice:5 belongs:1 lett:1 5a:1 5b:1 16a:3 vacuum:1 formal:1 imposed:1 polymers:2 reduces:1 integrals:2 evolutions:2 mathematical:1 some:2 2y:2 b1:11 b2:2 kdv:1 shall:1 integration:2 critical:1 connecting:1 bm:4 bn:5 bj:2 15a:1 discussed:2 stand:1 introduced:3 jν:2 letter:2 into:3 integral:1 references:1 operator:2 log:5 start:1 was:1 function:8 form:3 but:2 hn:7 hm:1 leclair:2 up:1 below:1 limit:8 b426:1 b432:1 problem:1 pm:1 ac:1 proved:2 defined:2 certain:1 abstract:1 aj:4 6b:1 general:2 13a:1 formulation:2 constructed:3 satsuma:2 functions:2 when:1 field:1 other:1 details:1 department:1 briefly:1 exp:20 time:2 polynomials:1 a1:1 15b:2 structure:1 independently:1 6b1:1 hirota:2
|
solv-int9510007.txt |@word represent:1 consider:3 remarkable:2 similarity:1 lack:1 results:4 four:1 eds:2 follow:2 remarkably:2 gl:7 row:1 whose:3 preserves:1 inverse:4 depend:1 funct:1 tr:9 γk:15 finally:2 γn:3 under:1 semenov:1 discretization:1 belonging:2 returning:2 very:1 could:2 choice:4 corollary:1 every:2 formula:3 difference:18 matrices:29 leads:2 obvious:4 hamiltonian:22 turns:1 notes:2 solution:8 deals:1 solved:3 interpolating:4 dealt:1 small:1 relation:8 anal:1 shansky:1 unversity:1 upper:2 lecture:2 direct:8 approximation:6 second:8 further:1 expressions:8 substitute:1 even:1 nonlinear:3 stands:1 brackets:5 diag:1 sum:1 analogously:1 expressed:2 d3:1 version:1 subspaces:1 new:2 consisting:2 satisfy:9 full:1 simultaneously:1 mem:1 respectively:1 hδk:2 proc:1 here:6 papageorgiou:1 canonically:3 identifications:4 groups:7 represented:3 equations:46 tian:1 remark:2 ekk:20 involved:1 studied:1 allows:2 periodic:16 resulting:4 poisson:14 stressed:1 usually:1 suitable:1 uniquely:4 formulated:1 transformations:2 family:1 prefer:3 brought:1 hamiltonians:5 santini:1 univ:1 use:3 takes:8 would:6 commun:2 ruijsenaars:3 contains:1 visit:2 negative:2 next:2 choosen:1 themselves:1 type:4 minor:1 more:2 fractions:9 successful:1 solitons:1 operators:1 dressing:1 validity:2 particular:2 known:2 cases:2 hold:2 iii:1 potential:1 springer:1 valued:1 recall:3 equation:26 work:3 values:4 following:22 my:2 example:1 proof:10 beautiful:1 lπ:1 give:2 calculation:2 relativistic:18 organized:1 purposes:1 dependence:2 dxk:1 want:1 allowed:1 simple:2 end:10 rather:1 maps:14 instead:1 ordinary:1 parameter:3 map:19 express:4 algebra:1 may:13 oscillators:1 space:4 different:5 consequence:4 levi:1 lax:14 recognizes:1 representations:2 fk:2 compatibility:4 types:2 forschungsgemeinschaft:1 dynamical:5 imply:3 interpolated:1 light:1 schneider:1 lines:1 deutsche:1 algorithms:1 sect:4 fundamental:1 representation:9 βk:37 order:2 bull:1 evolutionary:1 interpretation:1 help:5 hierarchy:8 indeed:1 over:1 satisfied:4 years:2 course:1 paper:1 through:3 lattices:7 mentioned:1 equip:1 still:3 its:2 before:3 ld:1 derive:10 group:11 thank:1 continued:10 solving:4 coordinates:6 li:2 forms:2 kuznetsov:1 lu:3 systems:15 mail:1 them:3 return:1 lambert:1 propose:1 acklund:1 introduce:4 mention:2 they:4 now:14 thes:1 discuss:2 above:1 deift:1 finite:3 equality:5 explains:1 university:1 identified:1 sufficiently:2 each:1 found:2 differential:3 directly:7 ek:24 hard:4 related:2 conventions:1 toda:22 our:5 operation:2 neighbourhood:3 out:3 matrix:26 discrete:25 since:2 lagrangian:10 chaos:1 research:1 hck:26 ref:2 math:7 turning:3 linear:2 circumstance:1 diagonal:1 standard:2 admits:6 yuri:1 put:1 subalgebras:1 e1:1 generate:1 log:7 hc2:2 definition:4 pairs:2 hc1:5 recipes:1 motion:7 hence:3 βn:2 first:10 xk:343 initial:6 xn:6 variables:13 supposing:1 rank:1 system:27 multiplying:4 done:1 least:2 another:1 impossible:1 open:9 given:4 checked:2 rewritten:4 similarly:4 introduction:1 eqs:1 twisted:2 construct:1 their:3 appl:1 statement:1 scheme:2 gives:1 fraction:1 ch:2 continuous:8 serve:1 part:8 because:6 x0:4 x1:2 completes:2 sections:1 approximations:2 integrability:6 winternitz:1 kth:1 supposed:2 powers:2 hz:5 symmetries:1 turned:2 say:1 substantial:1 close:1 recover:1 lie:1 newtonian:1 depending:1 convenient:3 calogero:3 note:12 rome:1 square:1 take:1 so:12 coincide:4 analogs:2 formulas:2 antoniou:1 centre:1 collaboration:1 algebraic:4 regular:3 connected:1 ht:20 definitions:1 phase:1 hu:2 appear:2 considered:2 professor:1 adopt:2 flow:8 physica:1 playing:1 nondegenerate:1 bracket:4 exp:186 left:3 physics:12 section:3 fact:2 show:1 supported:1 recipe:1 converge:4 notations:1 spaces:1 gauge:1 solutions:3 decompositions:1 d2:3 find:2 d0:1 d1:4 knowledge:1 hg:2 only:4 explicitly:1 postfach:1 integrable:17 moser:4 oct:1 capel:1 dn:7 do:1 dl:1 dj:2 dk:121 means:12 de:1 obtain:8 ones:8 closely:1 suris:6 during:1 αk:9 arxiv:1 factorization:13 method:1 financially:1 pang:1 qk:8 dpk:1 view:4 hλ:8 set:8 computed:1 reference:1 hη:4 up:1 see:9 terms:21 analog:2 subject:1 satisfying:1 ways:2 artificial:1 tend:1 symmetric:1 written:1 jth:1 invariant:6 boundary:2 conditions:2 recently:1 hosting:1 attention:1 however:8 veselov:2 vanishing:1 solv:1 lb:1 amer:2 uπ:1 received:1 last:3 treated:2 taking:1 equal:1 etc:1 admit:4 symplectic:17 context:1 attributes:1 expression:1 ck:110 relevant:1 cn:4 cl:1 appeared:1 ce:1 alone:4 conjugation:1 respect:1 cp:3 cu:1 ct:2 nijhoff:3 described:2 submanifold:2 hd1:4 due:1 int:2 workshop:1 pk:56 algebras:1 ak:36 define:9 relations:12 corresponding:4 both:6 concerning:1 subspace:1 coincides:1 gen:1 neumann:1 derivative:2 c2:1 c1:2 denote:6 present:2 case:17 expanded:1 value:6 will:3 suppose:1 hdn:7 hdk:45 loop:3 garnier:1 conjugate:1 non:3 encouragement:1 according:3 tu:1 c0:1 containing:1 verified:1 author:1 recursion:1 belong:3 same:8 equiped:2 unity:2 complex:2 proved:4 several:1 subalgebra:1 difficult:1 week:1 literature:2 reversion:1 flows:8 hand:2 moment:1 uni:1 infinite:4 recent:2 lower:2 well:2 obviously:5 without:2 solve:7 1ck:1 entry:1 model:3 subgroup:1 unities:1 just:8 less:1 hγk:23 resp:5 solvability:1 underlying:2 using:2 facts:2 momenta:10 speed:1 previous:6 visualization:1 intersection:1 preprint:1 yu:4 seems:1 lattice:13 belongs:1 conjugated:2 lett:6 easy:3 theorem:17 transformation:1 generalized:2 read:3 immediately:2 unique:2 helpful:1 modifications:1 hcn:7 like:5 follows:6 orlando:1 serves:1 separately:1 either:2 right:3 often:1 namely:3 some:7 examples:2 kdv:1 2qk:1 nonzero:1 lead:2 classical:3 decomposition:1 chains:1 δk:7 equivalent:28 bi:1 bk:8 bu:2 polynomials:1 although:2 hd3:1 approximating:1 hd2:2 about:2 working:2 most:2 column:1 theorems:1 factors:2 o:22 mutually:1 extensions:1 germany:1 introduced:3 soc:2 letters:6 inclusion:1 h2:12 into:4 down:1 pair:4 en:5 references:1 operator:1 amsterdam:1 leningrad:1 acknowledgements:1 additional:1 area:1 strictly:1 there:3 quadratic:4 way:2 mappings:3 was:2 recurrent:9 function:10 complete:6 form:23 triangular:4 but:2 transformed:1 construction:1 hl:2 hb:2 hc:2 ha:2 considerable:1 hd:2 versions:3 2πi:1 smooth:1 ωt:1 us:2 discretized:1 below:8 limit:3 ud:1 problem:15 similar:1 ub:1 constant:1 defined:14 certain:7 abstract:1 general:5 aq:2 proves:2 au:1 dη:4 dε:2 check:8 defines:3 nh:19 again:5 functions:12 compared:8 no:1 mathematik:1 tomei:1 when:4 bremen:3 kp:1 role:1 details:1 conclusion:1 bruschi:2 problems:2 ragnisco:5 a1:1 a2:1 sides:2 structure:8 implies:8 coupling:1 vinet:1 ejk:1 orbit:1 together:5 time:29 dϕ:8
|
solv-int9510008.txt |@word since:2 partial:2 consider:11 funct:2 lagrangian:4 global:1 dinate:1 invent:2 leads:1 scalar:2 proposition:9 follow:2 expressions:2 inverse:2 const:2 zone:2 paris:1 technique:1 tr:1 equate:1 chaps:1 under:5 semenov:2 degeneration:1 case:7 belonging:1 proved:6 straightforward:2 springer:1 induce:1 choice:1 corollary:1 every:4 interpreting:1 hµβ:1 formula:1 difference:1 condition:2 partitions:1 dim:9 hamiltonian:24 irreducible:1 deals:1 involution:4 vector:1 annihilates:1 indices:2 reyman:3 c32:1 configurations:1 canonical:1 upper:1 ten:1 direct:1 groupes:1 zero:8 zz:2 further:1 substitute:1 linear:7 putting:2 intimately:1 nonlinear:1 appear:1 diag:2 sum:1 µli:4 above:1 3l:1 obvious:3 ground:1 method:3 coefficient:2 respectively:6 realizations:6 component:3 reads:1 tangent:1 bj:3 groups:3 others:1 pakuliak:1 sine:1 equations:34 appears:1 change:1 obtained:3 shansky:2 remark:3 µ0i:2 institute:1 involved:1 leaves:1 allows:1 periodic:1 procedure:2 poisson:11 stressed:1 action:12 hν0:2 hν1:1 quotient:1 uniquely:1 family:2 substitution:1 wik:2 anomalies:1 apc:1 total:1 unit:2 derivatives:4 projector:1 prove:1 contains:1 negative:2 next:4 msn:1 going:1 themselves:1 mckean:1 type:5 theoretical:1 minor:2 more:1 untwisted:1 nauka:1 neglected:1 operators:2 curvature:4 herein:1 ebres:1 berlin:1 everywhere:2 known:1 cases:3 must:1 keeping:2 c42:1 equation:22 modified:3 hermann:1 values:1 ms:1 following:8 admits:4 example:4 proof:10 f1:3 f2:3 stated:2 dτ1:2 sense:1 sokolov:3 purposes:1 effectively:1 numbers:1 degenerate:4 arise:4 standard:1 rescaling:1 µj:2 boussinesq:10 provide:2 acts:1 pure:1 symposium:1 hi:5 parameter:4 classify:1 algebra:27 orbits:14 collection:1 lax:3 representations:1 geometrical:1 compatibility:2 constants:5 e24:1 realized:5 natural:1 e21:1 third:2 e23:2 explicit:5 correspond:1 element:3 diffeomorphism:1 sh:1 so:2 sn:1 fundamental:1 2u:1 representation:11 operate:1 order:3 restriction:5 evolutionary:6 interpretation:1 hierarchy:3 entries:3 choose:1 interpreted:6 paper:2 same:3 mentioned:1 y3:3 quasitriangular:1 its:5 itp:3 before:1 constituted:1 group:7 chosen:1 fix:3 affine:3 coordinates:9 forms:2 cubics:1 lr:3 systems:5 van:1 mail:1 variables:5 semisimple:2 yi:5 non:11 fixation:1 finitedimensional:1 isomorphic:1 units:1 hamilton:1 they:1 now:2 ordinary:1 easily:2 2v:1 gets:1 2r:1 frenkel:1 classified:1 l2:5 each:1 found:2 associative:1 constraints:4 homogeneous:9 el:1 differential:4 ei:1 related:5 constitute:1 extended:1 connect:1 our:1 differ:1 special:1 out:2 large:1 shown:2 kiev:1 space:4 restricted:1 furthermore:2 singular:1 crucial:1 gradation:5 denotes:3 acting:1 investigation:1 denoted:1 got:1 independence:2 nν:1 xxxiv:2 theory:6 diagonal:1 enveloping:3 tian:2 completely:1 base:1 e8:1 put:2 org:1 subalgebras:3 e1:1 anal:2 c52:1 definition:1 fixed:4 c73:1 h33:1 geometry:2 determining:2 motion:6 int:1 place:2 gordon:1 δij:1 hence:3 onto:6 βi:1 first:4 initial:5 intermediately:1 β2n:1 relate:1 conjugacy:2 number:5 rank:2 another:1 xr:3 h38:1 equating:1 given:4 similarly:2 introduction:2 unknown:2 accent:1 system:15 construct:5 their:2 intermediate:1 zeros:1 calculations:1 realization:9 scheme:5 structures:3 statement:3 mostly:1 completed:1 nauch:1 γ1n:1 manifestation:1 x2:3 x3:3 x1:4 βl1:1 than:2 coefficients:2 relative:3 determines:2 holds:2 lepowsky:1 second:4 hνν:1 classes:2 were:2 enables:1 hνα:40 decompose:1 w2:2 kazhdan:1 mind:2 αli:1 any:3 elsewhere:1 lie:9 wilson:1 constructions:3 jour:1 h25:1 convenient:1 latter:1 h21:3 h20:1 h23:1 note:1 concerns:1 analogy:1 xi:7 coincide:2 degenerated:3 heisenberg:2 investigations:1 αl2:2 αl1:2 algebraic:7 automorphism:1 pair:2 soliton:1 laurent:2 consequences:1 considered:1 clear:1 later:1 flow:5 traditional:1 proceedings:1 bracket:1 exp:1 vries:3 section:2 fact:3 purely:1 gauge:3 solutions:2 analogue:1 trivial:1 principal:7 bourbaki:1 invariantly:1 conics:1 e13:2 e12:2 assertion:4 topological:1 should:1 lemma:2 only:3 µn:4 integrable:13 circle:1 oct:1 meant:2 do:2 dl:1 legendre:2 subspaces:3 dh:4 means:3 de:8 new:1 combinations:1 dt:1 gen:19 dp:9 evolution:2 densities:6 arxiv:1 nλ:1 leur:1 involutive:1 contain:1 qi:2 drinfeld:3 qk:3 qj:2 set:7 constructing:2 exists:2 hν:1 hβ:2 hα:2 zones:1 y1:3 see:1 alg:1 result:2 w1:2 inequivalent:1 dµ:5 peterson:1 points:6 y2:2 inequalities:1 liouville:2 λn:3 symmetric:1 written:3 determined:6 µk:11 between:1 invariant:6 boundary:2 previous:1 αl:2 αn:2 terms:4 killing:1 vanishing:1 comm:4 solv:1 article:1 problem:5 topology:1 both:2 annihilators:8 equal:5 ir6:1 minus:1 admit:1 symplectic:2 embedding:3 casimir:3 quite:2 pde:4 zapiski:1 x2r:1 among:1 ci:1 ements:1 conclude:1 simple:1 continuation:1 lagrangians:1 corresponds:2 dimensional:8 2αn:2 mkdv:4 homogeneously:1 assertions:2 lagrange:3 respect:7 math:11 considering:3 pp:6 basis:7 trajectory:2 create:1 sl2:2 sl3:13 defined:3 reduction:2 describes:1 interest:1 basic:1 degrees:2 algebras:5 ak:2 define:2 ukraine:1 arises:1 corresponding:9 c23:3 formed:1 subspace:1 c1:1 presented:1 those:2 applied:1 arnold:6 heidelberg:1 will:4 sln:8 lomi:1 eii:1 eij:1 loop:25 miramontes:2 almost:3 vi:1 ir:25 thus:1 them:2 iv:1 ik:3 ij:1 dual:9 c0:1 different:5 generic:12 make:1 belong:2 enumeration:1 cartan:3 stimulated:1 complex:2 modification:1 hierarchies:4 finite:12 subalgebra:4 higher:14 independent:4 used:1 dimg:2 solved:1 singapore:1 trajectories:2 differing:1 flows:5 h32:4 principally:3 h30:5 h31:2 h36:1 h37:1 infinite:1 invariance:1 ematique:1 lower:2 hνβ:6 c63:1 without:1 h24:1 coordinate:2 entry:1 γil:2 dh3:3 dimension:1 usual:1 λr:1 c83:1 manifold:8 graded:2 proposed:1 less:3 being:4 resp:4 obtain:1 actions:2 grades:2 identify:2 integer:1 facts:2 λi:4 scattering:2 yet:1 functionally:4 λl:11 adv:2 york:1 preprint:3 ham:1 density:1 point:9 except:1 e31:1 belongs:1 theorem:10 c12:3 transformation:4 euler:7 real:4 represents:1 possible:2 cf:7 finding:1 immediately:2 unique:1 theor:1 necessary:1 follows:3 reduces:1 automorphisms:1 remind:2 δl:3 korteweg:3 integrals:6 stationary:18 reduced:1 mathematical:1 kac:3 because:1 methods:1 λk:16 sequence:1 some:4 algebraically:1 calculated:1 examples:1 apply:1 kdv:2 immovable:3 latters:1 describing:1 dimensions:1 lead:1 chamber:6 integration:2 classical:1 provides:1 scientific:1 equivalent:4 l1:2 adexp:1 expansion:1 βil:2 instability:1 cα:3 takes:2 actual:1 carried:2 world:1 novikov:3 generated:6 o:20 involutivity:1 moerbeke:1 statements:2 h2:2 h3:1 into:3 h1:3 functional:3 down:2 phase:2 appropriate:1 weyl:6 references:1 determine:3 sov:1 operator:2 rows:1 span:1 additional:2 there:3 appl:3 way:4 resulted:1 fasc:1 was:2 minors:3 naturally:1 function:2 complete:1 form:14 hr:1 triangular:1 but:3 construction:4 russian:3 adler:3 made:1 applying:3 annihilate:2 embedded:2 cik:3 up:2 us:5 below:1 verification:1 coadjoint:8 similar:1 called:1 mechanics:2 partition:2 associated:5 ad:10 ai:5 coincides:1 abstract:1 general:2 proves:1 exist:1 dλ:2 lcan:2 check:2 constructed:2 functions:17 nk:6 completeness:1 e32:1 integrability:1 fixing:1 when:2 field:1 other:1 becomes:1 nr:2 er:2 elements:3 denote:4 provided:1 µik:1 gradations:1 semin:1 polynomials:3 stay:2 commutator:1 develops:1 important:1 β1n:1 structure:7 matrix:10 independently:1 implies:2 using:1 physics:1 dτ:3 orbit:30 groot:2 hollowood:2 time:2 n1:2 n2:2 starting:1 once:1
|
solv-int9510009.txt |@word represent:1 concept:1 partial:1 consider:3 chain:2 pseudodifferential:1 results:1 leads:5 eds:1 ferreira:2 supplement:1 generalize:1 edu:1 sci:1 gm:1 gl:1 dickey:1 tr:11 tn:6 swieca:1 tj:3 tk:4 th:7 dressing:6 include:1 applied:1 belonging:1 proved:1 g2:1 rise:1 p0:1 induce:1 wave:1 lecture:1 emphasized:1 matrices:1 deformations:1 gurion:1 entire:1 school:1 presented:1 notes:1 t2:2 solution:4 t1:3 involution:2 proposition:1 eigenvalues:3 zn:1 wronskian:1 consistent:1 direct:2 jump:1 zero:3 deutscher:1 further:1 dynamics:2 obey:1 bilinear:2 established:3 nonlinear:3 plays:1 chicago:2 trivial:1 d3:1 current:2 above:3 view:2 new:1 d1:2 consisting:1 viii:1 coefficient:1 here:3 focused:1 ansatz:3 sheva:1 along:1 quite:1 equations:23 box:1 institute:1 study:1 reports:1 suggests:1 resulting:1 poisson:3 hospitality:2 studies:1 honor:1 involves:1 schur:1 via:3 see:2 family:1 brought:1 untruncated:1 tools:1 denotes:1 virasoro:1 recurrence:1 use:1 takes:4 usa:1 commun:1 recalling:1 jpn:3 suppl:1 next:2 nucl:1 call:2 therefore:3 harada:1 schulman:1 type:2 theoretical:2 more:1 israel:1 operators:2 ti:4 site:1 eξ:6 known:4 account:1 hamiltonians:3 φdφ:2 recall:2 equation:11 mn:1 mk:3 hopf:19 itself:1 concepts:1 following:6 making:1 example:2 proof:1 tau:2 process:1 expanding:1 lψ:1 high:1 assumptions:1 sense:1 dλi:1 string:1 recursive:1 darboux:7 discussion:1 get:1 write:1 how:1 numerous:1 symposium:1 widespread:1 verlag:1 sato:4 simplicity:1 product:1 mat:2 algebra:4 isospectral:1 fa:1 lax:24 compatibility:2 natural:1 dynamical:2 st:1 sj:2 so:3 allow:1 enter:2 banks:1 representation:2 acknowledges:2 order:1 talk:3 produces:1 hierarchy:28 produced:1 including:1 during:1 existence:1 satisfies:1 cole:2 its:1 expansion:1 group:1 ln:25 ll:3 lm:2 lk:6 coordinates:2 condition:1 mail:3 main:2 djm:1 possessing:2 yi:1 non:2 return:1 yn:1 obtaining:1 acklund:7 evolution:4 framework:1 qr:1 hamilton:1 they:1 now:5 yu:3 developments:1 ift:1 φk:4 40b:1 fully:1 university:3 hamiltonian:9 2y:1 hepth:2 sufficiently:1 theory:2 l2:1 l0:1 found:1 identifies:1 constraints:2 lectures:3 differential:9 successively:1 energy:2 related:2 t3:1 elementary:2 toda:5 used:1 quantum:2 our:1 eq:2 special:2 out:1 shown:4 matrix:19 solved:1 furthermore:1 since:2 douglas:2 research:1 grinevich:1 denoted:1 akademischer:1 evaluation:1 math:4 linear:4 tsarigradsko:1 diagonal:2 standard:2 admits:1 completely:2 hep:5 zimerman:1 svetlana:2 times:1 motion:13 turn:1 δij:8 hence:1 qn:3 first:3 initial:2 xn:1 features:1 symmetry:2 iλi:2 relate:1 variables:1 nhn:1 rank:1 aratyn:4 illustrate:2 given:7 introduction:1 sm:1 adjoint:1 system:14 least:1 their:2 seiberg:1 freiburg:1 realization:2 gives:2 turbulent:1 part:3 qlk:1 translation:1 coefficients:2 finitely:1 ben:1 cimento:1 integrability:8 matter:1 classes:1 ktk:1 rewrite:2 modern:1 any:2 centerless:1 mii:1 satsuma:1 wilson:3 mij:4 petviashvili:1 calogero:13 gravity:1 lij:2 note:2 generalized:8 tokihiro:1 kac:1 residue:1 fundamental:1 olshanetsky:1 shall:1 sequence:1 systems:5 extending:1 involving:1 pair:2 acknowledgements:1 class:4 pohlmeyer:1 orlov:3 hikami:1 partition:2 bracket:1 ohta:1 exp:4 physics:7 notion:2 fact:5 akhiezer:1 ugm:1 show:1 supported:1 recipe:1 shenker:1 relation:6 solutions:8 d2:1 find:7 nln:2 q1:2 based:2 parameters:1 universal:1 lemma:3 only:1 integrable:15 moser:13 oct:1 dn:2 abelian:1 dm:7 dk:1 di:3 regge:1 straightforwardly:2 ϕi:2 words:1 despite:1 dw:2 differentiating:1 takahashi:1 reveal:1 regarding:1 kadomtsev:1 qu:1 continuum:1 babelon:2 approach:1 arxiv:1 yield:1 investigate:1 common:1 qi:21 through:2 qk:3 qj:18 bulgaria:1 exists:1 imposing:2 enjoyed:1 j1:2 namely:3 w1:7 w0:1 wadati:1 λi:1 subject:1 nuclear:2 currently:1 bitnet:2 sites:1 written:1 determined:1 various:2 bruno:1 between:7 invariant:1 conditions:4 terms:8 august:1 wn:2 wm:2 however:1 wi:5 gratefully:1 jn:2 solv:2 linkage:1 viallet:1 many:3 taking:1 context:1 finds:1 among:2 simple:2 uic:1 hoppe:1 m10:1 interrelations:2 associated:1 kp:15 described:1 transformations:3 second:2 addition:1 moerbeke:1 locally:1 been:1 int:3 beer:1 belongs:1 interest:3 basic:1 pj:4 ph:1 pi:5 pn:11 abstract:1 define:4 obtained:3 generating:1 relations:3 corresponding:2 relevance:1 pacheva:2 derivative:2 prototype:1 present:1 p2:1 negev:1 p1:1 processes:1 defining:1 discrete:3 will:2 cast:2 while:1 multicritical:1 dλ:3 shiota:1 unitary:1 coupled:1 vi:2 vm:2 encountered:1 ik:1 ij:5 il:5 chudnovsky:3 qj1:1 ig:4 different:4 verified:1 grant:1 same:1 paulo:2 complex:1 φd:1 φi:5 hierarchies:4 constructed:1 φm:1 higher:3 independent:1 extended:1 qjn:1 singapore:1 appearances:1 interconnections:1 flows:6 v1:1 purpose:1 infinite:2 opportunity:1 identity:3 recent:1 off:1 well:1 burgers:17 position:1 model:19 usual:1 summer:1 construct:1 manifold:2 unesp:1 being:2 sofia:1 obtain:3 rest:1 ideas:1 b64:1 world:2 λk:1 λj:2 alternative:1 illinois:1 λn:1 nissimov:2 enters:2 infinitely:1 parametrization:1 signals:2 lattice:3 setting:1 lett:6 easy:1 natl:1 diagonalization:1 mod:2 plasma:1 transformation:5 scientific:2 take:1 identical:1 involutions:1 possible:1 admitting:1 vacuum:1 using:1 moody:1 theor:1 like:2 semi:3 alternatively:1 serves:1 specific:1 integrals:4 follows:5 calculus:1 acad:1 classical:1 truncated:8 some:2 springer:2 equivalent:6 choosing:2 respect:1 a10:1 gross:1 describing:2 lead:1 leal:2 manipulations:1 provides:1 prog:1 prof:2 proc:1 inserting:2 bg:1 ba:3 bn:6 arbitrary:1 illustration:1 step:1 visits:1 qnn:1 simpler:1 about:1 central:1 puts:1 origins:1 most:1 meaning:1 o:2 bgu:2 introduced:1 consequently:2 perelomov:1 soc:3 letters:1 presence:1 into:4 within:1 integral:1 nsf:1 remarks:1 hermitian:2 references:1 a8:1 operator:16 van:1 additional:1 support:1 there:4 reduction:2 way:2 ψn:17 naturally:1 function:17 complete:2 form:15 hr:8 hs:7 hk:8 construction:2 hn:1 hl:1 ha:1 october:1 applying:1 emil:2 embedded:1 cij:5 us:2 dφ:2 ui:1 problem:3 similar:2 called:4 ac:2 taylor:2 constant:4 qij:1 defined:3 ak:1 describe:2 bulgarian:1 ao:1 general:2 single:1 arises:1 exist:1 together:1 formulation:6 commuting:1 defines:1 grassmann:2 functions:6 compared:1 when:3 plugged:1 field:1 migdal:1 points:1 role:1 department:2 austauschdienst:1 generates:1 models:9 hirota:2 problems:1 polynomials:2 a1:12 a0:20 generated:1 important:2 qψ:1 structure:8 algebraic:2 implies:2 coupling:1 assume:1 baker:1 pseudo:1 orbit:1 governed:1 factorizes:1 warm:1 time:4 having:3
|
solv-int9510010.txt |@word limited:1 consider:6 results:1 integration:1 leads:1 depend:3 paris:4 concerned:4 γw:2 finally:2 critical:4 those:1 excluded:1 under:2 discovering:1 include:1 oversight:1 me:1 conjecture:2 straightforward:2 very:4 wishes:1 every:3 difficult:1 decide:1 redefinition:1 trouble:1 parameter:1 matrices:1 condition:32 four:1 presented:5 did:1 turns:4 list:4 solution:1 leave:1 discrete:24 scalings:1 manifestly:1 upr:1 prevent:1 tel:3 direct:1 second:17 further:6 implemented:1 canonical:3 even:3 aim:1 what:7 plays:1 appear:1 incompatible:1 d2:1 section:9 brief:2 find:17 poles:1 above:3 deal:1 new:6 3a:1 increasing:1 consisting:2 filled:1 coefficient:3 full:3 simultaneously:1 chose:1 degree:10 never:1 here:8 papageorgiou:1 behaviour:14 refinement:1 free:3 represented:1 along:1 quite:1 z0:13 appears:4 logarithmic:3 obtained:15 remark:5 study:10 studied:3 periodic:4 products:1 usually:1 complicated:3 studies:1 pathological:1 genuinely:1 followed:1 classification:4 vii:1 ǫq:1 logical:1 scaled:1 put:1 univ:1 readily:1 derivatives:2 use:1 takes:2 would:9 prove:1 remains:1 century:1 examined:1 negative:2 next:8 few:4 examination:1 taken:1 scope:1 stage:1 type:2 tell:1 reflects:1 more:3 formally:1 duality:5 ecole:1 clearly:6 becomes:11 acceptable:2 aware:1 everywhere:1 labelled:1 particular:8 known:2 cases:12 whatsoever:1 must:8 ramani:8 account:1 subcases:1 recall:3 equation:39 hopf:1 paragraph:2 values:1 publications:1 following:2 give:1 calculation:2 fax:1 involve:1 allowed:1 transcendent:1 rescaling:1 conversely:1 compatible:2 needs:1 recovery:1 painlev:26 rather:5 s2:1 discussion:5 holds:2 enlarge:1 write:1 how:1 criterion:3 answer:2 instead:4 ordinary:1 explains:1 priori:1 undertook:1 singular:10 may:5 after:20 singularities:19 mapping:40 tries:1 plane:1 compatibility:2 types:2 included:1 realized:1 occurence:2 whenever:1 sp:1 lines:1 lost:7 cascade:7 complexity:1 ones:1 so:4 allow:1 enter:4 putting:2 order:16 exclusive:1 essence:1 over:1 satisfied:4 feature:1 course:2 paper:2 through:17 argued:2 cole:1 its:11 before:6 perfect:1 derive:1 rapidly:1 interesting:3 actually:1 forms:4 absence:6 degrees:2 systems:4 derivative:3 main:2 alter:1 non:10 motivated:1 propose:2 nada:1 introduce:3 scaling:3 p14:2 they:3 identically:2 singularity:42 now:6 ther:1 possess:3 easily:4 term:1 2w:2 2q:2 lies:1 always:5 classified:1 possibilities:1 2a:2 2c:1 universit:1 decouple:1 characterized:1 mean:2 differential:3 arbitrariness:1 related:8 expect:3 reached:1 our:9 out:6 try:1 missed:1 solved:1 restricted:1 rep:1 since:12 rev:2 bad:1 replacing:1 behaviours:1 investigation:1 ra:1 rational:2 suffices:2 integrated:3 interchanging:1 linear:11 possibility:5 standard:1 difficulty:3 whereupon:1 ask:3 asi:1 perform:1 derivation:1 argument:2 starts:1 could:2 wrong:1 turn:4 consequence:1 assign:1 first:20 initial:6 peculiar:2 xm:3 feel:1 number:12 set:2 simplified:1 another:1 impossible:1 precisely:3 illustrate:1 given:8 exists:1 similarly:2 introduction:1 leading:2 interact:1 indeterminate:5 system:19 least:2 their:1 assumption:2 too:1 xiv:1 perfectly:1 recovered:2 gives:1 2ab:1 2ac:1 tool:1 exactly:3 rejected:1 part:1 somewhat:1 manifestation:1 x2:1 translation:1 than:2 coefficients:2 sections:1 iteration:3 integrability:7 determined:1 contrary:1 were:4 denominators:1 treated:1 result:1 exhibit:1 etage:2 rewrite:1 linearizable:2 mind:2 locations:1 affirmative:1 already:1 qualitatively:1 need:1 seen:2 recover:5 any:9 ax2:2 mappings:9 zero:3 latter:7 able:2 note:2 instance:2 take:8 analogy:2 solve:2 cnrs:1 continuous:26 unless:5 shall:4 who:1 reach:2 riccati:25 most:4 claims:1 intrinsic:1 class:3 branching:1 cause:2 observation:2 considered:4 axx:1 later:2 physica:1 astonishing:1 lpn:2 segur:1 principle:2 pattern:2 hietarinta:1 notion:2 fact:15 dover:1 precise:1 12b:1 12c:1 restriction:1 fifty:1 bring:1 relation:1 solutions:1 carefully:1 subtle:3 analogue:1 trivial:1 xxvii:2 fifth:2 make:1 aσ:27 based:4 parameters:3 writes:1 written:2 should:4 analytic:2 only:13 going:1 corresponds:1 transcendental:1 indeed:8 integrable:4 constant:3 oct:1 hope:1 do:5 his:3 dominant:2 means:4 dependent:3 dd:1 db:4 foremost:1 cannot:4 3b:2 atypical:1 evolution:1 qw:2 qx:1 arxiv:1 2b2:2 investigate:1 noncanonical:1 contain:1 london:1 fixed:8 view:1 strengthened:1 requirement:5 ars:1 reference:1 richer:1 namely:3 w2:6 pvi:1 contour:1 analog:3 still:3 αw:2 subsequent:2 review:1 artificial:1 label:1 outside:1 difficulties:1 various:1 between:1 probably:1 neither:1 conditions:8 terms:4 tricky:1 extend:1 initially:1 wm:1 however:18 implementing:1 vanishing:1 solv:1 diverges:2 both:2 hits:1 last:6 limits:4 σb:2 taking:2 equal:3 etc:1 tour:2 distinction:2 argue:1 whole:2 finds:1 comes:3 otherwise:1 among:1 afterwards:1 point:15 simple:1 character:5 period:1 analyzed:2 pole:1 cx:1 iterations:2 moreover:6 math:3 considering:1 unusual:1 pv:2 pw:1 equations:17 due:4 been:2 reduction:1 treat:1 basil:1 nato:1 location:5 firm:1 6a:1 determinant:1 6c:2 corresponding:2 quantities:1 sufficient:9 gap:1 2ǫd:1 confinement:25 demand:2 denote:1 present:4 case:47 p5:2 plain:1 homographic:5 value:14 will:6 ǫr:1 while:7 suppose:1 applies:1 irrespective:3 property:11 guide:1 coupled:5 thus:27 them:4 encountered:4 characterize:1 reads:2 itself:1 confining:9 dual:2 ym:5 vanish:1 alone:2 disappear:1 different:4 generic:2 divergences:1 lett:3 same:4 orders:1 appearence:2 palaiseau:1 complex:1 ince:2 finite:2 higher:2 independent:1 used:3 infinity:1 see:2 trivially:1 hand:6 resonance:17 infinite:10 ablowitz:1 shortly:1 expression:1 well:4 analysis:5 patterns:1 without:1 gambier:34 position:2 jussieu:1 grounds:1 interpret:1 just:6 being:6 when:13 guided:2 grammaticos:8 obtain:7 vanishes:1 underlying:1 properties:3 plagued:1 immediately:1 useful:1 previous:4 nx:1 enters:2 family:1 conclusions:2 had:2 quadratures:1 belongs:2 combine:1 treatment:1 easy:1 5e:2 guarantees:1 transformation:2 acta:2 nuov:1 depends:1 read:1 couple:1 possible:8 confines:3 confined:5 integer:5 variants:1 formal:1 necessary:3 like:3 excluding:1 follows:4 reduces:1 loses:5 specific:1 indication:3 polytechnique:3 integrals:1 arbitrary:1 become:3 terminology:2 draw:1 because:3 hinted:1 some:11 back:1 understood:1 sight:1 respect:3 small:1 ourselves:1 nonzero:1 provided:2 proceeding:2 lead:4 avoid:1 cφ:1 does:11 exit:1 inject:1 assuming:1 steps:21 either:5 denominator:3 algorithmic:1 bb:5 bc:2 rescale:1 retains:1 equivalent:5 each:1 analysed:1 expansion:4 step:1 although:3 explicitely:2 bx:1 periodically:1 simpler:2 about:1 actual:1 constraint:2 freedom:12 nonvanishing:1 mutually:1 important:1 ensure:1 stand:1 introduced:4 other:3 automatically:2 discretization:2 transcendents:2 into:2 bountis:1 obtaining:1 linearization:1 appropriate:3 references:1 movable:12 france:3 soon:1 log:2 assumed:1 there:8 question:2 start:7 way:8 exceptional:1 was:18 assumes:2 naturally:2 function:4 considerably:1 complete:2 form:22 ǫw:2 becoming:1 but:5 properly:1 repeatedly:1 level:2 true:1 he:4 absent:1 made:3 compute:3 whether:2 up:2 us:11 limit:14 today:1 problem:2 define:1 clear:2 obtains:1 detailed:2 ab:3 associated:1 play:2 int:1 certain:2 abstract:1 general:7 globally:1 examine:1 arises:1 exist:2 interchanged:1 ax:6 proceeds:1 piv:1 constructed:1 again:6 functions:4 cim:1 no:8 thanks:1 detail:1 rewriting:1 ny:2 book:1 role:3 appearing:1 confine:3 conclusion:2 happens:1 briefly:2 elements:1 preceding:1 time:1 problems:1 a2:1 qφ:1 variable:3 structure:4 matrix:2 ago:1 algebraic:1 implies:2 auxiliary:1 algorithm:1 assume:3 4p:1 na2:1 came:1 remarked:1 far:4 cpt:1 original:1 once:4
|
solv-int9510011.txt |@word logarithms:1 consider:3 chain:1 illustrates:1 leads:6 sim:1 go:1 follow:1 paris:2 concerned:1 technique:1 list:1 finally:4 present:4 include:1 me:1 straightforward:1 far:1 springer:1 putting:2 entries:1 condition:1 homographic:1 presented:1 turns:3 notes:1 having:1 t2:2 solution:1 fewer:3 leave:1 discrete:25 dealt:1 small:1 relation:2 upr:1 degeneracy:1 zn:2 d34:1 consistent:1 nonautonomous:3 past:1 integrability:2 further:2 xf3:1 canonical:2 even:2 aim:1 what:7 appear:1 section:4 4w2:1 above:3 capital:2 new:15 satisfy:1 full:5 led:3 here:8 papageorgiou:3 behaviour:1 ansatz:3 represented:1 quite:1 equations:28 extreme:1 obtained:26 remark:2 study:9 studied:1 allows:2 experience:1 prior:1 resulting:2 published:1 complicated:1 conveniently:1 genuinely:1 2δa:1 br:1 classification:2 explained:1 prefer:1 2wt:1 reserved:1 readily:1 standing:1 use:1 takes:1 would:2 analytic:1 double:1 france:2 call:1 taken:1 type:2 more:8 ecole:1 becomes:4 starting:5 2w2:2 2w3:2 discussed:1 particular:4 known:5 cases:6 iii:1 must:3 ramani:10 lowercase:1 recall:2 equation:51 work:2 modified:1 values:2 following:5 x4n:1 closing:1 example:1 f1:1 f2:4 f3:1 f4:2 division:1 process:2 numerator:5 accept:1 performed:3 degenerate:16 sense:1 painlev:21 six:3 how:2 criterion:6 acta:2 3w2:4 parameter:2 classify:1 may:1 after:1 mapping:5 curiosity:1 date:1 summarize:1 parallel:1 constants:2 λ2n:5 whenever:2 correspond:2 cascade:4 cannot:1 so:2 fundamental:1 every:1 order:12 restriction:1 essence:1 discretization:1 course:1 paper:4 through:25 y1:1 still:3 its:10 before:2 perfect:2 interesting:6 fix:1 solving:1 forms:16 systems:1 omitted:1 hidden:1 them:2 yn:9 acklund:1 introduce:2 arsenal:1 they:3 nov:1 now:6 nor:1 possess:1 easily:1 term:1 2w:9 indeed:1 2r:2 x0:3 always:2 2z:1 2d:2 2e:1 theory:1 2g:4 2a:2 2b:2 each:2 found:1 universit:1 mean:1 domain:1 differential:1 directly:1 there:7 reduce:3 related:6 conventions:1 obtains:1 proportional:1 our:3 special:7 out:4 shown:1 kazakov:1 restricted:1 since:4 rev:2 rational:2 denoted:1 lecture:1 occurs:1 math:4 6x2:1 linear:9 retrieved:1 bxn:1 story:1 possibility:2 standard:7 whereupon:2 besides:1 put:6 asi:1 generate:1 degeneracies:5 derivation:1 dubbed:1 starts:1 could:1 linearized:1 turn:1 place:1 unknown:2 βn:1 first:7 already:1 xn:238 miura:3 variables:4 number:3 simplified:1 another:10 reached:1 precisely:2 open:1 between:3 illustrate:1 given:7 publication:2 introduction:2 leading:13 relations:3 zxn:4 their:3 assumption:1 too:1 convention:2 perfectly:1 gives:2 free:2 tool:1 exactly:2 part:1 natural:1 translation:2 sheer:1 than:5 sections:1 piii:20 painleve:1 limiting:4 roberts:1 future:2 doubly:1 historical:1 were:1 w3:4 distinguished:2 w2:3 etage:1 rewrite:1 mind:1 exchanging:1 seen:3 recover:1 saw:1 clearly:1 satsuma:1 jour:1 mappings:4 zero:4 efficient:1 convenient:2 latter:7 able:1 ideas:1 instance:1 take:9 analogy:2 lhs:1 detector:1 4x0:1 4λ2n:2 bilinear:1 cnrs:1 continuous:31 unless:1 shall:3 rhs:6 denominator:5 riccati:1 algebraic:1 correponding:2 considered:2 physica:2 lpn:1 proceedings:1 principle:1 hietarinta:1 axn:8 fact:5 particularly:3 show:5 notations:2 gauge:2 solutions:2 trivial:3 find:19 d0:1 q0:4 based:1 parameters:13 should:3 entities:1 only:5 explicitly:2 rich:3 developed:2 thompson:1 integrable:3 capel:1 δxn:2 means:1 dependent:6 de:1 yielded:1 ones:5 closely:1 altogether:1 4λn:3 quispel:6 coalescence:12 arxiv:1 common:4 activity:1 discovery:1 exists:5 richer:1 see:2 bµn:1 result:3 pvi:3 analog:1 singularity:9 pattern:1 yet:1 initially:1 written:3 simplest:1 neither:3 x20:1 αn:2 wf:1 terms:1 do:3 importance:1 comp:1 complement:1 analogues:1 however:5 implementing:1 wt:4 solv:1 both:3 x2n:14 last:1 limits:21 many:2 taking:10 equal:1 etc:1 tour:1 2λn:4 comes:1 otherwise:1 among:1 alternate:1 point:2 simple:1 corresponds:7 simply:1 cancel:2 moreover:4 throughout:1 cxn:2 conference:1 pq:3 pv:16 second:3 basis:1 addition:1 simplification:3 due:1 been:2 much:1 25t:1 treat:1 interest:4 basic:1 nato:1 pi:23 arises:1 corresponding:2 quantities:1 confinement:8 xλn:1 c2:3 those:2 case:39 p0:5 novel:6 look:2 exponential:1 ǫn:4 value:1 transformation:5 will:8 while:5 suppose:1 property:1 procedure:2 examines:1 thus:7 non:1 encountered:1 ii:2 characterize:1 examined:3 confining:1 different:3 suggests:1 perform:2 make:1 same:4 any:5 palaiseau:1 largest:1 gets:1 higher:3 independent:3 used:4 infinity:1 cubic:1 counterparts:1 hand:1 delicate:1 µxn:3 recent:2 lower:3 2gw:1 well:6 analysis:2 obviously:1 gambier:3 very:2 just:8 less:1 being:3 grammaticos:11 obtain:6 valuable:1 properties:2 transforms:1 λn:23 enters:1 preprint:1 family:1 conclude:1 reasons:1 transformed:1 lett:3 easy:1 5e:1 remaining:2 vii:1 represents:1 possible:3 several:1 five:5 know:2 using:2 amply:1 δx:4 follows:2 reduces:5 manifest:1 yields:3 either:1 fully:1 multiplicative:2 δb:1 δa:1 namely:2 some:7 back:1 added:1 b0:2 b2:7 apply:1 proper:1 ourselves:1 ezin:1 xn2:3 lead:1 αxn:2 does:3 indication:1 polytechnique:1 equivalent:3 2c:2 host:1 although:1 intense:1 p34:10 x30:1 most:1 nijhoff:1 introduces:1 dependence:4 o:5 remains:2 done:1 outset:1 transcendents:1 letters:2 into:1 three:2 linearization:1 appropriate:4 references:1 determine:1 factor:4 coalescences:3 strictly:1 initial:4 question:2 transform:1 start:7 96g:1 way:6 translate:1 was:3 assumes:1 naturally:1 function:1 complete:1 form:38 ǫw:6 but:3 volume:1 true:4 count:1 up:1 us:7 limit:39 4w:1 autonomous:5 similar:1 expect:3 profusion:1 pii:20 ab:2 constant:8 int:1 abstract:1 proven:1 examine:1 exist:5 piv:14 again:1 no:2 when:7 detail:1 application:2 other:1 fokas:1 mathematics:1 conclusion:1 a0:2 a2:3 allowing:1 variable:7 structure:1 coupling:1 assume:1 cpt:1 4t:1 together:1 aµn:1 time:1 appl:1 requires:2 original:1
|
solv-int9510012.txt |@word φ1j:9 secondly:2 gu:1 partial:1 consider:2 φ1k:3 control:5 equalities:3 results:3 leads:2 eds:1 ψ1j:9 ψ1k:3 computation:3 obtaining:1 sci:1 expressions:2 research:1 c1:1 gh:8 devoted:1 careful:1 depend:3 technique:5 tr:19 tn:27 δhn:1 finally:2 th:2 under:7 presentation:1 worth:1 p2:31 very:2 rise:2 2ra:1 choice:1 corollary:1 manipulated:1 li:1 associated:1 matrices:4 condition:1 gg:1 obvious:2 hamiltonian:33 bn:1 suffices:1 solution:4 δh0:1 large:1 solved:1 convenience:1 vector:2 bq2:22 math:12 bq1:19 eigenvalues:1 anal:1 solutions:6 application:1 smaller:1 grateful:1 foundation:2 direct:2 zero:3 value:1 further:6 gm:1 theory:4 even:1 aim:1 what:1 nonlinear:6 appear:1 cˆi:3 ˆx:1 diag:2 section:4 expressed:2 hereditary:3 ˆb:3 fuchssteiner:2 above:9 bm:3 new:12 technology:1 increasing:1 method:3 satisfy:3 compact:1 simultaneously:1 d1:2 mel:1 here:5 inverse:1 china:4 separation:1 along:1 equations:23 ψij:4 remark:1 institute:1 involved:1 study:2 vectors:1 allows:1 resulting:4 ψlj:1 poisson:7 dickey:1 geng:4 cˆ0:1 uniquely:1 f0:1 φkj:1 shanghai:2 transformations:1 rodrigues:1 qˆ:1 zijk:2 ψil:3 establish:3 select:1 nonlinearization:17 takes:1 would:3 lemma:5 distinct:1 ψs:1 jpn:1 negative:1 few:1 noting:3 therefore:9 ψl:1 taken:1 qci:1 type:2 theoretical:1 more:2 sort:4 fellow:1 successful:1 becomes:4 ap1:1 award:1 berlin:1 everywhere:1 particular:1 involutivity:2 cases:2 fulfilled:1 must:1 springer:2 ma:12 recall:1 equation:8 ik:32 tohoku:1 ij:3 cao:3 novikov:1 following:15 arrive:1 example:3 stimulating:1 proof:15 wojciechowski:4 f1:9 f2:2 calculation:1 carroll:2 accept:2 involve:1 φij:4 want:1 sense:2 dk:4 needs:1 end:1 notation:1 φin:4 get:4 utilize:1 maps:1 pure:1 holland:2 ordinary:2 verlag:3 parameter:4 ψin:2 map:2 product:1 2bm:2 algebra:5 may:18 φ2j:9 use:4 tool:1 βl:2 lax:22 idg:1 representations:1 fk:5 fl:1 compatibility:2 constants:3 ψi1:2 ψi2:2 natural:2 effective:1 explicit:6 summing:1 exhibited:1 cannot:1 so:2 sn:2 sl:1 representation:4 ghn:10 order:10 holds:4 interpretation:1 hierarchy:21 indeed:2 over:3 choose:3 years:1 course:1 paper:2 including:1 signs:1 p1x:1 satisfies:1 its:4 rˆ:1 le:1 thank:1 2λb:1 2λc:1 interesting:2 temporal:9 coordinates:2 vtn:1 forms:1 absence:1 systems:34 relate:1 jacobi:3 derivative:4 main:1 fin:5 fim:5 loop:1 non:2 motivated:1 propose:1 acklund:1 introduce:3 adams:1 break:1 they:6 nov:1 now:6 discuss:3 ap3:1 possess:3 easily:3 several:1 equality:6 2q:7 2r:5 always:3 university:1 presented:2 sufficiently:2 2a:3 2b:3 2c:2 2n:2 difficult:1 side:2 2j:3 constraints:12 homogeneous:1 differential:4 financial:1 ej:4 energy:1 physica:3 idea:1 related:3 constitute:2 isospectral:2 φi1:4 combining:1 funct:1 our:2 tu:3 aˆ1:2 special:1 out:3 leave:1 shown:5 matrix:14 space:3 open:1 nuovo:1 since:2 rx:1 denotes:6 similarly:3 ra:3 rb:3 algebro:1 ref:2 interchanging:1 shows:5 aˆm:6 after:5 linear:3 kaup:3 standard:1 proponents:1 reason:1 complicated:2 york:1 ψ2k:6 ψ2j:9 approach:2 generate:1 additional:1 verify:1 pairs:13 determining:1 impose:1 times:2 motion:16 turn:1 hence:3 βn:1 generalizations:1 βi:2 first:10 xh:2 initial:2 humboldt:1 symmetry:25 miura:2 variables:4 gradf:1 xf:2 xg:2 engenders:1 least:2 ψx:4 covariants:1 given:7 rewritten:2 f1m:1 introduction:1 adjoint:13 amsterdam:2 system:41 construct:2 fm:21 their:5 assumption:1 fn:9 variational:4 structures:6 gives:2 relationship:1 2an:1 completed:3 exactly:2 proving:1 newell:3 2ai:1 part:1 somewhat:1 authors:2 completes:1 coefficients:2 kind:4 determines:3 dtn:1 roles:1 require:1 cimento:1 second:1 matter:1 determined:5 fˆ:4 f12:1 toward:1 minus:1 symmetries:4 involution:2 topics:1 generalization:1 rai:1 need:1 constrained:2 any:2 blaszak:1 lie:2 depending:6 studying:1 latter:2 phase:4 note:3 potential:8 take:3 performance:1 fj1:3 recursively:2 aprile:1 spectral:25 play:1 2am:2 trace:4 shall:1 object:2 most:1 cˆm:3 connected:1 remarks:2 class:1 soliton:31 don:3 especially:1 consequences:1 fjl:3 considered:1 ki:4 sometimes:1 flow:1 kn:6 km:1 bracket:4 rauch:3 physics:1 fact:1 λlk:1 oevel:3 show:2 manipulation:1 spaces:1 relation:7 akns:25 carefully:1 substituting:2 d2:2 find:4 d0:2 universitaet:1 q1:15 q3:7 q2:8 based:1 basel:1 should:2 2bn:1 only:5 2ˆb:1 2bi:2 integrable:15 constant:1 moser:1 local:1 pointed:1 hope:1 3n:1 dn:9 do:1 dl:4 dm:5 dj:1 cˆx:1 dh:1 means:2 dependent:3 µj:4 satisfied:2 methods:1 dym:2 ones:1 dx:4 ˆi:6 compute:4 interpreted:1 sorts:1 alexander:1 qr:1 determinants:1 sources:2 qx:1 transposition:1 arxiv:1 factorization:1 ˆm:7 qa:3 qc:3 involutive:10 qi:21 through:3 requirement:1 set:2 constructing:1 exists:1 national:1 differentials:3 j1:6 see:2 computer:1 result:2 discussions:1 terms:2 aroused:1 λi:5 eigenfunctions:3 enough:2 µn:1 various:1 irn:1 between:2 αi:12 geometric:1 reading:1 conditions:1 αl:1 αn:1 commute:1 jx:1 however:2 jl:7 ˆbˆ:1 huang:1 solv:1 uφ:1 p2x:1 informatik:1 mono:1 region:4 conclusions:1 f2n:3 deduction:2 etc:1 connection:1 symplectic:4 pitn:1 expression:7 fix:1 among:3 ci:10 cn:1 cm:4 simple:1 dimensional:12 analyzed:1 mkdv:1 cx:1 exhibits:1 polynomial:1 respect:3 throughout:1 considers:1 kp:3 zimmermann:1 submanifold:1 puts:1 aˆ:2 addition:5 δλj:3 due:2 been:2 int:1 interest:1 pi:22 fudan:1 define:2 determinant:1 corresponding:5 powerful:1 nikov:1 previato:1 gap:1 finished:3 observe:1 doesn:1 2ii:2 c2:1 worked:1 c0:1 former:2 present:1 case:7 p3:25 intriguing:1 p1:31 aix:1 arnold:2 intimately:1 euclidean:1 suppose:3 rbi:1 many:4 di:3 property:1 drs:1 procedure:3 garnier:1 coupled:1 vol:1 von:1 ir:1 thus:5 them:1 according:1 ii:22 φk:1 reads:1 flaschka:2 im:33 il:16 vx:4 bargmann:9 µk:3 φil:3 acknowledgments:1 binary:8 different:7 φs:1 φx:3 recursion:5 make:2 same:4 enrich:1 hierarchies:5 finite:13 qai:1 higher:3 φi2:2 independent:6 literature:1 i1:29 i0:6 i2:1 upon:1 effect:1 flows:8 hand:5 moment:2 purpose:1 potentials:1 infinite:2 fik:3 uˆ:3 identity:3 recent:1 paderborn:2 nevertheless:1 restricted:3 itself:1 commission:1 de:1 without:1 solve:7 sets:2 possesses:3 usual:2 manifold:1 proposed:5 generally:1 obtain:4 λc:2 λb:2 vˆx:1 λk:1 λj:27 ostrogradsky:2 λn:4 fokas:2 φtn:2 ˆb0:1 preprint:1 infinitely:1 seems:1 k0:2 transformed:1 lett:5 easy:2 theorem:12 dqi:1 generalized:3 eigenvalue:2 read:1 possible:1 fi1:13 know:5 bix:2 integer:1 accepted:1 moreover:4 hereafter:1 like:3 follows:7 δu:6 δr:1 δq:1 specific:2 yields:3 either:1 integrals:15 arbitrary:1 ˆbi:6 harry:2 stationary:6 mathematical:1 because:5 neumann:5 classical:6 successfully:1 some:9 b4:3 b5:2 b0:1 b1:2 b2:2 2qa:1 kdv:5 jln:1 nonzero:1 observing:1 dimensions:2 lead:1 schilling:1 integration:1 ak:1 defined:7 provides:1 who:1 reasonable:1 power:2 bc:4 elucidate:1 equivalent:2 each:3 bi:18 how:1 ragnisco:1 substitution:3 bx:1 properties:2 science:2 deriving:1 about:1 idx:1 constraint:14 bgh:4 ψtn:2 prove:4 discussed:1 o:2 2cn:1 important:1 2ci:3 idh:5 idf:1 germany:1 introduced:2 perelomov:1 soc:1 φ2k:6 into:9 integral:1 three:8 pair:3 right:2 references:1 determine:2 operator:4 algebras:2 often:1 gen:2 aˆi:2 deal:1 vˆ:25 fˆx:1 support:1 there:5 why:2 anderson:1 appl:2 inner:1 way:4 gin:1 analyze:1 function:2 interrelation:1 north:2 complete:1 form:1 but:6 hn:8 true:1 themselves:3 he:1 commun:3 made:1 applying:1 ux:2 whether:1 zij:3 utn:6 us:3 harnad:1 liouville:4 problem:18 cix:2 similar:3 called:5 examples:1 mechanics:3 separated:2 proved:2 ai:23 certain:1 abstract:1 b3:3 am:28 zeng:3 general:4 pix:1 conserved:1 exist:2 qix:1 formulation:2 ax:1 formalism:1 functions:6 integrability:5 mathematik:1 when:10 cˆ:2 field:3 other:8 spatial:24 mathematics:1 mupad:2 elements:1 denote:3 provided:1 symbol:1 time:2 problems:12 polynomials:2 helpful:1 a1:2 a0:1 generated:3 a2:6 variable:3 structure:4 algebraic:1 implies:2 geometrical:1 assume:3 values:1 tricks:1 required:1 curve:1 together:1 equivalently:1 2im:2 remarked:1 starting:2 original:1 once:1
|
solv-int9511001.txt |@word consider:2 similarity:3 aids:1 focus:1 expressions:2 equivalence:3 recurrence:1 tm:4 kokyuroku:1 applied:1 far:1 putting:1 difference:8 thiele:2 notes:1 solution:1 large:3 discrete:28 small:4 eigenvalues:1 anal:1 noted:2 zn:3 employing:2 nonautonomous:2 direct:1 approximation:1 second:1 odd:1 bilinear:3 what:1 nonlinear:1 stands:1 section:2 expressed:1 agrees:1 symes:2 version:1 new:5 method:1 coefficient:1 notions:1 respectively:4 here:1 papageorgiou:7 cylindrical:5 concluding:2 strong:1 equations:12 change:1 hankel:3 study:1 rhombus:3 amount:1 survey:1 noticeably:1 replace:1 duce:1 next:1 vol:1 msm:1 therefore:1 maxon:1 associated:1 type:1 more:2 successful:1 becomes:3 apparent:1 berlin:1 known:3 cases:1 ramani:4 springer:1 tokyo:3 ε2n:9 det:1 modified:1 ρn:12 mq:1 mp:1 following:9 fulfill:1 calculation:1 indicates:1 numbers:1 decaying:2 η2n:14 how:1 pair:1 instead:2 parameter:2 data:1 constants:2 accelerates:2 third:2 light:1 trilinear:2 algorithms:18 sm:53 equation:22 pointed:1 soc:2 interpreted:1 abstract:1 paper:1 through:2 japan:1 satisfies:1 its:2 before:1 τn:13 derive:1 rapidly:2 la:1 interesting:1 actually:1 whether:1 lr:1 systems:2 jacobi:1 mail:1 main:1 them:1 good:1 yn:11 introduce:2 they:1 nov:1 now:1 possess:1 2t:3 eigenvalue:1 2p:1 always:1 university:2 traced:1 2a:3 2c:1 2n:17 side:1 2k:4 el:1 directly:1 accelerator:2 series:2 idea:2 related:3 toda:2 our:2 eq:26 out:1 shown:3 matrix:2 since:2 rev:1 rational:1 lecture:1 ref:2 math:2 wisconsin:1 theory:1 clarify:2 completely:1 put:1 so:1 equa:1 exponentially:1 first:2 there:3 xn:10 variables:2 construct:1 another:2 passes:1 given:11 rewritten:3 introduction:1 eqs:1 relations:1 their:6 siam:1 scheme:1 recovered:1 gives:2 tool:1 continuous:1 than:3 coefficients:1 kind:1 roles:1 double:1 integrability:1 future:1 bauer:3 tion:1 comput:1 rewrite:2 generalization:1 correspond:1 say:1 need:1 seen:3 clearly:1 viewed:1 sat:1 acceleration:11 lim:1 converges:5 note:1 sciences:1 potential:7 take:1 performance:4 even:1 play:1 exactly:1 nτn:1 most:2 nothing:2 appear:1 soliton:9 considered:6 calculated:1 physica:1 order:3 ku:1 fact:4 madison:1 wynn:6 show:3 converge:1 relation:2 solutions:1 analogue:1 find:3 subtracting:1 based:1 spite:1 should:2 only:1 integrable:6 over:1 viewpoint:1 dependent:5 de:1 famous:1 words:1 despite:1 meguro:1 evolution:1 qr:1 determinants:5 showed:2 arxiv:1 twice:1 discussing:1 cǫ:6 satisfy:1 6uux:1 depends:1 num:1 result:4 accelerators:1 terms:2 satisfying:1 review:1 diverge:1 case:1 various:1 between:4 ucker:1 recently:1 uux:2 rims:1 numer:1 attention:1 jp:1 however:3 solv:2 originates:1 both:2 x2n:2 many:1 taking:1 according:1 shanks:3 among:1 cn:2 cm:42 sequences:2 moreover:2 ct:1 transformations:1 addition:1 been:2 defined:1 interest:1 expected:1 komaba:1 pl:1 define:1 determinant:2 imai:2 quantities:6 xxx:1 confinement:3 convergent:1 p2:2 p3:1 eration:1 look:1 p4:1 will:1 rationally:1 while:2 replaced:1 property:2 jpn:1 almost:1 characteristics:1 equal:1 itself:1 claimed:1 uxxx:3 different:5 same:8 finite:3 interpolation:1 used:1 again:1 numerical:3 hand:2 infinite:1 well:3 tsujimoto:2 analysis:2 solve:1 greatest:1 possesses:2 proposed:1 less:1 grammaticos:4 obtain:3 press:1 singularity:4 previous:1 tables:1 regarded:2 smith:1 except:1 εn:7 lett:4 brezinski:1 erique:1 transformation:7 generalized:1 aspects:1 rules:1 test:2 philos:1 mathematics:1 confined:1 integer:1 mod:1 aitken:1 alternatively:1 yields:3 popular:1 become:1 essential:1 mathematical:1 shed:1 right:1 often:1 sequence:7 some:2 back:1 understood:2 nagai:2 apply:1 kdv:24 though:1 fluids:1 does:1 proc:1 obey:1 slight:1 bm:3 equivalent:4 each:1 step:1 ratios:3 substitution:1 properties:1 acc:1 constraint:1 langer:1 discretization:4 cambridge:1 ηn:3 into:1 nonperiodic:1 because:2 references:1 operator:1 initial:2 transform:1 way:1 ed:1 forward:1 was:1 form:7 differences:1 analyse:1 but:3 ford:1 reminds:2 convergence:14 considerable:1 uu:1 ut:4 casorati:1 us:5 limit:6 problem:1 similar:1 called:3 ac:1 diverges:1 constant:1 int:2 ak:3 general:1 single:1 intro:1 relates:1 formalism:1 identities:1 defines:1 satsuma:2 functions:3 no:2 when:3 nf:2 field:1 other:9 remarks:2 department:1 tie:1 briefly:1 elements:2 calculating:1 hirota:4 problems:2 chance:1 important:1 variable:7 sides:1 faster:1 algorithm:40 values:2 rule:2 time:2 4d:1 original:3
|
solv-int9511002.txt |@word forger:1 global:2 results:1 leads:1 edu:2 reasoning:1 whose:1 inverse:1 tr:1 ıa:1 γj:6 γi:8 γn:13 th:1 under:1 analogous:1 applied:1 straightforward:1 very:1 summarized:1 exact:1 condition:6 solution:3 large:2 cnea:2 small:2 setup:1 fµν:6 consistent:1 cosh:5 b137:1 integrability:2 theory:2 spectral:5 aim:1 what:3 adds:1 cast:1 giving:1 current:4 axial:1 version:1 new:1 consisting:1 satisfy:2 respectively:1 here:6 sinh:5 fulfill:2 path:6 along:1 equations:4 appears:1 19b:2 obtained:2 instituto:1 antisymmetric:1 involved:1 study:2 studied:1 products:2 usually:2 makes:1 via:1 family:3 ai:2 apply:1 use:2 prove:1 ariel:2 finally:1 classically:1 f01:1 therefore:4 taken:2 means:2 tell:1 more:3 started:1 dxµ:1 curvature:5 appendix:2 employed:1 known:2 hold:1 iii:2 must:3 account:1 valued:3 integrating:3 rν:3 equation:7 work:1 modified:1 theories:1 infinitesimal:3 following:1 cab:2 lσ:4 figure:1 do:1 process:1 expanding:1 lorentz:5 something:1 want:6 sense:1 thing:1 provide:1 verify:2 discussion:2 holds:1 write:3 how:1 pure:1 significance:1 those:1 parameter:9 may:2 max:2 after:1 lax:16 coming:1 law:2 arch:1 compatibility:3 stress:1 whenever:2 centro:1 so:9 allow:1 lν:26 order:10 gµν:2 yamanaka:1 indeed:1 over:5 mainly:1 satisfied:2 years:1 paper:1 existence:3 still:1 its:5 before:1 group:3 chosen:2 fix:2 relativity:1 actually:1 choose:3 mail:2 argentina:1 main:1 easier:1 ly:1 eventually:1 non:18 inductively:1 fig:1 newman:1 nov:1 now:8 realize:2 rµ:5 term:3 equality:2 verifying:1 realistic:1 l2:2 each:3 found:1 side:1 subset:1 as1:1 arxiv:1 nγi:2 doing:2 series:4 related:2 tsov:1 our:1 eq:26 try:1 shown:3 space:4 rep:2 since:1 rev:1 looking:1 kent:1 rn:1 independence:1 linear:8 divergence:6 standard:1 indices:2 completely:1 pairs:1 derivation:1 impose:1 times:3 motion:1 ordering:2 lµ:31 think:1 first:5 origin:2 initial:1 vacua:1 symmetry:9 restrict:2 employing:1 directly:1 enumerate:1 b155:1 given:9 cartesian:1 introduction:1 leading:2 system:4 least:1 final:1 gives:3 dolan:2 exactly:4 part:1 somewhat:2 authors:2 x0:1 x1:1 than:1 kind:1 γj2:1 roberto:1 zero:11 ranging:1 enables:1 symmetries:1 rewrite:1 argument:1 generalization:4 20a:4 20b:2 uscher:1 need:1 tells:1 paths:2 built:1 depending:1 latter:1 aside:1 note:2 instance:3 square:1 take:1 continuous:1 clearer:1 pair:14 iterate:2 class:1 axially:2 constancy:1 pohlmeyer:1 constructed:1 kk:1 exp:1 usual:1 sigma:1 quantity:1 sector:1 selection:1 show:3 supported:1 dependant:3 anyway:2 gauge:5 solutions:3 trivial:2 find:4 based:1 parameters:3 written:3 should:6 only:7 explicitly:1 pretty:1 integrable:1 local:8 hope:1 dn:5 abelian:1 notation:2 get:5 dd:1 de:1 γn2:5 restart:1 continuum:1 fields:2 differential:1 gribov:1 obscure:1 fixed:3 set:2 constructing:1 reference:1 iteration:2 see:4 domain:1 conicet:1 nuc:2 analog:1 clarifies:1 γi2:2 γi1:1 tensor:2 below:1 symmetric:2 enough:1 between:1 invariant:2 boundary:3 conditions:3 preserve:1 multiplied:1 terms:8 weak:2 however:1 solv:1 configuration:1 undetermined:1 piece:2 last:1 reverse:1 many:1 taking:2 equal:1 etc:3 expression:1 relevant:1 point:5 seems:1 dimensional:9 cancel:3 moreover:1 testable:1 math:1 considering:2 sensible:1 jetp:1 described:1 transformations:3 second:2 basis:1 addition:1 19a:3 been:2 defined:5 much:1 interest:1 systems:1 enable:1 subspace:1 balseiro:1 gal:1 systematic:1 careful:1 former:1 present:1 case:4 pacs:1 will:2 euclidean:1 error:1 renaming:1 region:1 procedure:5 ive:1 vg:1 yangmills:1 thus:1 them:3 ii:2 dual:1 currents:3 different:3 verified:1 anymore:1 make:2 same:1 any:2 several:2 higher:6 independent:2 i1:2 i2:1 upon:1 action:5 purpose:1 infinite:2 invariance:1 identity:1 lower:1 weakly:1 charges:2 well:4 obviously:4 solve:1 components:1 consistency:3 position:1 model:13 soviet:1 self:1 left:4 manifold:1 just:1 being:1 obtain:6 scattering:1 conclusions:1 had:1 lett:1 easy:2 solvable:1 transformation:15 noether:1 breaks:1 sums:3 possible:2 vacuum:2 formal:1 sakharov:1 follows:1 benefit:1 steps:1 arbitrary:2 making:1 therein:2 omico:1 right:3 deal:1 some:3 chakravarty:1 neglecting:1 ourselves:1 proceeding:1 dimensions:5 integration:1 asking:1 particular:1 expansion:2 constructive:2 step:1 although:1 about:2 o:15 dependency:1 bariloche:2 introduced:1 op:1 own:1 into:1 within:1 obtaining:1 garc:1 down:1 included:1 because:6 references:3 operator:1 hep:1 area:1 assumed:1 there:1 u0:2 u2:1 conservation:2 way:7 xµ:1 was:3 function:2 form:1 but:5 construction:2 true:2 october:1 inside:2 up:9 us:4 uo:1 un:8 limit:4 iterated:2 cit:1 minkowsky:1 problem:2 define:1 called:1 taylor:3 associated:1 int:1 abstract:1 contribute:1 general:4 conserved:5 ar:2 exist:1 chau:1 check:1 physical:5 no:4 when:1 field:5 priori:1 spatial:1 generates:1 calculating:1 models:1 vega:1 problems:1 a0:2 meaning:1 bounded:1 variable:2 building:1 implies:1 physics:1 factors:1 equivalently:1 time:4 4d:1 starting:3 once:1
|
solv-int9511003.txt |@word limited:1 code:3 partial:3 consider:5 rev:5 splitting:5 ginzburg:4 commute:1 during:3 consists:3 implement:1 devoted:1 whose:1 fronts:5 inverse:1 depend:1 show:2 dp:1 finally:2 stable:2 summarizes:1 case:2 scienti:1 straightforward:2 very:3 eckmann:1 results:1 lyapunov:4 veri:1 bringing:1 special:1 entire:1 scholl:1 hamiltonian:2 turns:3 solution:4 t0:1 large:3 phase:1 small:3 round:1 smaller:1 speci:3 estimates:1 direct:3 approximation:1 second:4 chen:1 dynamics:3 estimated:1 ode:1 spectral:14 errors:11 advantageous:1 section:3 while:1 expressed:1 above:1 new:3 method:13 contrast:1 respectively:1 realizations:1 component:2 here:2 understanding:1 ranges:1 reported:3 les:1 decay:1 concluding:1 november:1 equations:4 z1:1 obtained:2 ahead:2 institute:1 study:2 larger:1 8x:1 commonly:1 periodic:2 published:1 usually:2 hospitality:1 noticeably:1 fourier:5 spatio:4 der:1 involves:2 technique:1 spatially:4 convolution:3 explained:1 replace:1 pulls:1 total:2 univ:2 derivatives:2 use:3 takes:1 would:3 sake:2 positive:2 frog:2 next:1 discrepancies:1 few:2 associated:1 livi:1 more:3 aronson:1 formally:1 brings:1 line:2 opposing:1 particular:5 known:3 cases:3 iii:2 cation:2 account:1 avoiding:1 equation:6 work:4 column:2 remain:1 values:11 columns:1 waller:1 averages:1 example:2 performed:3 figures:1 chosen:2 organized:2 states:6 pushed:2 minimum:3 pulling:1 numbers:1 want:4 arise:1 information:2 end:1 torcini:5 rather:1 means:1 regions:2 cgle:12 fourth:1 instead:1 ordinary:1 parameter:6 sin:1 simplicity:1 product:1 de:5 after:3 physik:2 water:1 multiplication:2 choice:2 data:1 grow:1 shraiman:1 third:1 maybe:1 lines:1 su:2 complexity:1 cannot:4 so:4 oppo:1 ned:1 representation:1 acknowledges:1 pulled:1 order:9 typical:2 operations:2 torino:1 dx:1 saarloos:1 over:1 fft:2 stability:4 course:2 paper:5 through:1 committed:1 methoden:1 its:2 superior:1 le:2 thank:2 directional:1 ln:3 temporal:4 solving:1 better:1 complex:7 systems:14 erences:2 main:1 spreading:1 maximal:1 non:5 thereby:2 practice:2 impossible:2 collide:1 introduce:1 landau:4 they:1 half:1 front:21 now:2 discuss:1 kpp:1 represents:1 petrovsky:1 2s:1 always:1 university:1 each:6 instability:2 european:1 referred:1 schemes:3 ei:1 map:1 ed:1 reduce:1 related:3 paradigmatic:1 extended:7 yoshida:1 expect:1 measurement:5 our:6 eq:7 es:1 out:3 shown:3 network:1 space:8 furthermore:1 since:4 crucial:2 chaos:7 increase:1 fellowship:1 nite:7 formula:2 integrated:2 math:1 shows:1 numerical:1 linear:6 graduiertenkolleg:1 mechanisms:1 wuppertal:2 possibility:1 standard:1 completely:1 ect:1 nition:1 estimate:1 bring:1 recipes:1 keep:1 exponentially:3 generalizations:1 neglect:2 speeds:3 origin:1 number:3 system:7 cients:1 clear:1 employing:1 done:3 another:1 reached:1 precisely:1 open:1 size:1 interchange:1 given:4 perturbation:5 table:4 introduction:1 theoretische:1 least:1 needed:2 perturbations:2 1e:2 brevity:1 dfg:1 scheme:5 bosch:1 ranging:2 recovered:1 gives:1 centered:1 moscow:1 exactly:2 greenside:2 part:1 rst:4 translation:1 than:2 distance:1 preventing:1 princeton:2 iteration:1 namely:2 limiting:1 recording:1 oono:1 amplitude:1 were:1 providing:1 powers:1 keefe:1 function:2 unchanged:1 reduction:1 measure:1 defect:1 say:2 tables:1 any:4 elsewhere:1 zero:2 min:1 essentially:3 latter:1 responsible:1 proportional:1 mechanism:1 take:1 algorithms:4 coincide:1 many:1 accuracy:3 play:1 sure:1 scripta:1 though:1 mclachlan:1 most:1 nonlinear:1 germany:1 successive:1 remarks:1 measured:4 class:3 workshop:1 observation:1 nonlinearity:2 pseudospectral:1 axx:1 trotter:1 behaviour:1 physica:2 typeset:1 wacker:1 velocity:3 ky:1 left:1 typically:1 sum:1 fact:1 precise:1 particularly:4 phenomenon:1 disturbances:6 supported:1 multifractal:1 x2:1 hohenberg:2 keywords:1 chaoticity:1 july:1 help:1 indicator:1 parameters:4 implementation:1 commutators:1 explain:1 outside:1 negligible:1 should:8 only:7 jaj:1 factor:2 integrate:1 employed:1 local:5 achieve:1 ser:1 do:1 di:18 express:1 ones:1 closely:2 progress:1 erent:5 routine:2 grassberger:5 runs:1 exhibiting:2 goldenfeld:1 acknowledgments:1 europhys:3 albeit:1 kernel:3 computed:1 reference:1 achieved:1 unpublished:1 kolmogorov:1 observed:3 alessandro:1 sec:2 considered:1 discussions:1 recently:1 forthcoming:1 techniques:1 phases:1 said:1 exponent:3 sites:1 propagates:1 state:3 smallest:1 various:1 ered:1 between:2 invariant:1 boundary:4 conditions:4 comparable:2 terms:3 nature:3 comp:1 jr:1 gratefully:1 article:2 ja:1 both:4 cos:1 etv:2 ett:1 paquette:1 kaneko:2 treated:1 region:3 la:1 according:1 agree:1 propagation:21 coe:1 pde:5 expression:1 etl:1 con:4 ci:1 relevant:2 co:1 point:1 simple:2 corresponds:1 community:1 factorize:1 cult:1 simply:1 iterations:1 universitat:1 moreover:1 throughout:1 along:2 kapral:2 described:3 ciently:1 addition:1 due:5 been:7 cient:2 spread:2 transformed:1 pro:3 fig:2 gesamthochschule:1 corresponding:1 concerning:1 precision:4 bull:1 c3:2 last:2 c1:1 evidence:1 present:7 applied:2 eip:1 multi:2 novel:1 limits:1 exponential:2 pacs:1 solid:1 tolerate:1 value:1 will:24 near:1 replaced:1 behavior:1 error:4 situation:2 property:1 procedure:1 ix:2 vf:11 coupled:1 chaotic:10 bergische:1 thus:7 iv:2 ii:2 characterize:1 reads:1 itself:1 ic:3 numerische:1 containing:2 italy:1 perform:1 suggest:1 make:1 cross:1 same:4 parts:2 split:1 units:1 und:2 several:4 higher:5 erence:3 used:1 guration:4 see:4 initialization:1 extention:1 hand:1 average:4 compared:2 moving:1 cleaning:2 contribution:1 suitable:1 kept:1 intermittent:1 solidi:2 locality:3 well:3 analysis:6 bohr:1 edge:1 coordinate:4 position:1 model:1 usual:2 xed:3 satis:1 culties:1 velocities:1 just:2 being:1 able:1 accurate:2 identically:1 rest:1 ne:2 shape:3 intervals:1 transforms:1 turbulence:1 campbell:1 useful:3 speed:7 yet:1 adv:1 rewriting:1 disturbance:4 conclusions:1 seems:5 except:2 eld:7 mathematically:1 2nc:1 belongs:1 combine:2 lett:8 mod:2 piskunov:1 momentum:1 real:3 noticeable:1 tests:1 easily:1 read:1 possible:1 increases:1 grid:3 know:2 press:3 using:3 unique:1 ruled:1 dimensional:4 theor:1 necessary:2 erential:4 sizes:1 follows:2 performing:2 candy:2 unstable:5 resolved:1 unperturbed:2 eec:1 because:3 methods:4 grids:1 some:4 back:1 library:1 growth:1 respect:1 duration:1 peter:1 neglecting:1 ourselves:1 transport:1 dimensions:1 avoid:1 novelty:1 integration:17 per:1 conservative:1 leap:2 equal:1 prog:1 steps:8 propagating:2 bose:1 refer:2 inserting:1 collet:1 instabilities:1 step:9 revtex:1 found:2 proceeded:1 properties:1 proceed:1 comparison:1 about:1 instantaneously:1 o:5 involving:1 propagate:1 suggestions:1 introduced:5 discretization:1 cambridge:2 followed:1 previously:1 into:8 within:4 rendering:1 appropriate:1 references:1 tiny:1 operator:5 accumulated:1 ciency:1 schrodinger:1 van:2 log:1 comparing:1 assumed:1 strictly:1 there:3 transform:3 quadratic:1 viscous:1 was:1 lowest:1 tlim:1 2vf:1 form:2 phenomena:2 but:8 repeatedly:1 adopting:1 vl:6 dissipative:2 slope:1 us:8 discretized:1 economic:1 limit:2 problem:1 similar:2 called:3 regimes:2 strongly:2 saturate:1 lattices:1 classic:1 int:2 steady:1 abstract:1 combining:1 general:3 simulations:1 partly:1 trailing:1 machine:1 helge:1 codes:3 nag:1 no:2 dashed:1 whereas:1 nc:10 when:2 detail:1 elds:1 application:4 other:4 weinberger:1 details:1 spatial:7 pumir:1 er:1 politi:5 topic:1 problems:4 much:1 ole:1 important:2 fisher:1 furthest:1 bch:2 algorithm:10 assume:7 baker:1 interval:1 pseudo:6 together:2 having:1 transient:2 time:18 backward:1 resolution:2 cpu:1 once:1
|
solv-int9511004.txt |@word allowed:2 consider:21 similarity:4 equalities:3 varying:1 results:12 leads:1 scalar:2 proposition:1 lln:1 expressions:3 depend:3 technique:4 h2α:2 finally:1 preserved:1 th:2 under:3 nodes:8 presentation:1 applied:4 ll1:1 springer:2 summarized:1 discretizations:2 difference:55 exact:3 condition:13 z12:1 solution:2 leave:3 discrete:12 small:17 speculation:1 round:1 zn:2 employing:1 direct:2 approximation:45 zero:3 further:2 dynamics:1 substitute:4 linear:2 3y:1 nonlinear:1 brackets:4 section:2 expressed:1 nondegeneracy:1 establishes:2 new:2 method:2 raton:1 satisfy:3 notions:1 respectively:1 groups:17 represented:2 consideration:2 november:1 xα:73 equations:56 z1:9 z2:9 obtained:2 institute:1 involved:1 study:3 studied:4 allows:3 leaving:4 resulting:7 action:7 makes:1 composed:1 family:2 analyzing:3 summation:1 apply:1 should:1 establish:3 derivatives:8 use:6 would:1 lemma:11 comparing:1 therefore:11 taken:1 means:1 tekhniki:2 introducing:1 formally:3 becomes:3 operators:1 stable:7 corrected:3 validity:1 berlin:2 appendix:5 virtue:6 particular:3 known:2 cases:2 hold:1 must:6 account:2 valued:1 equation:67 work:2 modified:1 unknowns:3 remain:1 infinitesimal:16 values:7 concepts:1 following:31 example:13 proof:9 f1:3 calculation:2 expanding:1 preserving:2 yα:15 sense:2 sought:2 conversely:2 weaken:1 information:1 needs:3 end:1 z22:2 describes:1 acts:1 write:6 hαi:3 methodology:4 criterion:7 instead:1 ordinary:6 verlag:2 parameter:20 replacing:1 respective:1 nullify:1 applications:1 levi:2 produce:1 fi:2 fm:1 fn:1 natural:3 lemmas:1 element:1 so:2 allow:1 lα:13 definitions:4 order:17 holds:2 developed:3 satisfied:5 equality:3 through:3 satisfies:2 still:1 its:6 ima:1 derive:1 group:51 xl:2 ln:2 ll:2 solving:4 forms:1 omitted:1 mail:1 defining:2 easier:1 non:3 dal:1 outlined:2 practice:1 noticing:2 introduce:4 dak:4 they:1 identically:1 nov:1 now:4 yu:1 smoothness:1 easily:3 term:5 2p:3 2r:1 always:1 university:1 2x:1 possibilities:1 each:2 found:3 side:6 referred:1 subsystem:1 arxiv:1 transform:2 viniti:2 dorodnitsyn:2 series:2 hard:1 reduce:1 approximates:3 related:1 itogi:2 used:7 obtains:4 combining:1 our:2 approximated:1 avoided:1 special:1 really:1 canada:1 shown:2 space:4 furthermore:1 since:2 research:1 may:6 acting:5 internet:1 perturbed:1 induction:14 math:2 shows:1 exactly:1 theory:3 admits:1 statistics:1 definition:7 derivation:1 determining:3 similarly:2 florida:1 times:1 appearing:1 mesh:2 xα0:21 first:30 reversing:1 xi:4 xn:13 symmetry:5 u1:9 variables:11 hkα:12 xf:3 number:2 rank:1 comprised:1 restrict:1 xy:9 approximately:2 another:1 size:1 equating:1 given:8 perturbation:7 rewritten:1 their:8 introduction:1 system:28 relations:4 needed:1 perturbations:2 brevity:1 calculations:2 speaking:1 gives:3 moscow:2 continuous:3 boca:1 authors:1 x2:1 translation:1 x1:12 completes:1 unfortunately:1 equated:2 approximations:10 second:1 winternitz:2 were:1 naturally:1 treated:3 symmetries:6 derivative:3 rewrite:4 correction:3 noninvariance:2 say:1 z0:1 manipulating:1 need:1 seen:3 windsor:2 viewed:4 lie:6 convenient:1 latter:2 answering:1 εp:48 εr:11 εm:5 εl:6 k1:5 εi:18 build:1 analogy:2 finding:1 accuracy:1 added:2 fundamental:2 decreasing:1 algebraic:12 said:2 formulae:8 analytically:1 constructed:1 observation:1 prolongation:8 considered:5 neighboring:1 points:4 notion:1 fact:7 laws:1 show:1 notations:1 purely:1 spaces:2 relation:5 solutions:3 substituting:3 analogue:1 trivial:1 find:5 based:1 knowledge:2 parameters:4 than:1 analytic:3 only:7 going:1 local:2 do:1 dl:1 above:15 notation:1 get:6 dependent:1 fluid:1 da:3 dz:1 despite:1 lattices:1 stability:1 conditions:1 differential:67 cik:1 contain:1 analytical:1 fixed:1 ai:8 requirement:3 set:15 constructing:1 exists:1 hα:39 j0:67 arrives:1 up:1 observed:1 see:10 result:4 terms:6 chose:1 satisfying:3 olver:1 uα:90 written:4 closed:1 between:4 αi:3 invariant:22 approach:3 notice:5 recently:1 utt:1 extend:4 analogues:3 hypothesis:5 solv:1 suggested:2 both:3 last:1 many:2 taking:2 according:4 participating:1 expression:6 finds:1 ck:1 ci:1 ch:1 cm:3 ca:1 respect:14 considering:2 pp:3 described:1 transformations:14 basis:1 addition:1 simplification:1 lα0:4 due:2 been:2 appears:1 int:1 reduction:1 cauchy:3 interest:1 basic:1 utilizing:3 dk:4 direction:2 corresponding:11 sufficient:5 hi:17 ensuring:1 stems:1 gazizov:3 former:1 those:2 case:6 formalization:2 invariants:1 value:1 remaining:1 will:6 while:2 suppose:2 di:2 property:1 leaves:6 procedure:2 resolved:1 vol:1 equal:2 reads:2 rid:1 ie:2 inc:1 author:1 perform:1 powers:1 make:1 same:5 any:2 arguments:2 uα0:27 finite:48 higher:1 independent:6 extended:6 maeda:2 upon:1 hand:6 changing:1 invariance:11 identity:1 fˆ1:4 crc:2 no:1 analysis:8 obviously:1 solve:1 components:3 english:1 coordinate:1 model:5 arising:2 left:5 being:1 generally:1 3p4:1 obtain:9 finitedifference:1 λf:2 questions:2 immediately:4 functionally:1 previous:2 letting:1 adding:4 integer:1 seems:1 ujα:1 interested:1 transformed:1 lett:1 easy:1 theorem:20 transformation:4 noether:1 εk:30 read:2 possible:4 grid:11 press:1 using:22 formal:1 necessary:4 sizes:7 follows:17 performing:1 admitted:8 server:1 separately:1 δl:1 yields:1 arbitrary:3 soviet:1 differencing:2 because:4 methods:2 some:17 deduce:1 examples:2 provided:2 demonstrates:1 avoid:1 2xy:2 does:3 assuming:2 steps:1 demonstrated:3 equivalent:2 l1:1 conventional:1 expansion:4 step:9 substituted:1 although:3 εh1:3 losing:1 approximating:4 properties:13 rearranging:1 about:1 prove:11 introduces:1 o:112 carries:1 a2:2 ensure:1 introduced:4 discretization:4 computational:1 statements:1 previously:1 into:8 h1:12 linearization:1 square:1 references:1 determine:2 operator:19 ontario:1 additional:1 there:1 question:2 approximate:25 conservation:1 handbook:1 way:5 ed:1 forward:2 az1:1 analyze:1 was:1 ibragimov:4 function:18 complete:1 form:2 becoming:1 denoting:1 but:2 volume:1 hk:1 properly:1 hn:12 hm:4 russian:2 true:9 he:1 made:1 applying:5 ux:1 whether:1 ut:1 smooth:6 cin:2 us:3 fˆ0:4 below:1 un:20 limit:1 uk:4 continuously:1 demonstrate:1 problem:3 similar:2 called:3 yα2:2 hiα:9 taylor:4 defined:3 abstract:1 describe:1 proven:3 general:7 dξ:1 single:1 proves:2 right:1 physical:1 again:3 functions:7 analyticity:1 differentiable:1 baikov:3 locality:2 when:7 application:3 valid:3 details:2 nauki:2 department:1 mathematics:1 nu:1 node:6 denote:1 problemy:2 models:1 setting:1 ξi:1 a3:1 important:9 ξn:1 variable:2 sides:2 implies:3 longer:1 assume:5 starting:1 interval:1 together:3 having:2 appl:1 dϕ:3 requires:2 original:7
|
solv-int9511005.txt |@word secondly:1 partial:2 consider:2 pointing:1 brownian:1 results:2 fxxx:2 eη:8 fronts:2 const:2 chinese:1 shanghai:1 finally:2 program:1 under:2 analogous:1 worth:1 applied:1 wave:16 exact:13 condition:1 presented:3 notes:1 stuttgart:1 list:1 solution:22 leave:1 solved:1 biological:1 anal:1 inspection:1 equation:71 enjoy:1 smaller:2 2k2:1 direct:3 pulse:2 painlev:2 traveling:16 2aξ:2 further:5 bilinear:4 nonlinear:17 advantageous:1 section:5 expressed:1 fuchssteiner:5 above:4 new:5 ek3:1 ek2:1 ek1:1 edited:5 hasn:2 mem:1 respectively:2 genes:1 here:1 agreement:1 china:1 ansatz:9 along:1 equations:20 2ki:1 change:1 obtained:5 remark:2 conviction:1 institute:1 study:1 studied:1 allows:1 resulting:1 gene:1 studies:1 named:1 useful:1 tools:1 prove:1 found:1 contains:1 process:1 therefore:5 mckean:1 type:1 von:1 more:4 introducing:1 engender:1 berlin:1 particular:1 known:2 cases:3 must:2 taub:1 springer:1 ma:3 science:1 originally:1 following:8 making:1 dec:1 example:3 νu:1 wang:4 give:2 calculation:1 µa0:1 sense:1 ann:1 νa:1 νb:1 tan:4 yang:1 discussion:1 maps:2 nontrivial:3 pure:1 ordinary:3 obius:1 map:1 lan:1 ft:2 singular:3 fx:2 after:2 plane:1 waves:4 eugenics:1 constants:5 dw3:1 jiang:1 liquid:1 explicit:17 correspond:1 so:2 acknowledges:1 order:1 mannheim:1 a02:3 a03:1 a01:2 cohen:1 course:1 paper:1 through:2 signs:2 existence:1 satisfies:1 cole:4 its:3 roots:1 solitary:3 group:1 ln:4 interesting:1 solving:1 aronson:1 actually:1 absence:1 lu:1 choose:5 travelling:4 coti:1 non:1 combustion:1 thereby:1 bernoulli:2 acklund:4 investigated:1 scaling:1 they:2 front:2 now:1 association:1 possess:1 term:1 failed:1 goldstein:1 always:1 university:1 possibilities:1 2a:3 2b:3 2a2:11 2n:2 2k:3 arxiv:1 financial:1 ek:2 osaka:1 idea:1 related:1 frequency:1 yield:1 our:2 special:6 out:4 large:1 shown:2 acknowledgment:1 algebra:1 crucial:1 increase:1 may:16 amplitude:1 pan:1 lecture:1 ref:3 math:9 shows:1 foundation:1 linear:5 interactions:3 favored:1 contain:1 seventh:1 standard:1 krishnan:2 beginning:2 generate:2 advance:2 interaction:1 r1:9 geometry:1 determining:1 cw2:1 moment:1 motion:2 incorporated:1 3a20:1 generalizations:1 first:2 humboldt:1 number:2 engenders:2 xx:2 done:1 construct:1 another:2 2a1:2 maple:1 ser:1 given:4 similarly:2 introduction:1 unknown:2 relations:1 their:3 calculations:1 moscow:1 acquire:2 newell:2 authors:1 population:1 diffusion:7 kind:4 second:1 matter:1 µki:1 were:2 decompose:1 generality:3 topics:1 modern:1 generalization:1 7th:1 ans:3 mupad:1 take:1 any:3 uξξ:3 fxx:2 burgers:2 fxt:2 k3:2 k2:4 k1:2 εi:1 generalized:6 exactly:1 opposite:1 riccati:9 satisfying:2 germany:1 remarks:1 america:1 probabilistic:1 class:5 don:1 considered:2 kj:4 ki:2 fx3:1 points:1 exp:2 kx:6 physics:2 bulletin:1 wavenumber:1 quantity:1 parkes:1 particularly:1 show:2 relation:1 solutions:58 trivial:1 find:2 universitaet:1 should:1 analytic:2 only:4 explicitly:1 integrable:1 partially:1 hopf:4 hereman:1 εb1:2 get:3 fluid:1 petrovskii:19 ones:2 gen:3 coth:5 aξ:4 evolution:2 qu:1 conditions:3 coalescence:2 differential:7 2b1:2 method:6 mapped:1 analytical:1 including:1 bramson:1 set:2 computed:1 exists:1 physically:1 kolmogorov:23 up:1 see:1 computer:1 result:3 discussions:1 lnf:1 techniques:1 uξ:2 αu:2 αt:1 µu:6 kj2:1 kj3:1 written:1 un:1 various:2 µa:1 µb:1 notice:2 terms:1 fitzhugh:3 missing:1 alexander:1 however:3 wt:1 comm:1 solv:1 both:1 informatik:1 cot:3 equal:1 propagation:3 σx:1 whole:1 kamke:1 point:3 simple:2 leipzig:1 dimensional:1 analyzed:1 cancel:1 proved:1 appeared:1 transformations:4 wien:1 due:2 been:4 int:1 cauchy:2 combined:2 basic:1 fudan:1 conte:1 generating:1 aj:1 corresponding:1 nonconstant:1 bull:2 worked:1 present:1 case:14 look:1 exponential:1 tanh:8 transformation:13 will:1 property:7 a21:2 jpn:1 ki3:1 vi:1 refs:1 thus:4 uxx:11 ii:1 need:1 reads:1 whitehead:2 different:1 combination:1 fibers:1 make:6 same:8 finite:2 luxemburg:1 independent:1 extended:1 cubic:2 numerical:1 v1:2 v2:2 v3:2 v4:2 purpose:1 urich:1 ablowitz:1 identity:1 break:1 mech:1 paderborn:2 well:1 analysis:3 concrete:1 without:2 solve:3 model:1 possesses:2 proposed:4 wxx:1 obtain:3 rest:1 bandwidth:1 4a0:1 speed:1 blow:1 note:6 kluwer:2 instance:2 conclude:1 quadratures:5 wall:1 verse:1 lett:4 easy:1 solvable:4 piskunov:21 gave:1 real:5 bio:1 five:4 know:1 integer:1 vξ:8 loss:3 osungen:1 like:1 lost:2 follows:1 interestingly:1 velocities:1 yields:3 arbitrary:9 works:2 essential:1 δa:1 mathematical:2 old:2 methods:2 εa1:2 successfully:1 some:8 b0:4 b1:5 b2:1 mirror:1 proper:1 kdv:4 nonzero:2 2d:1 vol:1 genetics:1 univ:1 extensively:1 defined:1 assuming:1 δb1:1 equivalent:1 bi:7 bt:8 bv:1 bw:1 substitution:2 atze:3 tanh2:1 discussed:2 generated:2 important:2 practicable:1 nerve:3 soc:2 computational:1 differentialgleichungen:1 into:10 three:11 tanaka:1 references:1 span:1 u5:13 u4:12 support:1 there:5 u1:11 transform:1 u3:16 u2:15 accordingly:2 appl:2 way:1 analyze:1 was:2 ibragimov:1 function:2 µb0:1 form:5 but:3 convergence:1 he:1 ut:12 ωt:6 us:1 ωi:1 below:1 ωj:1 ui:3 kawahara:1 problem:3 similar:1 ab:3 constant:2 choosing:1 3fx:2 nagumo:3 ai:10 abstract:1 describe:4 am:1 general:7 teubner:1 av:1 crystals:1 again:1 functions:2 no:3 mathematik:1 mathematica:1 when:14 application:3 other:1 weinberger:1 test:1 mathematics:3 boccara:1 a11:2 a13:1 a12:2 time:1 problems:3 a1:41 a0:11 a3:27 a2:34 variable:2 fisher:14 nonintegrable:2 vice:1 assume:1 casts:1 tricks:1 required:1 hirota:1 starting:1
|
solv-int9511006.txt |@word represent:1 partial:5 consider:11 chain:14 limited:1 particular:4 results:3 leads:1 scalar:1 consists:1 gn:87 gm:2 gk:2 reasoning:1 polinomials:1 analiz:1 devoted:1 whose:1 inverse:1 depend:6 tt:2 equivalence:2 contained:2 nonlocal:1 pˆn:1 present:1 under:4 analogous:1 characterised:1 case:24 belonging:2 straightforward:3 orthogonal:2 very:4 rise:1 conditions:36 choice:2 difference:22 exact:1 rn:17 condition:12 generalised:8 obvious:1 presented:2 positions:1 list:2 solution:13 discrete:4 lemma:3 second:6 biological:1 zn:7 approximately:1 periodicity:1 direct:3 approximation:1 zero:16 follow:1 dynamics:1 odd:1 expressions:1 linear:4 even:4 what:1 nonlinear:32 section:6 expressed:1 version:4 reconstruction:1 fractional:1 new:5 bn:26 exercise:1 satisfy:8 compact:1 led:4 degree:1 respectively:2 spacing:1 here:7 discretisations:1 represented:3 equations:49 obtained:12 great:1 institute:2 shift:2 study:1 changed:1 allows:1 reason:1 usually:1 fourier:1 involves:1 uniquely:1 via:2 divide:1 classification:13 9a:1 9b:1 prefer:1 summation:1 apply:1 total:2 tools:2 unit:1 derivatives:4 use:2 would:3 prove:9 sake:1 positive:2 stated:1 bundles:1 negative:1 next:2 few:8 moro:1 taken:1 themselves:3 volterra:11 type:5 more:11 zeroes:1 introducing:8 nkc:1 brings:1 operators:2 carrying:3 varying:3 known:2 cases:7 encountered:1 g2n:2 must:14 logarithm:1 account:4 defines:1 thanks:1 equation:42 work:4 modified:2 theories:1 values:4 following:21 arrive:1 example:16 proof:6 nearest:2 compare:3 give:2 calculation:4 sokolov:2 high:4 numbers:2 verlag:1 needs:1 uxxx:1 end:3 goal:1 provide:4 di:7 write:3 nontrivial:2 instead:2 ordinary:2 classify:1 classifying:5 proc:1 blocks:1 mat:3 algebra:1 may:2 after:3 derived:4 applications:2 levi:2 4th:1 law:16 fn:126 recursive:3 transposed:1 explicit:1 correspond:1 su:1 think:1 generic:1 cannot:3 so:13 sn:16 fundamental:2 enter:1 definitions:1 order:31 evolutionary:4 over:4 eqs:1 satisfied:4 paper:1 reconstruct:1 existence:9 satisfies:5 its:9 before:4 sciences:1 le:1 ln:11 fix:1 systems:2 mail:2 main:3 defining:2 possessing:1 correspondence:1 acknowledgments:1 yn:17 dan:1 introduce:1 framework:1 they:5 identically:1 nov:1 now:8 discuss:1 possess:1 articles:1 ϕn:24 several:1 name:1 always:6 classified:1 21c:1 2q:1 sufficiently:2 iff:4 each:2 universit:1 difficult:2 side:2 mean:1 mikhailov:2 differential:21 series:2 reduce:4 related:2 toda:11 used:2 our:2 approximated:1 eq:29 out:6 accomplish:1 solved:2 res:7 u2n:9 rev:2 research:2 rf:16 stud:2 denoted:2 formula:5 get:17 math:8 shows:2 foundation:1 extention:1 theory:4 written:2 fisica:1 quite:1 completely:2 complicated:1 term:2 generate:1 additional:1 definition:4 derivation:1 english:4 could:6 length:11 place:1 consequence:1 βn:20 generalizations:1 strictly:1 first:17 already:2 symmetry:29 miura:2 variables:9 number:2 transform:1 peculiarity:1 instances:1 done:1 construct:6 another:3 precisely:3 linearisable:1 given:15 perturbation:2 introduction:2 dipartimento:1 system:2 least:6 needed:1 appl:2 constants:4 calculations:4 variational:11 2fn:4 gives:2 holomorphic:1 statement:1 academy:1 recursively:1 continuous:4 zeroth:2 immediate:2 part:1 arctanh:1 than:3 coefficients:8 λun:1 kind:5 showed:1 approximations:1 integrability:4 limiting:1 classes:13 str:1 were:2 powers:2 russia:1 lowest:1 symmetries:31 derivative:15 rewrite:2 pass:1 argument:2 curves:1 say:6 vn2:1 seen:1 any:18 depending:6 able:2 k2:4 k1:6 generalized:11 finding:2 lhs:4 canonical:16 spectral:1 play:1 nobody:1 rhs:5 sets:3 algebraic:1 lists:1 class:9 yamilov:7 32a:1 considered:1 neighboring:1 calculated:2 request:2 kn:9 points:5 principle:1 exp:4 χn:5 physics:1 notion:1 fact:9 laws:22 show:1 supported:1 relation:2 solutions:3 trivial:2 find:3 d0:2 knowledge:1 enough:1 should:2 2bn:2 only:17 going:1 integrable:11 constant:6 local:19 γn:4 dn:7 dl:1 dm:3 dj:1 dk:4 exceptional:2 dependent:9 de:1 proces:1 ones:2 applying:1 differentiating:1 rfs:3 evolution:7 surveys:2 densities:7 fields:2 arxiv:1 expansions:1 requesting:1 sum:3 nauk:3 require:2 qn:26 coefficient:6 set:14 exists:1 imposing:1 nun:1 see:16 result:2 krichever:4 said:1 fn2:1 review:1 roma1:1 symmetric:1 state:3 future:3 various:1 ladik:1 simplest:1 invariant:5 approach:7 αn:7 available:1 notice:4 terms:10 shabat:5 importance:2 however:6 derive:7 hypothesis:1 solv:1 δan:4 vanish:1 ja:1 jb:1 2pn:1 both:5 collaborators:1 last:5 many:4 taking:5 density:9 c5:2 equal:2 comes:1 otherwise:1 among:1 cn:27 space:1 point:13 simple:2 corresponds:1 grants:1 lattices:1 respect:3 speak:1 considering:2 transformations:7 dun:1 three:5 been:3 int:2 reduction:1 much:1 interest:2 basic:2 pn:41 empty:1 define:9 direction:1 relations:1 corresponding:2 sufficient:1 residue:1 assert:1 covered:1 c3:1 c2:2 c1:3 denote:1 c7:2 c6:1 those:6 c4:2 applied:1 look:1 unlike:1 tanh:3 might:1 means:2 conserved:15 queuing:1 will:25 cast:1 while:5 intas:1 pˆ:2 procedure:3 u2xx:1 2un:1 coupled:1 almost:1 thus:9 non:1 vn:40 f2n:2 reads:3 conf:1 ia:1 denumerable:1 ib:1 different:11 italy:1 lengths:1 make:1 vries:1 same:7 orders:1 complex:5 split:2 proved:3 finite:1 φn:5 higher:8 independent:6 clear:1 extended:1 numerical:1 dgn:1 hand:2 constraining:1 necessity:1 infinite:6 frequently:1 ablowitz:1 a2n:1 frechet:8 well:2 analysis:1 thought:1 rome:1 solve:1 roma:3 five:2 model:2 soviet:1 possesses:1 2gn:1 left:3 world:1 just:7 being:3 obtain:7 vanishes:1 subcase:1 transforms:2 using:7 alternative:2 yet:1 previous:2 adding:1 preprint:1 readers:3 δpn:4 had:1 lattice:13 add:1 priori:2 transformed:1 easy:1 theorem:15 compares:1 apart:1 transformation:5 take:1 depends:3 enable:1 possible:2 21b:1 know:2 21a:1 integer:1 formal:12 modifications:1 necessary:2 follows:1 reduces:2 δu:3 korteweg:1 either:2 sezione:1 arbitrary:14 conclusion:1 essential:2 right:2 leningrad:1 some:10 springer:2 b4:2 b5:2 b6:2 b7:1 examples:2 b2:1 moreover:3 2qn:1 b8:1 ourselves:4 nonzero:1 provided:1 projection:2 polinomial:1 integration:2 comments:1 does:1 provides:2 assuming:3 chains:6 inserting:2 biology:1 scientific:2 power:2 ufa:4 equivalent:16 restrictive:1 step:1 concreteness:1 simpler:1 integers:1 carried:3 extension:1 novikov:4 theorems:2 dependence:1 reduced:5 compatible:2 range:1 a2:1 neighbor:1 introduced:2 consequently:8 restrict:1 publishing:1 into:18 functional:1 due:1 down:2 because:1 references:1 δun:5 operator:14 theoretically:1 log:22 support:1 there:8 approximate:15 long:3 start:2 conservation:38 way:15 was:1 function:30 32b:1 complete:3 form:18 conjugacy:1 but:16 construction:2 hn:16 russian:9 highest:5 true:2 partially:2 infn:2 compute:1 ux:2 ut:1 up:2 us:17 um:2 below:1 un:268 limit:3 uk:2 uj:2 problem:3 called:2 b1:1 associated:3 uspekhi:3 defined:6 certain:2 ak:1 b3:1 general:4 transl:3 engineering:1 proves:1 exist:5 physical:1 functions:10 no:2 when:4 detail:1 b9:1 field:6 other:4 role:1 mathematics:3 nice:1 elements:1 calculating:1 models:1 symbol:1 problems:3 visits:1 a1:3 a3:4 important:3 a5:3 a4:1 variable:3 cnr:1 sides:1 building:1 fk:8 implies:7 assume:2 requires:1 required:1 together:1 appendix:8 correlates:1 acterized:1 time:4 quantity:1 starting:4 once:1
|
solv-int9511007.txt |@word replacing:1 represent:1 concept:1 managed:1 consider:7 remarkable:2 results:4 forger:3 during:1 consists:1 partial:4 expressions:2 zinn:1 contributions:3 forget:1 whose:3 wess:1 chain:7 tt:1 technique:3 nonlocal:4 simplify:1 charge:11 ℜe:1 those:4 th:2 under:2 fermionic:2 ingredient:2 applied:1 conjecture:1 confirmation:1 presently:1 advantage:1 very:2 reader:1 dokl:2 choice:2 graphic:24 every:4 matrices:3 condition:1 quantized:1 presented:1 list:1 solution:1 prototypes:1 math:8 basu:1 inversions:1 exhibits:1 commented:1 application:2 work:6 direct:2 mussardo:1 sign:1 b137:1 second:5 b135:1 picked:1 follow:1 further:2 theory:15 spectral:1 nonlinear:2 sub:1 brackets:6 section:1 interactions:2 expressed:2 maillet:3 current:24 version:1 above:4 new:7 tips:1 method:9 viii:1 satisfy:2 altogether:1 ibid:1 respectively:1 gathered:1 neveu:5 here:2 b269:1 inversion:1 represented:2 along:1 equations:1 calculate:2 obtained:1 instituto:1 exemplified:2 involved:1 inspired:1 simply:1 pick:1 makes:1 named:1 followed:1 extra:1 vii:1 integrations:4 replace:2 brought:1 durham:1 anomalies:1 barcelos:1 apply:2 drinfel:2 establish:1 abdalla:12 bended:1 use:3 takes:1 would:4 commun:5 recalling:2 contains:2 finally:3 next:3 ψj:1 comparing:1 nucl:6 ψi:9 therefore:7 usp:2 taken:3 conservation:1 iteratively:1 until:1 diagrams:6 more:1 sort:1 hermitean:1 clearly:1 suggestions:1 curvature:4 4j1:1 tested:1 stanishkov:1 opposing:1 investigation:1 particular:1 known:2 cases:1 hold:1 iii:4 must:7 account:2 valued:1 practicing:1 origins:1 quartic:1 erratum:1 recall:2 equation:2 fµν:2 theories:6 remain:1 itself:1 modify:1 three:1 following:11 example:2 mackay:2 indicated:1 do:1 calculation:3 relativistic:1 organized:1 smirnov:1 generically:1 states:1 impeded:1 realization:1 yang:2 end:2 straightforward:2 rather:2 verify:2 write:1 far:1 sia:1 currents:2 justin:1 answer:1 parameter:2 simplicity:1 product:4 description:1 algebra:48 may:4 φ2i:2 after:6 containing:2 diagram:8 produce:1 zachos:2 b402:1 summarize:1 efficiently:1 transposed:3 stress:1 third:1 sp:1 explicit:1 perform:1 kacmoody:1 so:2 sect:5 fundamental:1 representation:2 rothe:1 order:1 typical:1 erasing:1 produces:1 hierarchy:2 developed:1 over:1 dy:1 satisfied:1 symbols:2 course:1 paper:4 through:2 statistical:1 signs:1 existence:1 satisfies:2 its:5 before:2 aper:1 derive:3 group:2 thank:2 recover:1 chosen:2 interesting:2 inclusion:1 boson:2 actually:4 absence:1 production:1 ls:1 jacobi:1 derivative:2 hidden:2 main:2 might:1 deformation:1 supersymmetry:4 eventually:1 non:51 within:2 combination:1 propose:2 acklund:1 investigated:1 obeyed:1 mention:1 they:4 half:4 mallick:1 nov:1 now:4 discuss:2 haldane:1 easily:1 term:8 dirac:3 always:1 hamiltonian:2 arrows:1 2d:1 arrow:1 each:5 found:2 constraints:6 baxter:2 differential:1 directly:1 related:2 conventions:1 constitute:1 elementary:4 literature:2 expect:3 quantum:11 our:2 eq:3 event:1 out:2 conjectures:1 shown:2 precisely:1 matrix:9 space:1 tianjin:1 rep:1 since:1 rev:4 transforming:1 ajk:1 ajl:1 conjectured:1 print:1 b281:1 sch:1 ref:13 announced:1 exactly:1 plet:1 linear:21 associate:3 ısica:1 free:3 standard:5 moody:1 resumed:1 definition:2 pairs:1 interaction:1 derivation:2 could:3 iterative:3 motion:1 massive:2 generalizations:1 first:7 origin:1 already:2 symmetry:7 qkl:4 symbolic:1 number:5 exact:1 yangians:2 simplified:1 relations:4 another:2 clarity:1 computed:3 given:4 checked:2 introduction:4 curtright:2 eqs:2 sjα:2 construct:8 their:5 confirming:1 intermediate:1 fermions:2 calculations:2 convention:1 white:3 ukc:1 final:2 listed:1 dolan:1 shell:2 relationship:1 continuous:1 b331:1 part:6 too:1 authors:1 translation:2 than:1 kind:3 last:2 isolation:3 imply:1 preparation:1 supposed:1 aesthetic:1 naturally:1 minus:2 perturbative:1 bootstrap:2 symmetries:1 pasquier:1 sal:3 ann:1 zamolodchikov:2 uscher:2 seen:1 seem:1 constrained:1 tells:1 symmetrized:3 hopelessly:1 built:1 rotations:1 depending:1 check:1 convenient:1 able:4 oriented:1 instance:5 potential:3 take:4 analogy:1 finding:1 canonical:1 kac:1 even:1 play:1 towards:1 shall:3 twodimensional:1 sets:1 cnpq:1 systems:1 algebraic:10 involving:2 connected:1 nothing:1 acknowledgements:1 class:1 ka:3 bjk:1 considered:1 kl:46 proceedings:1 chiral:1 exp:1 justify:1 sigma:16 bulletin:1 laws:1 precise:1 neto:1 show:1 jµ:23 supported:2 hopf:1 purely:2 relation:1 solutions:1 find:4 lessons:1 knowledge:1 should:4 bernard:3 only:1 explicitly:1 black:3 indeed:1 integrable:10 local:34 pointed:1 hope:1 abelian:2 his:1 triangle:1 notation:1 means:8 dependent:1 de:5 da:1 tbj:1 dx:20 rˆoles:1 applying:2 schoutens:1 singapore:1 b308:1 fields:2 transposition:2 arxiv:1 2b1:2 2b0:1 contain:1 revealing:1 set:4 constructing:1 achieved:1 j0:64 j1:35 j2:1 namely:1 result:2 progress:1 maharana:1 brazil:1 satisfying:2 review:2 written:2 µn:1 various:1 between:9 invariant:3 geometric:1 brunelli:3 approach:1 notice:4 terms:10 extend:1 adding:2 component:1 were:7 however:4 js:1 efficiency:1 vanishing:1 jo:1 solv:1 come:1 outcome:1 improved:19 many:1 taking:1 according:4 contract:1 assure:1 contribution:1 finds:2 comes:1 sake:1 among:1 affine:1 abbreviate:1 corresponds:3 cd:1 dimensional:7 anti:1 confirmed:3 away:1 bν:3 writing:1 most:1 described:2 transformations:2 ezin:2 stages:1 computing:1 due:1 been:6 int:4 much:2 b354:1 basic:1 expected:1 contraction:10 define:2 adopted:1 supersymmetric:21 scalars:1 itzykson:1 concerning:1 remark:2 zero:1 understand:1 7a:1 mail:2 prescription:1 present:2 case:4 resulting:2 structures:2 remaining:2 will:7 ail:1 while:2 replaced:8 monodromy:3 aik:1 property:3 conformal:2 procedure:8 remembering:1 ix:1 vi:1 thus:1 them:2 surface:1 iv:1 ii:4 skipping:1 reads:3 ij:45 ia:3 ic:1 ib:1 fermion:1 disappear:1 different:3 null:3 develop:2 2j1:4 generic:1 demands:1 same:5 any:1 paulo:2 read:2 parts:1 split:1 fabc:1 φi:15 φj:5 several:1 higher:1 zumino:1 used:3 see:1 cubic:9 hand:1 uses:2 internal:1 infinite:6 frequently:1 identity:4 recognized:1 off:3 proceed:1 charges:58 underlies:1 analysis:1 lumps:1 components:6 thoroughly:1 model:29 87b:1 left:5 bending:5 2js:1 graded:2 just:1 less:2 b240:1 das:2 obtain:2 bµ:17 diagrammatic:5 world:1 localize:1 alternative:2 scattering:3 λn:2 λm:1 previous:2 note:1 preprint:1 generator:4 conclusions:2 regarded:1 criticality:1 exclusively:1 improvement:1 iψ:2 other:7 lett:10 easy:1 pointing:1 mod:4 transformation:3 scientific:1 build:1 noether:1 bil:1 bik:1 semicircles:1 2j0:9 rules:20 sums:1 possible:4 early:1 possibly:1 provide:1 using:7 poses:1 helpful:1 necessary:1 like:4 particle:1 follows:4 intertwiner:5 steps:1 integrals:1 fully:1 become:1 vdl:1 replacement:2 because:2 methods:7 classical:8 sequence:2 some:10 searching:1 understood:1 added:1 b0:30 examples:3 moreover:2 proper:2 30c:1 gross:5 dimensions:2 lead:1 confirm:1 dropping:1 though:1 fapesp:1 comments:2 critical:2 provides:1 chains:11 participation:1 majorana:2 branco:1 obey:3 power:1 equivalent:1 bo:1 jbµ:1 step:10 b210:1 br:4 substitution:1 super:1 properties:4 simpler:1 about:2 simplest:1 actual:1 yangian:11 extension:4 constraint:4 lgn:1 discussed:1 o:19 addition:1 range:1 obeys:2 buchholtz:1 intertwiners:1 introduced:4 jν:6 generalized:1 rendered:2 presence:2 previously:1 into:3 bjl:1 integral:1 jα:3 chooses:1 lagrangean:3 remarks:3 gomes:2 zuber:1 references:1 inverting:1 sov:2 operator:3 algebras:7 factorized:3 bosonic:15 hep:2 deal:1 few:1 wznw:2 there:2 transform:1 long:3 noticed:1 start:2 board:1 quadratic:2 way:3 decisive:1 was:5 opposed:1 complete:3 form:2 pohlmeyer:2 but:7 symbolized:1 construction:2 contractions:8 encoded:1 line:2 ha:2 partially:1 made:1 compute:4 leclair:1 ut:1 up:10 us:8 theoretical:1 below:7 b7:1 limit:3 problem:1 isolating:1 similar:3 called:2 b1:19 ab:1 associated:4 qij:13 defined:5 certain:1 abstract:1 linearity:1 ao:2 general:5 conserved:12 corresponding:6 universidade:1 constructed:1 tedious:2 again:1 imsc:1 no:1 tip:3 vanishes:2 schwinger:3 field:13 interested:1 program:1 you:1 massless:1 briefly:1 repeat:1 intend:2 a10:1 calculating:1 models:19 symbol:1 vega:3 important:1 a7:1 82b:1 sotkov:1 structure:3 semicircle:2 d28:1 implies:2 longer:1 algorithm:6 d21:1 physics:2 proposed:3 rule:1 appendix:3 time:1 starting:1
|
solv-int9511008.txt |@word represent:3 concept:1 partial:4 consider:5 remarkable:1 switched:1 c16:1 results:4 2c1:1 four:2 eds:1 ǫa1:1 proposition:6 consists:1 2c3:1 gi:2 devoted:1 whose:3 inverse:3 depend:1 tx:1 paris:1 tt:3 technique:2 γt:3 finally:8 investigation:2 those:2 under:8 analogous:1 te:1 necessary:2 case:14 already:1 straightforward:1 vt:2 rise:1 translations:1 dell:2 wave:8 sons:1 putting:2 should:3 summarized:1 exact:6 condition:7 leads:1 hamiltonian:1 turns:5 t2:3 solution:15 fewer:1 integrated:1 deals:1 solved:4 convenience:1 vector:2 universal:1 small:4 satisfying:1 ij0:1 zn:1 ξik:1 miller:1 direct:1 cosh:6 3a3:1 scrutinize:2 zz:2 rigorous:1 further:2 theory:6 subscripts:1 index:1 what:1 nonlinear:3 plays:1 stands:1 frameworks:2 section:1 brief:1 expressed:7 estabrook:2 pui:1 version:6 lptens:1 above:1 y1t:3 method:9 satisfy:1 efficacious:1 respectively:5 component:2 here:4 behaviour:1 reported:1 them:1 ansatz:1 sinh:5 situation:1 consideration:3 equations:29 appears:1 change:1 obtained:4 search:1 trans:1 study:5 studied:2 allows:4 sbornik:2 suggests:1 dover:1 procedure:2 share:1 studies:2 involves:1 via:6 useful:2 a21:2 explained:2 z1:1 a22:1 conditions:1 apply:1 total:1 derivatives:1 use:4 handled:1 would:1 prove:2 positive:2 contains:1 properties:3 a51:2 few:2 a53:2 a52:4 a55:2 therefore:6 a57:1 ip:1 taken:1 a58:2 stage:1 type:13 entails:2 subsection:1 introducing:2 formally:1 said:1 afford:1 becomes:3 operators:11 stable:1 c15:2 appendix:11 basically:1 eλ:1 particular:4 known:1 cases:4 hold:1 iii:3 potential:2 eβ:2 keeping:2 rotational:1 defines:1 recall:3 equation:38 constraint:1 modified:8 theories:1 mu:1 infinitesimal:3 nine:2 concepts:3 following:8 making:1 arrive:2 example:5 proof:2 f0:15 f1:5 challenging:1 give:6 calculation:1 arise:2 organized:1 purposes:1 indicates:2 minimum:1 cartan:1 ǫf1:4 sense:5 tan:1 times:1 a29:2 e2u:2 needs:1 ρ2t:1 recursive:1 deserves:2 provide:3 s2:1 di:4 feature:2 write:2 how:2 nontrivial:4 criterion:1 soliani:1 answer:1 ordinary:4 parameter:10 map:1 yxx:1 express:1 mat:1 algebra:58 may:3 suppose:5 after:2 derived:4 hence:5 yxi:1 dj0:1 coming:5 account:2 verified:1 derives:1 compatibility:4 constants:5 collecting:1 2x2:1 branches:1 third:1 whenever:1 consequently:2 explicit:4 so:10 fundamental:1 sl:1 representation:6 first:4 order:5 furnish:2 kbk:1 holds:2 help:3 produces:1 hierarchy:1 insight:1 displayed:1 interpreted:2 symbols:1 course:1 paper:2 through:2 y1:13 existence:3 satisfies:3 y2:14 its:2 before:1 respect:2 group:25 ln:10 interesting:3 solving:2 c18:2 boson:3 li:5 forms:1 resort:1 gtt:1 systems:4 jacobi:7 derivative:2 main:3 correspondence:2 yk:2 combination:3 obtaining:2 finitedimensional:2 introduce:1 yx:3 they:1 c14:1 nov:1 now:10 yt:3 2t:3 easily:3 february:1 2w:1 hereafter:1 2s:1 invariants:1 meu:2 2z:2 establishing:1 ussr:1 2a:2 each:1 x10:4 inherent:2 universit:2 eǫt:3 eu0:1 characterized:1 constraints:2 differential:15 simplicity:1 doing:4 series:3 related:6 toda:6 finish:1 expect:1 combining:2 eu:25 our:4 ew:1 eq:77 special:8 out:11 emerges:1 shown:4 matrix:4 space:1 furthermore:8 since:7 rx:1 denotes:3 u0x:1 conclusions:1 geom:1 istituto:1 heavenly:1 get:7 ref:4 occurs:1 math:4 wiley:1 linear:8 inessential:1 abramowitz:1 ascertain:1 fisica:2 free:1 standard:1 admits:3 completely:3 york:2 put:1 puu:1 hand:5 beginning:2 e2:4 applications:1 could:1 omit:1 keep:1 plane:2 consequence:1 dipartimento:2 heuristically:1 xj:3 a56:1 xi:2 symmetry:26 variables:6 xf:1 number:1 rank:1 linking:1 xx:4 2a2:4 adopted:1 another:4 fi:1 methodological:1 precisely:2 lebrun:1 equating:1 given:7 checked:1 their:2 introduction:2 eqs:30 system:8 relations:11 indicate:1 perturbations:2 brevity:2 statement:1 realization:11 scheme:1 gives:3 a33:1 ξj2:2 ξj1:2 a30:3 a37:1 calculations:1 mostly:1 a34:2 a39:3 continuous:6 whitham:1 x8:1 part:1 authors:1 x2:24 x3:18 2ie:4 x1:15 x6:1 than:1 coefficients:5 x5:1 wide:1 kind:1 determines:1 df1:1 second:5 annihilation:3 a47:3 a44:2 determined:4 a42:2 a43:1 a40:1 a41:2 tackled:1 enables:1 distinguished:1 a48:2 perturbative:4 2q:1 symmetries:8 a32:1 mind:2 reader:1 notwithstanding:1 wyy:1 need:1 seek:1 any:8 a36:2 lie:45 fxx:1 zero:2 describe:1 essentially:1 self:4 able:1 gravity:1 k3:2 instance:3 k1:5 concerns:1 generalized:2 analogy:1 finding:1 subject:1 kac:1 a38:2 shall:7 kak:3 mimics:1 algebraic:4 involving:1 connected:2 significant:1 nothing:1 a31:2 class:4 αt:1 prolongation:27 considered:3 clear:2 coincides:4 physics:1 8a2:1 fact:5 quantity:2 emerging:1 ibragimov:2 show:2 anyway:1 friction:2 obtains:1 spaces:1 relation:4 solutions:18 wahlquist:1 d2:1 find:8 b6:2 based:3 commutators:2 noteworthy:2 topological:2 x7:1 values:1 analytic:1 only:3 generators:12 x4:13 factor:1 integrable:2 local:1 briefly:1 abelian:2 dj:2 means:5 yti:1 straightforwardly:1 da:4 define:3 a35:1 words:1 new:2 dt:1 procedures:1 mui:1 arxiv:1 expansions:3 2b2:2 yield:2 investigate:1 contain:2 fixed:1 view:2 endowed:1 reveals:1 requirement:1 set:4 harrison:2 achieved:3 δjk:1 ξαi:1 j0:3 j1:4 df0:1 relative:1 see:25 sec:4 result:4 y0:11 wtt:1 springer:1 y3:5 techniques:2 muu:1 a46:2 exploited:4 lut:3 commutation:11 ytt:1 uα:5 below:3 written:3 a45:2 closed:8 between:7 conceptual:1 invariant:7 approach:15 x20:4 side:2 basis:1 notice:4 terms:9 do:1 constituted:1 attention:1 focus:1 however:3 jr:1 killing:1 reproduces:1 hypothesis:1 jointly:2 solv:1 utx:1 uσ:1 both:5 c20:3 c21:3 2n:1 elaborating:2 many:1 taking:3 hint:1 c5:1 equal:1 display:1 fulfilled:1 fiz:1 connection:4 context:4 casimir:1 tangent:1 contribution:1 a49:2 expression:1 leu:3 cj:2 presumably:1 groups:4 characterization:1 simple:4 seems:1 corresponds:4 dimensional:24 analyzed:1 cx:1 framework:2 polynomial:1 associated:9 diff:1 resorting:2 transformations:11 pu:2 equivalent:1 three:2 been:5 strategy:2 int:1 reduction:1 cauchy:1 ensured:1 hawking:3 basic:1 algebras:5 abstract:2 annihilating:1 choose:1 arises:2 corresponding:3 2ix:2 commutes:1 lecce:3 concerning:2 theorem:7 remark:4 βtt:1 c9:2 observe:1 determination:1 systematic:1 olver:1 c3:2 c2:5 c1:12 c0:9 c7:1 c6:1 present:4 c4:4 applied:2 k2:4 c10:1 look:3 exponential:4 affirm:1 ǫi:2 t0:4 value:1 ǫl:2 aim:2 euclidean:5 while:5 ǫp:8 replaced:2 ǫv:1 ξ0k:2 ǫt:3 ǫz:1 ǫy:1 property:4 characterizing:1 ein:4 a20:1 ix:1 seven:2 a23:2 a24:3 a25:2 a26:1 a27:2 a28:1 vi:2 thus:5 non:2 uxx:4 iv:2 ii:2 characterize:1 reads:1 examined:1 im:1 dual:1 ready:1 k0:2 qx:1 different:1 italy:3 admitted:2 pseudopotential:9 admit:1 same:5 lbl:2 read:1 arguments:1 finite:16 subalgebra:1 start:1 independent:3 used:4 possible:4 running:1 infinite:4 build:1 invariance:2 identity:8 subgroups:1 off:1 baikov:2 scenario:1 nucleare:1 no:2 well:1 analysis:4 academic:1 solve:3 machinery:1 components:2 english:1 otherwise:1 arising:2 latter:3 left:1 construct:2 just:1 among:1 wxx:1 stegun:1 wybourne:1 obtain:10 aspect:2 integer:1 yet:1 y1l:2 previous:3 heuristic:1 preprint:1 generator:4 field:6 point:9 character:1 c19:1 setting:3 transformed:1 lett:1 easy:1 propositions:1 c13:1 c12:1 c11:1 moody:1 c17:1 transformation:1 euler:1 take:3 aspects:1 definitive:1 represents:1 rules:1 devised:1 term:2 five:1 appendices:1 using:7 vλ:1 moreover:1 formal:1 generated:1 pertinent:2 like:3 follows:1 substitution:2 ignore:1 yields:7 loop:1 sezione:1 arbitrary:7 become:1 qxx:1 works:3 reduced:10 therein:1 a15:1 interest:1 namely:2 tells:1 creation:3 some:8 a61:2 a62:2 ξo3:1 b4:4 b5:2 deduce:2 a16:1 b0:60 examples:3 b2:35 b3:23 extended:1 dc0:2 happens:2 provided:1 vol:1 dimensions:3 lead:1 investigations:1 integration:5 comments:2 manipulations:1 uyy:1 provides:7 bessel:5 saveliev:1 inserting:3 3b3:1 obey:2 power:1 bn:2 bj:10 bk:31 step:11 although:1 found:3 gazizov:2 ǫb1:2 gibbons:3 takes:1 x30:4 extension:1 commutator:3 bgi:2 x40:5 discussed:1 meaning:1 o:7 essential:1 practical:1 mutually:1 important:3 yp:1 ic0:1 y2t:3 dz:1 mathematical:1 ξ1k:1 into:8 within:1 integral:5 isomorphic:1 down:1 a9:1 exploiting:2 references:2 determine:2 einstein:1 operator:5 infer:1 next:1 physical:1 deal:3 a50:2 assumed:1 strictly:1 initial:1 approximate:32 u2:1 surprising:1 a64:1 handbook:1 physicists:1 way:2 infinitedimensional:1 u0t:2 sections:1 a54:2 function:12 complete:3 form:14 a60:1 regard:1 but:2 a59:3 construction:1 link:2 matematica:1 a63:1 truncation:1 ux:9 instructive:1 whether:2 ut:11 smooth:1 up:2 us:28 theoretical:1 krichever:1 liouville:6 utt:5 ix3:1 problem:5 ix1:1 similar:5 called:3 b1:63 fulfills:1 constant:8 choosing:2 defined:9 certain:4 ak:29 aj:15 e1:2 deep:1 denote:1 dξ:4 quantum:1 single:1 right:1 rule:1 nazionale:1 conversely:1 commuting:3 constructed:2 again:1 functions:6 compared:1 integrability:3 rxx:1 cos:2 when:2 application:2 other:8 role:2 details:1 quantities:2 theor:1 sufficient:1 conclude:2 a14:1 a17:1 elements:7 a11:2 a10:4 a13:1 a12:2 models:1 resembles:1 a19:3 a18:2 a1:69 a0:58 a3:27 a2:44 a5:1 a4:3 a7:2 a6:4 variable:8 a8:4 structure:1 building:1 implies:3 auxiliary:3 assume:2 established:1 dτ:2 together:2 equivalently:1 c8:1 time:1 ξc1:2 4e:1 starting:4 original:1 classical:1 once:1
|
solv-int9511009.txt |@word limited:1 similarity:2 desirable:2 ginzburg:4 consists:2 σim:1 whose:5 aui:1 presents:1 γj:25 δhm:2 δhj:7 γm:1 under:1 geom:2 γg:21 ℜk:7 divergent:1 conjecture:1 rise:2 q1µ:1 every:1 summarized:2 bringing:1 dubrovin:12 specify:3 exponential:2 solution:15 δh0:1 convenience:2 vector:7 differentiates:1 indices:1 straight:2 consistent:4 direct:2 surrounding:2 second:18 rigorous:2 even:6 sheeted:6 ˆc:1 above:20 new:6 contributes:3 hamiltonjacobi:1 consisting:1 coefficient:1 simultaneously:1 κj:2 mem:1 here:112 represented:3 path:10 quite:1 ωa0:2 obtained:2 property:2 suitably:1 study:6 changed:1 denominator:1 glg:1 analysts:1 nonspecial:2 suitable:10 changes:5 der:1 schur:5 yamada:1 projection:1 classification:1 discontinuous:5 explained:1 visibly:1 replace:1 visible:3 modulated:2 hindsight:1 total:1 univ:3 derivatives:10 would:14 δhn:2 motivate:1 bundles:1 chooses:2 logτ:2 noting:1 call:1 therefore:5 survive:2 type:12 until:1 decomposable:1 γn:2 separated:1 qde:5 nσn:1 tions:1 ti:24 infusion:1 curvature:3 berlin:2 correspondingly:2 qds:1 hold:5 must:7 mg:4 mc:1 pursue:2 ml:3 work:10 mi:1 theories:3 flaschka:1 im:1 example:37 mz:2 indicated:33 give:6 generically:1 involve:4 indicates:3 want:5 verlinde:6 times:13 cursory:1 yang:2 end:2 thing:1 provide:2 takebe:1 how:6 nontrivial:2 hanany:1 w20:2 symposium:1 ordinary:1 teichm:1 sato:1 description:1 replacing:5 thermodynamic:1 after:7 linearizes:1 lax:11 summarize:2 law:1 meaningful:1 constants:5 attempt:2 third:6 hasty:1 βi:7 hypotheses:2 recursion:1 order:29 xj:8 over:11 vary:5 satisfied:2 satisfies:6 integrands:1 before:12 somewhere:1 exhibits:2 writing:4 better:4 complex:6 differently:2 osgood:1 fij:1 schmidt:1 eventually:2 gunning:1 affected:1 they:5 singularity:3 bank:1 represents:5 invariants:9 althought:1 hepth:1 reasonable:3 each:3 side:5 associative:2 mean:1 qji:1 series:6 applicable:1 arrives:2 extract:2 dǫ:2 precisely:2 jimbo:1 egoroff:2 urbana:1 crucial:1 dsn:6 unrelated:1 multiply:2 adapt:1 ri:2 interchanging:1 rk:2 dispersive:3 customarily:1 linear:7 associate:1 given:28 free:2 standard:17 ntn:2 uiuc:1 r0:1 chiral:2 r2:4 starts:1 ds2:4 creates:1 δij:10 δik:4 cµν:1 xuj:1 organize:1 features:2 qkl:3 nhn:2 primary:15 ℓi:2 another:6 quasihomogeneous:2 illustrate:1 rewritten:2 similarly:8 manakov:1 needed:4 zeros:20 observations:1 φri:5 kamchatnov:1 φsi:4 aoyama:1 serve:2 minahan:1 formulate:1 whitham:27 somewhat:9 abandoning:1 begins:1 roles:1 princeton:1 approximations:1 integrability:1 normalizing:1 preparation:1 matter:2 classes:2 1n:2 powers:6 minus:1 extracting:1 sees:4 modern:2 spectrum:8 manner:3 seen:4 seem:2 obviously:2 contents:1 relatively:1 convenient:1 latter:6 isolated:1 thorough:1 oriented:1 circles:1 residue:3 object:1 birkh:1 metrics:1 involving:15 dθj:1 qxxx:1 phase:5 don:2 observation:1 neighborhoods:3 matone:1 flow:6 bracket:3 saying:1 dickey:2 reductions:1 λq:1 xω1:5 iǫ:2 gauge:4 solutions:23 civita:1 tempted:1 eliminated:1 d1:5 situations:20 explain:1 appended:1 topological:5 intrinsically:1 hamiltonians:4 dn:1 do:9 dj:3 establishes:1 klein:1 df:8 dg:3 inoperative:1 dz:46 dx:40 dy:4 dw:1 dt:7 du:1 dr:1 ds:46 dp:87 dq:8 bar:1 covering:7 fields:4 bad:2 θj0:2 nα:5 4πi:4 clarified:2 generally:12 δjk:2 tb:1 num:4 w2:9 w1:13 w0:7 discussions:1 dµ:12 prototypical:2 techniques:2 said:1 away:1 symmetric:5 µn:4 µi:7 µj:12 drawn:3 sorts:1 ucker:1 approach:8 accord:1 terms:34 nature:4 wn:2 were:2 wk:4 wj:3 wi:2 modulational:2 unnormalized:1 wx:1 suggested:3 essentially:2 fnm:6 genus:18 adapted:2 fnj:1 gorsky:1 nˆ:1 prilozh:6 applicability:1 polynomial:12 symmetries:4 commutative:2 puts:1 basis:12 simplification:2 been:4 much:1 interest:5 basic:4 θj:11 θk:3 ergodic:2 θi:15 supersymmetric:4 bnm:2 quantities:6 concerning:1 θg:3 rescalings:1 coherent:1 spelled:1 spin:4 manifolds:8 originate:1 ǫu1:3 aim:1 near:20 suppose:2 applies:3 endpoints:1 leaves:1 procedure:5 ix:1 shiota:1 yangmills:1 dφα:1 ii:1 characterize:1 ik:27 ij:1 desideratum:1 il:1 exterior:1 cong:1 cαβγ:6 uxxx:7 suggest:3 make:9 superpotential:3 hierarchies:2 independent:10 fuss:1 i1:1 i0:2 hand:5 auser:1 potentials:7 normalization:14 cycle:5 weakly:2 epx:1 preceeding:2 dispersionless:39 left:5 just:1 mills:1 3p2:1 lǫ:3 facts:3 scattering:9 previous:4 adding:1 infinitely:1 zakharov:1 regarded:2 qx2:1 leibnitz:1 belongs:1 benney:2 easy:2 iσ:1 plasma:1 iθ:1 bands:4 possible:4 plenum:4 boxes:1 loge:2 background:9 unique:2 mironov:1 arbitrary:6 immersions:1 right:5 deal:2 φmn:2 oly:1 confusing:2 dense:1 icm:1 comments:2 exposition:2 disappears:1 meanings:1 kruskal:1 additively:1 illustration:3 shifting:2 permitted:2 proceed:1 dˆ:6 o:43 distinct:2 plus:4 konopelchenko:2 rigor:1 slightly:4 automatically:1 considerations:1 soc:3 statements:1 ppi:1 pλ:1 obtaining:1 ut:6 down:3 pair:2 ussr:1 wα:1 sov:1 abel:4 22s:2 often:7 vafa:2 segment:1 initial:1 accordingly:1 conservation:6 way:7 was:5 launching:1 m0:5 form:77 removes:1 mysterious:2 pp0:5 removed:1 true:3 subtracted:1 k1s:2 absent:1 builds:1 adler:1 supp:2 compactification:1 wψ:2 krichever:21 levermore:1 k1i:2 examples:9 proved:3 moore:1 up:11 abstract:1 a1y:1 convergent:1 dξ:5 conserved:5 proves:1 exist:4 dλ:62 dζ:35 believable:1 dβ:1 check:2 physical:1 ni:11 nj:4 nk:4 nm:8 eventual:2 no:10 whereas:7 nc:1 nd:1 vanishes:5 ng:4 nz:4 interested:1 role:7 holding:3 solitons:1 φ2m:2 ns:1 nt:1 nw:4 picture:5 models:2 felt:1 convincing:1 logλ:1 ξj:3 logθ:9 miranda:1 variable:7 stoke:1 gets:3 jones:1 dω:15 assume:9 dτ:19 together:1 ramification:3 χi:3 time:12 n0:9 n1:10 quantity:2 logarithms:2 chain:1 global:8 invent:2 leads:18 remarkably:1 certainly:1 inverse:7 depend:2 clarification:3 zone:11 technique:1 passage:2 quasi:12 infinitesimally:1 analogous:3 circumstances:1 yvi:1 string:1 orthogonal:1 ηij:1 ηii:2 choice:5 entries:1 exact:1 riemann:77 solves:2 presented:1 irreducible:1 travels:1 solved:1 fourier:1 ωts:1 upper:1 mn:7 says:6 jacobians:3 farkas:1 dealing:6 sign:2 dsα:1 substitute:1 spectral:7 adds:1 appear:5 goes:1 jumps:2 satisfy:6 αij:2 understanding:1 tangent:2 alone:2 along:7 xα:1 appears:2 change:10 shift:2 rethink:1 vectors:3 u3k:3 prym:1 poisson:2 domains:2 studies:1 emerge:4 useful:3 griffiths:1 extra:1 martellini:2 inducing:1 bs:3 ls:1 marked:4 working:1 prove:1 eυ:2 positive:6 mumford:2 properties:13 live:1 explicitly:6 eguchi:1 associated:8 schulman:1 diagrams:1 introducing:1 pα:23 everywhere:1 eζ:2 eα:1 eγ:1 eβ:1 logarithm:1 valued:3 deformed:2 nemeschansky:1 reappear:1 values:3 tortuous:1 following:19 degenerate:2 φvi:4 expanding:3 sense:11 carroll:11 allowed:2 nonlin:1 evidently:6 normalize:1 s3:3 s2:10 discussion:10 uǫt:1 write:30 fourth:2 parameter:4 ruhr:1 map:5 product:3 rept:1 r2k:2 mat:2 may:7 ω2s:1 residues:7 applications:1 levi:1 produce:1 designed:1 ω2n:4 date:1 data:3 compatibility:9 sz:1 sx:1 natural:16 explicit:6 yielding:2 su:2 sj:7 si:2 aβ:1 so:71 sn:26 sm:4 sc:1 representation:3 restricted:1 subsections:1 mbm:1 indeed:6 pointed:1 mainly:3 course:3 counterclockwise:1 cuts:7 still:1 derive:1 group:3 acknowledge:1 interesting:6 sα:10 tori:3 τc:1 coordinates:32 forms:6 listing:1 main:3 matches:1 chelsea:2 evolution:2 introduce:1 scaling:1 φˆn:1 hamilton:2 base:1 identically:4 nov:1 now:94 discuss:6 developments:7 qt:2 term:15 kra:1 revert:1 wdvv:6 roch:1 αexp:1 spinor:1 domain:8 square:8 ei:4 ek:6 ej:4 ee:1 fixes:2 eg:1 hypergeometric:1 ea:4 eb:3 gaps:6 ey:8 ex:14 ez:3 illinois:1 ep:1 es:6 alvarez:3 shown:6 space:31 axiomatically:1 kummer:1 ζg:2 lagrangian:1 cancels:2 u2k:3 looking:2 modulation:4 investigation:2 rational:1 algebro:1 formula:15 correct:9 shows:5 earlier:3 theory:54 state:2 derived:3 governing:1 treatments:1 complicated:2 ζn:2 ord:5 λcn:2 e1:3 e0:1 e2:1 cycles:11 derivation:1 question:1 dλn:2 transition:1 motion:3 turn:2 ζs:1 place:2 rewrites:1 think:14 first:40 origin:1 xk:1 xi:1 xn:1 eǫ:1 pn1:1 omitted:1 variables:40 coming:1 xy:1 simplified:1 directly:5 ring:2 open:5 horizontal:2 xu:15 little:2 φ2x:1 sheet:3 nqn:3 2ωp:1 fmn:13 indicate:4 returns:1 types:2 structures:4 hyperelliptic:19 speaking:1 gives:12 enneper:1 hα:12 obtains:22 continuous:1 eliminates:1 pnk:1 x2:21 x3:10 x0:1 than:6 coefficients:7 connections:12 πs:7 require:3 ωxx:1 gii:2 cavalier:2 ia1:1 ia2:1 pre:1 topics:3 argument:6 say:13 any:25 ideas:7 note:77 potential:10 take:18 coincide:1 primaries:1 formulas:24 begin:6 multiple:3 normal:2 uyy:4 δkj:1 correlation:3 liouville:1 surv:4 algebraic:10 sheets:1 remarks:9 analytically:1 inserted:3 αt:2 γi:2 especially:4 considered:3 average:5 later:10 duplication:1 typically:1 laws:4 precise:5 show:4 imagines:1 notations:3 spaces:13 fifth:1 homology:10 slow:19 aφ:1 aψ:8 dick:1 enough:1 analytic:2 only:29 going:2 quasiperiodic:1 mulase:1 normalizations:3 viewpoint:1 get:9 jtj:1 ki:2 expectation:1 expects:6 aα:1 cannot:2 negative:1 invariant:3 aλ:6 clearest:1 differentiating:4 prime:9 reveal:1 regarding:2 yield:1 summary:1 cij:1 implying:1 kernel:27 quasiclassical:1 stipulation:1 relative:7 namely:6 ωxy:1 declares:1 unaltered:1 rmn:1 concern:2 surfaces:16 αs:2 satisfying:8 eigenfunctions:8 dk1:1 ways:1 subsequent:1 review:2 definite:2 outside:4 αb:1 between:13 αi:8 geometric:1 αm:2 across:1 αn:1 notice:1 vertical:1 matveev:1 jq:1 jm:1 densely:1 comm:8 multiplier:4 jets:2 jetp:1 σj:5 σi:9 σn:5 dkp:26 x2j:1 many:10 σg:53 according:2 σe:2 dkn:1 expression:4 comes:1 among:2 characterization:1 period:10 pole:22 assertions:1 cancel:2 moreover:2 considers:4 0a1:1 computing:1 dzα:2 workshop:2 foliated:1 wants:3 direction:3 formed:1 qsm:6 nres:1 6q:4 observe:3 external:1 careful:1 spirit:7 case:10 u1k:4 processes:4 developing:2 σl:1 cancelled:1 situation:27 conformal:3 tentatively:2 characteristics:2 metric:9 different:7 develop:2 same:7 pad:1 arguments:1 constructed:2 resλ:2 extended:2 resα:6 siegel:1 running:2 delicate:1 changing:1 totally:1 kαi:11 ckij:1 sssr:3 disregards:1 roughly:1 without:4 ujk:2 coordinate:9 model:5 otherwise:1 dimension:2 manifold:6 being:1 when:16 aǫ:2 valuable:1 resk:2 relevant:2 correspondences:1 φti:3 flavor:1 speed:1 heuristic:2 lezioni:1 seems:10 except:6 lets:1 setting:3 lett:7 extensive:1 momentum:4 tietze:1 real:9 aspects:2 around:10 2u:1 using:17 mod:6 vertically:1 velocities:1 expository:1 either:4 integrals:10 characterizes:2 multiplicative:1 inter:5 specifies:2 βnj:1 cabc:1 retrace:1 deduce:1 specified:2 thinks:6 nonzero:1 provided:3 confirm:1 recorded:1 extensively:1 critical:5 provides:2 venakides:1 refer:10 welcome:1 scientific:6 power:1 uniformly:1 equivalent:9 eiπ:1 ragnisco:1 inherent:1 qnm:8 refers:2 comparison:3 ok:2 origins:1 theorems:1 discussed:7 generated:1 r1:1 evident:1 act:1 referred:1 perturbed:1 locally:1 image:1 bjk:2 bjj:1 ηi:2 ηt:1 references:3 determine:8 operator:7 gomez:1 ercolani:1 hep:10 log:70 prepare:1 dkα:1 strictly:1 equates:1 dispersion:1 start:2 lot:2 assumes:4 complete:1 szeg:2 qjm:1 regard:1 divisors:6 ωy:7 ωx:6 rush:1 ωq:10 multiplicity:1 ωs:22 6uux:3 ωt:8 ωi:56 ωk:17 ωj:47 ωn:8 ωa:37 russ:5 ωb:15 ωg:5 connect:2 uia:3 ab:4 ad:2 ag:9 ai:50 ℑx:1 ak:25 describe:2 am:2 general:26 aq:1 uip:2 examine:1 vn:2 formulation:1 ay:1 gradients:4 fill:1 again:10 completeness:2 izvestia:1 field:11 valid:2 mathematics:3 d2g:1 briefly:1 separate:1 symbol:1 vertex:4 dq1:1 a1:66 a0:25 a3:1 a2:7 bounded:3 tricky:1 curve:4 cherednik:1 hirota:11 appl:7 starting:1 strings:3 represent:3 sci:1 consider:16 gesztesy:1 scalar:3 c2:1 follow:9 expressions:4 dα:6 weierstrass:4 referring:1 tw:9 tt:2 equivalence:5 h2α:1 ts:3 nonlocal:2 tq:4 tn:45 kβ:1 kα:21 tm:2 tj:20 tk:13 th:16 dressing:1 te:5 presentation:1 ta:12 kσ:9 fay:14 returning:1 very:8 mpm:1 corollary:1 witten:1 sonnenschein:1 fab:3 difference:1 deformations:1 condition:7 treating:1 hamiltonian:2 t4:1 t2:4 t3:2 t0:14 t1:14 large:5 adjust:1 independence:1 small:8 anal:7 linearizing:1 neighborhood:4 periodicity:4 zero:17 pass:2 further:28 reina:1 canonical:9 bilinear:13 what:5 nonlinear:5 tsuchiya:1 brackets:1 section:58 stipulated:1 brief:1 yankielowicz:1 version:4 intersect:1 method:1 full:3 qm0:8 loose:1 modify:1 ansatz:2 november:1 strong:1 equations:63 matching:1 generalizing:1 increments:2 divisor:26 δqn:2 tempting:1 periodic:13 pick:4 action:7 via:115 family:3 requiring:1 rkl:2 establish:2 ψx:5 takes:10 twj:2 finally:7 ψt:1 ψj:3 nucl:4 taken:3 minor:1 more:33 flat:10 vk:4 knows:7 operators:10 constructs:3 basically:1 particular:19 known:2 producing:1 presumed:1 keeping:1 recall:37 equation:31 det:1 examined:3 den:4 marshakov:1 hawley:1 nonsingular:3 deg:1 f0:2 f1:7 compare:3 stated:1 dui:2 beautiful:1 numbers:1 arise:12 phrase:1 unramified:1 axis:2 information:7 needs:2 rather:3 acts:2 occasionally:1 reject:1 acta:2 priori:6 creature:2 fp:1 simplicity:1 tried:1 τij:6 algebra:12 fx:1 ζi:3 ζj:1 ζk:1 singularities:5 orbits:1 bkj:1 bkk:1 φ2s:5 fb:2 plane:4 dokl:3 waves:5 fi:2 fj:4 geometrical:3 concentrating:1 fm:4 fn:1 contrived:2 xui:1 perhaps:5 speeds:1 fundamental:2 fα:4 funct:3 hierarchy:25 developed:7 advised:1 ffm:1 paper:1 through:3 signs:1 y2:2 excitations:1 its:8 roots:2 tˆi:4 energies:1 affine:4 φb:3 actually:1 systems:1 jacobi:6 might:3 yi:2 dzdw:1 motivated:1 yn:1 framework:2 yu:1 yw:2 yv:14 easily:3 2w:1 2p:1 2q:2 2s:8 always:1 2y:1 2f:3 2g:21 turns:1 2l:5 found:2 2n:12 2i:3 characterized:3 2k:8 constructing:1 weight:2 energy:4 used:21 recapitulate:1 toda:8 expect:3 sketched:2 quantum:3 beyond:1 event:1 really:1 leave:1 discrete:1 robert:1 since:26 denotes:6 handles:2 dxdy:3 denoted:1 induced:1 kodama:9 imagine:1 ask:1 φdx:1 beginning:5 generate:4 definition:11 pairs:3 omit:3 takasaki:2 exhibited:1 feel:1 number:10 linking:1 done:1 construct:3 entrain:1 funkts:1 extendible:1 passes:1 differ:2 perturbation:1 minimality:1 introduction:5 leading:10 least:4 tradition:1 2fb:1 assumption:1 aa1:1 identity:18 calculations:3 holomorphic:34 akad:3 immediate:2 part:5 differentiate:2 tft:6 translation:2 shrunken:1 kind:15 determines:6 cyclic:1 double:6 dta:2 kini:1 determined:16 fˆ:2 treated:2 motivation:1 multivalued:11 conjugate:1 null:2 orders:5 paths:3 constructions:1 jour:13 depending:8 zp:6 extracted:1 k1:8 k0:4 generalized:2 analogy:2 jacobian:4 2te:1 t2i:1 play:4 most:1 comparisons:1 nothing:3 measured:1 soliton:6 tλ:2 orlov:3 kj:2 clear:7 sometimes:2 cover:2 kn:6 km:1 tα:15 traditional:2 ext:1 kp:47 exp:71 kx:3 physics:5 cdf:1 particularly:1 cdn:1 relation:4 3u:5 carefully:2 find:1 τg:4 parameters:10 schiffer:1 writes:11 factor:8 ablowitz:1 integrable:5 resp:27 abelian:8 invoke:1 dependent:1 express:7 mclaughlin:4 famous:1 cd1:1 lattices:1 2dα:1 schottky:1 arxiv:1 common:2 activity:1 forster:1 set:16 fucito:2 achieved:1 unpublished:1 see:27 arc:1 gurevich:1 arg:1 contour:3 hejhal:1 ergodicity:3 pictures:1 pisa:1 uβ:1 2πiδ:1 various:14 2πiβ:3 subscript:1 conditions:5 recently:1 creating:1 missing:1 ikx:5 analogues:6 veselov:1 incommensurate:1 cijk:1 vanishing:2 uψ:2 solv:1 both:3 last:4 connection:9 symplectic:2 context:8 forgotten:1 pde:4 zk0:2 finds:2 arbitrarily:1 point:26 simple:13 corresponds:15 whatever:1 dimensional:4 simply:8 bα:3 bβ:2 kernels:19 pp:15 pq:1 described:2 perspectives:2 pt:3 px:7 py:3 due:2 z1:5 reduction:3 dropping:1 pg:17 pj:18 pk:4 pi:37 pn:20 po:1 pl:1 pm:4 generating:5 hurwitz:18 great:2 else:1 understand:2 nonconstant:1 gag:1 surveys:1 duke:1 p2:8 p3:3 p0:16 p1:29 look:15 p4:1 ǫi:1 expanded:1 bψ:1 ǫn:3 while:5 replaced:1 behavior:3 ǫt:4 ǫy:1 ǫx:5 loop:1 detailed:3 vol:2 averaging:42 overlooked:1 itself:2 vanish:3 eigenfunction:1 jz:1 σn1:2 ǫl1:1 lbn:1 higher:1 development:4 calculation:4 literature:2 lie:2 flows:4 moment:3 uses:8 uˆ:2 recent:2 lower:1 rodin:2 kashiwara:1 analysis:3 picks:2 de:45 i2m:1 consistency:1 λs:1 things:2 gelfand:2 applicandae:1 intervals:1 λg:5 questions:1 world:7 λk:20 λj:17 λi:16 λn:18 λm:6 cut:5 conclusions:2 theorem:19 qmn:7 transformation:2 euler:3 build:1 bij:4 bii:7 big:2 kawamoto:1 matters:5 formal:4 modifications:2 envisioned:1 follows:20 nakatsu:1 ignore:1 collect:1 continue:2 yields:7 essential:3 mathematical:1 sketch:5 methods:1 some:63 back:2 b0:4 b1:8 uspekhi:1 curious:1 pψ:1 scale:2 affects:1 sfb:1 integration:11 connecting:3 prog:1 proc:4 minimal:3 varying:1 bg:4 ba:16 bc:1 bm:7 bn:29 aj:23 bi:28 bj:21 bk:18 step:3 become:2 relating:1 subtract:1 gibbons:3 pβ:5 integers:2 works:1 l1t:1 novikov:9 regular:3 idk:3 uǫ:1 consequently:6 bloch:11 computational:1 φxx:1 reidel:1 omitting:1 martinec:1 into:4 within:1 integral:5 isomorphic:1 appropriate:8 pdλ:11 conceivably:3 springer:9 u1:11 u0:26 fast:3 u2:5 sections:3 elsewhere:1 sde:1 delta:1 line:5 aqi:1 2πif:1 uy:1 ux:8 consist:1 2πi:52 characteristic:6 2πin:3 cin:1 us:25 2πn:2 2πit:1 uo:1 un:16 ui:31 uk:5 uj:21 similar:1 called:12 constant:10 worthwhile:1 defined:28 tβ:1 pseudodifferential:2 lehrbuch:1 doesn:1 globally:1 single:8 associates:3 physica:1 kl:2 kdv:35 fizika:1 defines:10 ks:2 2dp:1 amounts:1 fixing:2 multipliers:1 rewriting:2 application:1 points:33 department:1 elements:1 generates:2 problems:5 polynomials:8 helpful:1 meaning:3 allowing:1 puncture:1 vaccaro:1 structure:14 implies:19 required:3 holes:1 na2:1 equivalently:6 eξ:5 requires:2 having:11 partial:2 gp:1 gamba:2 results:9 gx:1 illustrated:1 eds:2 ǫa1:1 edu:1 go:6 gn:4 adjustment:3 gj:3 concerned:1 young:1 uniqueness:1 dijkgraaf:2 include:1 g1:12 ωss:1 implicitly:1 cγαβ:6 wave:11 putting:1 resonant:6 entire:2 riemannhilbert:1 wronskians:1 transmission:1 positions:1 notes:6 try:6 noted:1 lˆ:5 zn:3 zi:7 zj:6 zk:3 zg:4 za:1 zb:1 jump:1 imply:3 zz:6 odd:5 analogue:7 zs:2 giving:2 aαβ:1 analogously:1 expressed:11 consistently:1 poles:26 kyoto:1 preserved:1 exercise:1 3d:1 led:2 degree:11 respectively:10 desired:2 objects:3 q2n:1 z0:31 δωa:1 z2:2 remark:13 dividing:1 involved:1 suggests:2 survey:1 admissable:2 makes:4 involves:7 transformations:2 liml:5 imaginary:2 use:11 asymptotic:6 recalling:1 next:12 few:3 examination:1 normalizes:1 permutations:1 formally:11 started:1 becomes:10 observing:1 normalized:26 wi0:2 morozov:1 dωα:5 crosses:1 frobenius:20 averaged:8 reproduce:1 unknowns:2 infinitesimal:2 obvious:4 codimension:1 averages:4 proof:6 tau:12 chosen:1 process:4 purposes:2 lψ:10 dk:34 hodograph:2 notation:25 pure:3 holds:1 occur:2 superstrings:1 varies:2 forest:2 instead:6 npn:3 ta0:2 singular:3 gardner:2 abuse:2 multiplication:2 ties:1 varied:1 λ2j:9 realized:1 λ2i:8 λ2n:2 λ2m:12 lines:1 correspond:11 diffeomorphism:1 darboux:1 realizes:1 allow:1 s1:8 s0:5 produces:1 symbols:2 cambridge:1 including:1 looks:7 mentioned:1 lg:20 le:6 lb:2 la:5 ln:9 lj:3 lect:1 lt:2 lr:1 choose:2 covered:1 defining:5 greater:1 material:4 landau:4 mention:3 cutting:2 maslov:1 das:1 documented:1 realize:1 uˆt:1 university:1 traced:1 sufficiently:2 magnitude:2 l2:4 l0:17 l1:37 warner:1 subset:7 dωh:3 dωi:2 dωj:5 dωk:4 dωe:3 dωa:9 related:11 w10:2 elementary:5 frequency:1 computable:1 our:14 aˆ1:6 special:6 out:9 respects:1 matrix:10 res:16 rev:6 gaum:3 gˆ:5 grinevich:5 stud:1 lecture:1 math:38 t02:1 discontinuity:2 diagonal:3 clarify:4 completely:1 collection:1 dω1:3 interaction:1 geometry:2 could:12 keep:3 length:1 derivations:1 hence:18 retain:1 teor:1 phrased:1 heuristically:1 there:35 ψxx:4 f1j:3 taniguchi:1 f1n:5 adjoint:11 πi:1 πn:1 system:9 relations:18 their:4 intermediate:1 siam:2 floquet:5 udx:1 exactly:6 wiley:1 zλ:1 branches:1 zα:3 punctures:7 bek:1 holland:1 bother:1 limiting:2 result:4 false:1 unchanged:1 curves:10 λ2g:11 need:3 apparently:6 linked:1 viewed:1 angle:1 studying:1 able:1 gravity:3 associativity:1 gψ:1 lectures:3 gα:3 connected:4 preliminary:2 sist:1 intrinsic:1 class:10 linearized:4 parametrize:1 fjn:1 neighboring:1 ensues:1 face:1 proceedings:1 χn:9 χm:1 χj:5 fact:13 selection:2 akhiezer:2 text:2 purely:1 miwa:1 agrees:5 principal:2 q1:7 q0:3 q2:2 based:9 knowledge:1 dp1:1 should:15 lemma:2 2πiα:1 local:22 achieve:1 means:12 displayed:5 michigan:1 mgn:16 xdp:1 procedures:5 qs:31 determinants:1 densities:4 differential:48 expansions:5 nauk:4 qe:1 qf:2 qi:7 qk:1 fixed:12 qm:1 ql:1 view:6 moduli:24 modulo:8 computed:2 exists:5 variations:1 differentials:58 turbulent:2 ωq0:1 hδ:2 mj:2 bobenko:1 uux:2 phases:1 nondegenerate:3 rims:1 torus:4 tend:1 written:14 difficulties:1 identification:2 closed:3 theta:25 boundary:2 email:1 meromorphic:37 attention:1 2pu:2 theisen:1 importance:2 however:16 τm:1 key:1 τj:1 amer:3 2pn:1 limits:9 freely:1 taking:2 τi:5 fulfilled:1 etc:33 sβ:2 passing:2 generic:1 comment:1 cj:2 unclear:3 cn:4 conclude:1 cc:1 landauginzburg:1 cg:4 cf:104 m11:1 distinguish:2 cba:2 respect:2 cp:3 trajectory:1 cauchy:20 slowly:1 certain:5 degrees:1 define:14 arises:9 corresponding:20 sufficient:1 derivative:2 prescription:2 present:3 ap:1 contexts:1 value:2 choices:2 will:104 vi:3 vj:2 wkb:2 thus:63 surface:41 vq:2 vs:4 dual:4 claimed:1 ℑk:2 φq:2 φr:1 φs:1 φt:5 φv:1 φx:2 φa:4 unity:3 parts:3 φg:1 units:1 φi:4 finite:16 φn:13 difficult:1 practice:1 upon:5 functions:47 parametrized:2 mzn:1 expand:2 reflection:1 nevertheless:1 0n:1 modeled:3 well:11 thought:4 sets:4 position:2 arising:4 usual:3 restore:1 less:3 half:2 obtain:24 underlying:1 qij:1 uller:1 momenta:1 glue:1 preprint:2 gmn:1 guts:1 killed:1 lattice:5 add:1 nor:2 putative:1 bochum:1 inversion:1 manners:1 vα:3 increases:1 qj:5 five:1 know:1 press:3 immediately:3 intersection:1 insert:3 tl:2 necessary:4 like:8 sissa:1 δu:5 δs:1 δq:12 δn:1 δi:2 δf:3 δg:2 δe:1 amendment:1 because:1 qed:1 classical:12 smoothly:2 2qx:1 algebraically:2 σi1:1 growth:2 choosing:1 diff:1 iˆn:1 proofs:4 iˆj:2 lead:2 does:3 intersections:1 ps:16 σik:2 qn:41 expansion:6 βij:1 bundle:5 although:3 cα:2 entirely:1 simpler:1 about:8 asks:3 extension:5 introduces:3 dependence:6 surge:1 compatible:2 2cn:2 important:13 introduced:2 create:1 h2:1 h0:1 h1:6 additional:5 sugaku:1 pairing:1 quadratic:3 2m:14 asymptotics:3 function:84 ef:1 north:1 hs:3 miraculously:1 but:53 hj:2 construction:2 hn:1 dωb:2 tering:1 convergence:1 hf:6 namikawa:1 compute:3 places:1 whether:2 smooth:3 ωpr:2 record:1 below:33 limit:12 problem:2 display:1 mechanics:1 int:1 recognize:1 universal:5 denote:3 periods:6 inj:4 relates:1 θn:3 ing:1 identities:2 qα:2 spell:1 dpα:2 variety:2 detail:5 dωq:5 other:24 compares:1 details:5 branch:18 theor:1 expressible:1 variation:2 stay:1 gap:3 coupling:1 lyon:1 baker:1 factors:7 rule:1 iψ:1
|
solv-int9512001.txt |@word represent:1 consider:1 remarkable:1 funct:1 rev:1 results:1 llt:1 eds:2 scalar:1 computation:1 remarkably:1 gl:9 contributions:1 inverse:3 lkj:4 lkk:19 lki:3 tu:1 tr:3 recurrence:1 finally:1 analogous:2 applied:1 belonging:1 straightforward:2 springer:1 putting:1 entries:1 discretizations:6 tridiagonal:3 difference:5 continued:2 condition:1 notations:1 hamiltonian:9 positions:1 notes:1 solution:1 solved:2 interpolating:2 anal:1 unversity:1 upper:2 lecture:1 approximation:3 second:2 expressions:4 canonical:1 will:3 nonlinear:3 appear:3 brackets:1 section:2 version:1 above:1 new:2 bn:3 led:1 mem:1 got:1 proc:1 here:2 papageorgiou:1 water:2 following:9 groups:1 depend:1 principle:1 equations:7 appears:1 obtained:1 remark:5 dec:1 ekk:1 ekj:3 shift:1 garnier:1 allows:1 poisson:4 uniquely:1 useful:1 family:1 namely:1 highly:1 brought:2 santini:1 apply:1 use:4 additive:1 takes:2 would:1 prove:1 positive:2 live:1 comparing:1 linear:4 opposed:1 taken:1 type:3 minor:1 fractions:1 successful:1 solitons:3 operators:1 factor:1 holm:2 given:7 producing:2 account:1 recall:1 equation:18 modified:2 obvious:2 capel:1 canonically:1 arrive:3 proof:4 beautiful:1 nearest:1 give:1 relativistic:3 share:1 states:1 way:2 want:1 exclude:1 simple:3 yang:2 end:3 turn:1 rather:3 holds:2 maps:5 veselov:2 numerous:1 ordinary:1 explains:1 priori:1 r2n:1 product:1 express:2 algebra:1 may:4 oscillators:1 after:3 orbits:1 applications:1 levi:1 lax:9 short:1 dynamical:2 light:1 schneider:1 explicit:1 deutsche:1 so:9 representation:2 βk:26 order:2 least:1 interpretation:2 help:3 βk2:2 hierarchy:2 indeed:1 soc:1 years:2 xi:6 pang:1 letters:5 satisfies:1 its:3 group:2 matrices:5 lk:2 conjugation:1 li:1 forms:1 kuznetsov:1 lt:1 drawback:1 systems:10 mail:1 main:1 non:1 impulses:2 introduce:1 framework:1 now:7 yu:4 deift:1 several:2 turns:2 found:1 side:3 characterized:1 baxter:2 arxiv:1 directly:1 formulate:2 map:1 related:1 applicable:1 toda:8 our:1 special:1 out:2 matrix:22 discrete:23 gradient:1 since:1 lagrangian:8 chaos:1 research:1 re:2 formula:4 induction:3 correct:1 math:7 shows:1 theory:1 diagonal:1 standard:2 base:1 advantages:1 yuri:1 put:1 ruijsenaars:1 generate:1 definition:1 motion:2 introduction:1 hence:4 retain:1 first:3 xj:21 xk:107 initial:3 xn:15 symmetry:1 someday:1 rank:1 xy:1 relations:1 another:1 little:1 rewritten:1 ordering:1 eqs:1 system:16 construct:1 their:2 appl:1 statement:3 dfg:1 scheme:4 speaking:1 calculations:3 ch:1 continuous:8 serve:1 2ak:1 part:2 x2:3 x0:1 x1:12 peaked:2 variational:1 approximations:1 integrability:4 winternitz:1 future:1 symmetries:1 correction:1 seen:1 any:1 complete:2 lie:2 εx:1 convenient:1 calogero:3 lii:8 lij:1 lik:2 potential:1 square:1 generalized:2 analogs:1 formulas:3 shallow:2 antoniou:1 centre:1 most:1 germany:1 but:1 letter:3 nothing:1 coincides:1 physica:1 bracket:3 diagonals:1 exp:86 physics:10 sum:1 fact:1 quantity:1 supported:1 recipe:4 discovered:1 bring:1 spaces:1 relation:3 substituting:1 trivial:1 cholesky:2 every:1 written:2 lemma:5 only:2 postfach:1 equipped:1 integrable:21 moser:4 local:1 hope:2 do:1 get:3 de:1 ones:2 suris:6 report:1 lattices:4 subscript:1 evolution:2 approach:2 differential:1 factorization:6 method:1 financially:1 qd:1 set:1 imposing:1 hη:1 depends:1 result:2 terms:3 analog:1 subject:1 satisfying:1 expert:1 nondegenerate:1 symmetric:1 enough:1 invariant:1 boundary:2 conditions:3 multiplied:1 recently:2 attention:1 flow:1 p2k:1 however:2 key:1 solv:2 amer:1 received:1 last:2 equal:2 etc:1 symplectic:3 attributes:1 expression:3 hold:1 point:1 appeared:2 cf:1 dimensional:1 simply:1 constant:1 peakons:14 camassa:2 kp:1 considering:1 nijhoff:3 described:1 submanifold:1 due:4 int:3 workshop:1 asymptotics:1 pj:20 pk:36 pi:6 ak:13 field:1 corresponding:3 tomei:1 quantities:1 gen:2 else:1 neighbour:1 general:5 present:3 case:4 intriguing:1 value:2 aim:1 suppose:1 shall:1 property:1 loop:1 almost:1 ii:2 reads:2 author:1 recurrent:1 same:3 lambert:1 complex:1 finite:3 see:1 upon:2 flows:1 hand:4 uni:1 recent:2 lower:3 nevertheless:1 recurrently:1 position:1 model:3 resp:1 obtain:2 underlying:2 thanks:1 tilde:1 momenta:1 visualization:1 preprint:1 hpj:1 seems:1 lattice:19 belongs:1 lett:5 theorem:9 identical:1 read:3 possible:2 admitting:1 corresponds:1 immediately:3 lji:3 modifications:1 ljj:10 necessary:2 like:2 identifying:2 follows:5 velocities:1 serves:2 collect:1 integrals:1 nice:1 because:1 leningrad:1 classical:4 some:9 deduce:1 examples:4 kdv:1 2xk:1 describing:1 though:1 manipulations:1 does:1 decomposition:1 chains:1 equivalent:2 continuing:1 bi:1 bk:15 polynomials:1 subtract:1 commun:2 favorite:1 ejk:2 o:6 mutually:1 extensions:1 introduced:1 other:1 discretization:3 statements:1 h2:3 into:5 obtaining:1 pair:3 right:3 references:1 operator:2 algebras:1 neumann:1 log:1 strictly:2 there:3 relegated:1 approximate:1 quadratic:1 fraction:1 mappings:3 was:5 function:8 elsewhere:1 form:7 triangular:5 ht:7 construction:2 counterparts:1 considerable:1 made:1 algorithm:1 versions:2 smooth:1 up:1 us:2 discretized:1 demonstrate:1 problem:4 called:1 b1:3 mechanics:1 proved:7 defined:5 certain:1 abstract:1 describe:1 denote:2 exist:1 formulation:6 dη:2 dε:1 again:1 no:2 mathematik:1 generally:1 bremen:3 hpk:23 application:4 setting:2 remarks:1 hpn:2 conclusion:2 bruschi:3 ragnisco:5 a1:3 generated:1 included:1 structure:2 implies:1 using:4 assume:1 vinet:1 hp1:2 space:1 orbit:1 together:1 time:34 requires:1
|
solv-int9512002.txt |@word φ1j:9 gu:5 sci:5 consider:2 qiao:1 funct:1 equalities:1 integration:1 leads:1 eds:3 ψ1j:9 grateful:1 gn:1 expressions:1 c1:3 gh:10 devoted:1 whose:1 inverse:3 const:1 shanghai:1 tr:7 tn:20 δhn:1 uniqueness:1 under:4 very:2 rise:1 2rc:2 2rb:2 dokl:1 every:1 matrices:1 condition:1 obvious:1 hamiltonian:28 induction:1 solution:1 large:2 vector:3 eigenvalues:1 anal:1 trv:4 zhuang:1 zj:1 10b:1 10a:1 direct:1 integrability:5 further:4 dψ2:1 dψ1:1 linear:1 spectral:7 what:1 nonlinear:8 stands:1 section:2 hereditary:1 above:3 new:4 increasing:1 method:2 simultaneously:1 ibid:1 here:3 china:4 along:1 observing:1 19b:1 obtained:1 remark:1 institute:1 allows:2 poisson:3 geng:5 involves:1 uniquely:1 control:3 technique:14 blaszak:1 rodrigues:1 9a:1 requiring:1 9b:1 establish:1 select:1 readily:1 nonlinearization:20 expresses:1 would:1 prove:1 distinct:1 contains:1 fordy:2 few:2 noting:1 therefore:5 associated:5 φix:1 sort:1 introducing:2 jpn:1 engender:1 successful:1 becomes:1 odinger:1 curvature:1 berlin:4 particular:1 known:1 foundations:1 hold:1 must:1 springer:3 ma:5 science:1 equation:4 work:1 mu:1 flaschka:1 cao:7 novikov:1 following:7 making:1 dec:1 example:2 stimulating:1 wojciechowski:3 f1:3 give:3 calculation:1 idr:2 sense:1 involve:2 φij:1 14b:1 o:1 want:2 14a:1 evidently:1 verlag:3 boussinesq:1 recursive:1 darboux:1 verify:2 get:1 acta:4 ψij:1 parameter:1 ψin:1 konopelchenko:2 r2n:1 product:1 algebra:2 may:7 φ2j:9 φi1:1 lax:34 end:1 compatibility:2 constants:1 ψi1:1 introduced:1 natural:2 lines:1 provide:1 so:2 representation:10 order:2 holds:2 dx:3 hierarchy:7 vary:1 satisfied:1 years:1 paper:2 including:1 satisfies:1 still:3 derive:1 2λa:2 2λc:2 ln:1 vtm:1 exhibits:1 li:8 forms:1 systems:38 constitutes:1 jacobi:2 derivative:1 variables:3 them:2 yj:1 propose:1 rσ1:1 introduce:1 19a:1 they:2 now:3 discuss:1 easily:1 finite:8 dirac:22 2q:5 2r:5 university:1 presented:1 2ej:2 2a:3 2b:2 2c:2 2n:1 referred:1 differential:5 ej:1 series:4 idea:3 constitute:1 operator:4 f0:1 extended:1 gfn:8 our:1 out:1 rt:1 shown:2 matrix:1 furthermore:2 since:4 rx:1 denotes:1 fx:1 investigation:1 rn:2 ref:8 math:26 common:1 foundation:1 theory:3 8b:1 8a:1 quite:2 quart:1 nth:3 complicated:1 besides:1 ψ2j:9 generate:1 pairs:34 sinica:5 impose:1 times:1 motion:5 exhibited:1 first:3 simplifies:1 symmetry:13 possessing:1 number:1 l37:1 relations:1 directly:1 2a1:1 xu:4 equating:1 little:1 rewritten:1 fn:15 introduction:1 adjoint:26 vandermonde:1 system:15 construct:1 fm:2 1a:2 their:4 f1x:1 1b:2 xiu:1 variational:1 structures:6 2an:7 acquire:1 newell:1 2ai:1 part:8 jordan:1 somewhat:1 authors:1 jiang:1 coefficients:1 kind:6 determines:1 holland:1 roles:1 df1:1 zero:5 preparation:1 determined:2 exhibit:3 symmetries:2 7b:1 7a:1 explicit:1 generalization:1 iσ2:1 need:2 constrained:3 any:1 relatively:1 lim:4 lin:1 note:3 instance:1 potential:1 take:2 interior:1 play:1 continuous:1 trace:2 shall:5 involving:1 connected:1 elucidates:1 phase:1 acknowledgements:1 class:2 soliton:11 nonlinearity:1 considered:1 later:1 kn:7 km:2 bracket:1 similarly:1 sorts:1 abraham:1 physics:4 bulletin:1 fact:2 12a:1 12b:1 selection:1 oevel:1 show:1 reductions:1 supported:1 relation:1 solutions:5 substituting:1 find:3 based:1 should:1 2bn:1 only:2 geometric:1 integrable:12 meng:1 ratiu:1 extent:1 his:1 cheng:2 means:3 dependent:3 express:1 aσ1:1 ones:2 words:1 invariant:1 during:1 interpreted:2 dr:1 gen:5 liu:1 evolution:2 qr:2 qx:2 arxiv:1 2b0:1 involutive:7 fixed:1 view:1 set:1 smooth:1 national:1 see:8 discussions:1 terms:2 aroused:1 eigenfunctions:9 various:1 between:1 progress:1 boundary:4 conditions:5 qt2:1 transpose:1 however:1 key:1 solv:1 σj:1 taking:1 deduction:2 symplectic:3 expression:1 cj:2 ci:12 cn:7 point:1 northeastern:1 2nd:1 dimensional:12 cx:1 simply:1 coordinates:2 interrelations:1 polynomial:2 respect:6 vtn:4 considering:1 ensures:1 commutative:1 equivalent:1 δλj:3 due:1 been:4 int:1 reduction:1 interest:1 b0x:1 φin:1 fudan:1 choose:1 generating:3 aj:7 corresponding:1 both:1 quantities:1 r4n:4 equations:2 bull:2 c3:1 c2:4 worked:1 c0:1 present:1 applied:1 klaus:1 aix:1 arnold:1 will:2 cast:2 soc:1 property:2 region:1 procedure:3 coupled:1 refs:1 thus:6 tu:7 reads:1 itself:1 vx:6 bargmann:3 binary:14 different:3 shaw:1 author:2 φx:5 recursion:1 same:2 akns:1 parts:4 pauli:1 φi:7 hierarchies:8 several:1 higher:2 independent:1 used:1 singapore:1 cubic:1 upon:1 flows:4 infinite:1 identity:2 recent:2 mech:1 schr:1 nevertheless:1 concrete:1 solve:2 sets:1 left:2 manifold:2 proposed:5 profs:1 being:3 dφ1:2 obtain:7 dφ2:2 manipulation:1 world:1 λj:9 ostrogradsky:2 λn:3 fokas:1 φtn:1 preprint:1 conclusions:1 conclude:1 wen:1 quadratures:2 other:1 lett:10 easy:1 5a:1 transformation:1 5b:1 advances:1 possible:1 l89:1 bix:1 equality:5 moreover:3 prominent:1 imposed:1 like:2 systematically:2 follows:4 δu:13 integrals:5 become:2 qxx:2 stationary:1 mathematical:2 because:5 methods:2 namely:1 exposed:1 chin:4 ψx:2 some:4 begin:1 addisonwesley:1 b0:1 examples:1 b2:5 δbn:1 kdv:1 jln:1 nonzero:1 sidorenko:2 dimensions:1 lead:1 broad:1 l17:1 2qa:2 2c1:1 l13:1 defined:2 linearly:1 prof:2 refer:1 gratitude:1 11a:1 scientific:1 11b:1 bn:7 each:1 bi:14 bj:2 although:1 bx:1 properties:2 stage:2 about:1 constraint:12 ψtn:1 commun:1 discussed:1 generated:2 idp:1 idq:1 addition:1 2cn:5 important:2 2ci:1 constraints:9 gibbons:1 raised:1 into:3 remarks:1 references:1 sov:1 qrx:1 amsterdam:1 classical:2 springerverlag:1 support:1 there:2 anderson:1 ψi:7 way:2 ed:1 was:1 function:8 north:1 form:2 regard:1 but:4 hu:1 construction:2 hn:2 line:1 hinton:1 marsden:1 made:1 applying:1 consist:1 characteristic:1 utn:8 us:5 theoretical:1 liouville:10 henan:1 2qb:2 problem:6 cix:1 similar:3 called:2 b1:3 mechanics:3 ab:1 constant:2 ai:23 certain:1 abstract:1 b3:1 determinant:1 zeng:6 general:3 exist:2 physica:2 ax:1 aφ1:1 aφ2:1 functions:6 rxx:2 when:5 vanishes:3 field:3 setting:1 spatial:8 mathematics:1 frolov:1 denote:1 symbol:1 problems:5 polynomials:2 includes:1 a1:3 a0:1 a3:1 a2:5 massachusetts:1 generalized:1 sides:1 structure:1 scientia:1 implies:2 assume:1 vigorously:1 4n:1 equivalently:1 time:6 appl:4 4a:1 4b:1 original:1 once:1
|
solv-int9512003.txt |@word limited:7 partial:2 consider:4 global:5 results:2 four:2 eds:3 commute:1 comments:1 grateful:1 wj0:1 wj1:1 relationships:1 mazur:2 inverse:4 depend:4 fellowship:1 hump:2 passage:2 finally:1 monotonically:4 contours:2 under:1 analogous:4 very:2 springer:1 dokl:4 wave:6 every:3 exact:1 condition:1 common:1 dubrovin:4 riemann:18 roy:1 did:1 turns:2 solution:53 reg:1 leave:1 solved:2 convenience:1 interchanging:1 splitted:1 anal:1 rk:3 noted:2 work:2 coefficient:1 direct:2 sign:1 second:1 invention:1 picked:1 substituting:2 further:1 dynamics:1 odd:1 shows:2 canonical:1 putting:1 will:6 nonlinear:3 appear:1 axes:1 expressed:2 uniform:6 annals:1 poles:3 above:1 frank:1 new:6 acknowledgments:1 satisfy:2 evolving:3 respectively:2 here:5 behaviour:2 desired:3 magnetism:1 expansion:3 represented:1 const:1 along:2 equations:17 implicit:1 obtained:8 remark:5 dec:1 splitting:1 institute:2 until:1 vectors:1 allows:1 completely:2 accomplished:3 resulting:1 poisson:2 domains:4 ξk:8 uniquely:2 boundedness:5 formulated:2 natural:1 convolution:1 family:2 gurevich:9 coinciding:1 modulated:1 apply:1 planck:1 takes:1 would:1 distinct:2 contains:2 physics:1 ψj:1 ψk:1 linear:6 program:1 examination:1 therefore:4 schwenn:1 compactly:1 type:4 refs:6 more:3 separated:1 introducing:1 pavlov:3 r5:5 fokas:1 marks:1 separates:1 known:3 producing:1 must:1 account:2 valued:1 integrating:1 recall:1 equation:15 averaged:11 obvious:2 following:4 making:1 arrive:5 compare:1 figure:1 give:2 discussed:2 choice:1 arise:1 involve:1 sphere:3 assumptions:1 dxj:1 degenerate:1 sense:2 sought:1 ideology:1 axis:1 terrestrial:1 hodograph:15 darboux:2 divided:2 breaking:12 regions:1 how:1 nontrivial:1 vital:1 forest:1 pure:10 sij:1 ordinary:1 parameter:5 oscillatory:1 tbr:2 r2k:37 mat:1 singular:5 modulation:1 max:4 earlier:2 singularities:4 dx2:1 consequence:3 plane:6 lax:2 waves:4 date:1 fi:2 geometrical:2 data:13 constants:1 physical:2 dynamical:1 imply:1 explicit:2 correspond:3 subdomains:1 provide:1 so:6 doklady:1 fundamental:5 decreasing:4 representation:9 order:1 wind:2 restriction:2 hierarchy:7 over:2 katlenburg:1 course:1 including:2 cuts:1 mentioned:1 existence:2 y2:1 its:1 tending:1 thank:1 ln:1 appl:7 resolving:2 absence:1 parts:3 fig:10 zybin:1 serre:1 them:1 w5:1 lindau:1 propose:2 investigated:2 framework:1 they:1 identically:1 singularity:2 now:7 discuss:2 developments:1 matched:1 easily:1 term:1 finite:5 equality:1 invariants:5 limits:2 2g:19 2a:2 2b:4 each:1 found:2 1ak:1 2k:9 el:5 multiphase:6 differential:3 formulate:2 evolve:1 series:5 journ:1 frequency:2 handles:2 ionosphere:1 our:1 transitions:3 special:2 really:3 large:1 shown:3 accomplish:1 acknowledgment:1 space:9 res:1 since:1 parametrizing:1 research:1 looking:1 r2g:27 contained:1 investigation:1 grinevich:1 formula:2 ref:3 ri:11 rj:21 predicted:1 foundation:1 after:1 theory:3 fulfilment:1 diagonal:5 tian:3 bowshock:1 york:2 ψ2k:8 usual:1 put:1 asi:1 beginning:2 r4:1 definition:7 ercolani:1 r1:37 r2:33 r3:34 transition:7 times:1 motion:2 turn:1 βg:1 place:1 unknown:1 hence:1 teor:1 pitaevskii:5 speeds:4 first:8 xj:1 there:1 omitted:2 variables:3 number:10 u0:8 another:1 precisely:1 between:1 kλ3:1 dispersive:2 given:6 perturbation:3 hyperbolic:1 introduction:1 revealed:1 interact:1 system:22 construct:4 their:3 assumption:1 zeros:1 calculations:1 hyperelliptic:1 gives:3 holomorphic:2 moscow:2 dissipationless:1 zeroth:1 whitham:12 part:3 x2:4 branches:2 translation:2 x1:4 coefficients:3 center:1 mclaughlin:2 effective:1 sections:1 require:1 summary:1 namely:5 final:1 project:1 express:1 were:5 powers:1 russia:1 symmetries:1 coalesced:1 contradict:1 lines:1 mind:1 coalesces:2 multivalued:2 need:1 tτ:1 seek:1 any:7 lie:2 zero:8 min:3 studying:1 latter:1 potential:5 generalized:5 analogs:1 formulas:2 begin:1 continuous:2 multiple:4 shall:6 caustics:1 algebraic:2 breakings:2 germany:1 significant:1 phase:36 workshop:1 considered:6 neighboring:1 chosen:3 coincides:2 drive:1 points:13 overdetermined:2 kx:1 vries:1 fact:3 laws:1 science:1 supported:1 purely:1 radio:1 solutions:13 earth:1 consequent:1 d2:4 find:1 d1:3 alfvenic:1 slow:1 ratio:1 parameters:1 assertion:1 should:4 analytic:7 only:9 greenberg:1 inherited:1 integrable:1 hopf:3 continuity:1 do:4 means:6 occuring:1 de:1 satisfied:1 ones:2 dx:3 distinctly:1 combinations:1 dt:1 boundary:12 evolution:12 arxiv:1 troitsk:1 nauk:1 hydrodynamic:2 contain:2 analytical:1 cycles:3 view:2 kernel:3 requirement:4 set:2 imposing:1 differentials:1 respect:1 zones:1 depends:1 w3:4 result:3 w1:3 captions:1 discussions:2 terms:6 contour:1 surfaces:4 phases:2 tsarev:1 boundaries:4 outside:1 difficulties:1 αg:2 simplest:3 theta:1 αk:3 conditions:12 multiplied:1 notice:1 recently:2 nature:1 matveev:1 weak:3 wj:24 wi:4 however:2 comm:8 modulational:1 solv:1 jetp:5 distribution:1 topology:3 both:3 numerically:1 many:2 taking:2 according:1 distinguished:1 propagation:1 connection:1 genus:6 whole:1 ck:3 english:1 afterwards:1 point:5 simple:1 corresponds:3 dimensional:2 consideration:7 v2k:3 moreover:2 fruitful:1 math:16 accomplishing:1 described:3 transformations:3 basis:3 addition:2 locally:3 three:3 been:5 int:1 much:1 interest:1 abstract:1 systems:2 oth:1 generating:9 corresponding:5 xxx:1 uncommon:1 gap:5 tightened:1 6u:1 func:1 c2:9 c1:14 surveys:4 present:3 case:16 multi:1 splits:1 unlike:1 krylov:5 akad:1 frequences:2 examine:1 value:11 aim:1 coalescing:1 intas:1 aid:1 region:1 procedure:1 real:11 seven:1 vol:1 vi:3 vj:10 thus:1 surface:14 equal:1 ii:1 strain:1 itself:2 ready:1 different:1 sharapov:1 grant:2 russel:1 make:1 government:1 same:1 complex:1 emphasize:1 φk:9 independent:2 arrives:2 see:9 cubic:1 nonanalytical:1 numerical:1 upon:1 monotonic:1 flows:6 hand:2 parametrized:2 moment:1 edges:1 infinite:2 normalization:3 recent:1 off:1 modes:1 depending:1 well:1 obviously:2 components:1 sets:1 position:1 soviet:1 left:2 nonanalytic:1 generally:4 obtain:3 rest:2 marsch:1 intervals:1 λg:11 thanks:1 immediately:1 useful:1 yet:1 conclusions:1 zakharov:1 conclude:1 hoppe:1 wright:1 nato:1 lett:3 transformation:1 euler:2 take:1 identical:1 represents:3 unlimited:1 possible:1 plenum:1 five:2 press:1 turbulence:1 theor:1 imposed:1 like:6 follows:4 reduces:1 specific:1 remind:1 korteweg:1 either:2 integrals:1 arbitrary:15 topologically:1 right:1 some:7 b0:2 choosing:1 specified:2 kdv:23 matching:4 scale:1 describing:1 avoid:1 investigations:1 integration:2 overlap:2 does:4 decomposition:1 provides:4 venakides:2 eisenhart:3 proc:1 mode:1 ij2:1 bg:2 deleted:1 equivalent:1 oscillating:1 bj:1 bk:1 step:1 permitted:1 stage:4 comparison:1 carried:1 novikov:5 introduces:1 o:1 compatible:2 a2:1 characterized:1 together:1 duke:1 soc:1 pergamon:1 into:12 within:1 integral:2 domain:6 hyperbolicity:4 due:1 lies:1 appropriate:3 references:1 determine:1 sov:4 proportional:1 abel:4 descibed:1 additional:6 her:1 suffice:1 initial:34 transform:1 dispersion:2 start:2 conservation:2 way:5 was:8 naturally:1 function:18 complete:1 form:19 soliton:1 forming:1 δkm:1 eastman:1 but:1 construction:2 solar:2 russian:7 removed:1 true:1 made:2 characteristic:6 2πk:1 smooth:3 ωt:1 us:5 theoretical:1 krichever:2 placed:1 below:2 limit:3 levermore:4 demonstrate:2 problem:24 clear:1 instead:1 pij:3 ag:2 qij:3 defined:6 certain:3 ak:9 aj:1 am:1 direction:1 proven:2 general:12 globally:1 single:17 dλ:8 formulation:1 commuting:6 check:3 constructed:5 functions:17 courant:1 when:7 valid:3 remarks:1 branch:3 papers:1 out:3 applications:1 briefly:2 superposition:1 a1:1 a0:2 a3:1 important:4 bounded:1 variable:5 proceeding:1 goursat:1 independently:1 regime:1 using:4 dω:18 assume:1 cauchy:2 required:1 curve:7 governed:1 xbr:1 arisen:1 time:4 international:2 requires:1
|
solv-int9512004.txt |@word vessiot:1 gu:1 partial:1 consider:4 gq:3 results:1 ds:1 gx:1 leads:2 commute:2 generalize:1 gb:1 ga:7 edu:1 constants:1 follow:2 expressions:1 gj:2 causes:3 soc:3 preserves:1 inverse:2 depend:5 albrecht:1 paris:2 vinogradov:2 equivalence:1 encourage:1 γt:1 quasi:2 erentiels:1 arisen:1 th:3 hermann:1 aux:1 presentation:1 subtleties:1 g2:4 g1:12 g0:6 far:1 end:1 choice:3 lecture:1 existing:1 entire:2 wetensch:1 etudes:1 level:4 did:1 cause:1 notes:1 integrating:1 list:1 solution:11 fewer:1 pullback:1 solved:1 vector:17 minimal:1 realization:5 gauge:3 saveliev:2 originally:1 homomorphism:1 smaller:1 consistent:1 direct:1 messy:1 zero:7 zx:1 zy:4 chen:1 further:2 xf2:1 odd:2 theory:1 even:6 nonlinear:2 appear:3 contemp:1 sum:1 expressed:2 reminiscent:1 version:2 gi:4 above:2 new:9 avenues:1 increasing:1 method:1 etriques:1 coefficient:2 edited:1 evolving:1 led:1 realizations:6 leurs:1 here:1 understanding:1 desired:1 objects:1 tangent:4 others:1 adjoined:1 path:1 along:2 sine:4 equations:24 obtained:1 search:1 involved:1 leaves:1 vectors:1 leaving:1 recently:2 products:1 θa1:1 usually:2 california:1 silbermann:1 studies:1 sci:1 via:3 followed:2 f1:16 france:1 requiring:3 f2:7 replace:1 pf1:1 a23:1 limn:1 summation:1 total:3 schief:1 select:2 contragredient:3 standing:1 derivatives:4 use:1 would:5 commun:1 distinct:5 e1:8 contains:2 determined:1 chooses:1 e0:2 therefore:3 taken:1 generators:8 themselves:2 type:5 tell:3 minor:1 more:4 introducing:1 coupled:1 becomes:2 operators:8 curvature:7 berlin:1 particular:1 known:1 projective:1 cases:1 cornelius:1 iii:8 must:6 erieurs:1 springer:2 valued:3 dodd:2 science:1 equation:14 work:4 mj:7 infinitesimal:1 values:2 achieve:1 following:4 making:1 dec:1 ulf:1 example:4 most:1 f0:8 wedge:1 sub:1 triple:2 give:1 process:6 expanding:1 involve:1 assumptions:1 cartan:5 allowed:1 xac:1 standard:1 uab:1 robinson:4 occur:1 dxa:2 verlag:3 information:3 respective:1 requirements:3 grenander:1 divided:2 hugo:1 dwb:3 dwc:1 dwa:1 before:2 acta:5 sin:2 fp:2 map:1 proc:2 description:1 algebra:20 may:6 fy:1 earlier:4 mapping:1 applications:4 shadwick:4 fi:3 fj:3 truly:1 compatibility:1 fn:2 introduced:1 dynamical:2 effective:1 twisting:2 explicit:1 cascade:1 maintain:1 so:8 allow:2 sl:4 definitions:1 pulled:1 order:4 restriction:4 pa:1 indeed:1 over:13 satisfied:1 characteristic:1 abstract:1 course:2 banach:4 existence:1 still:5 eb:3 its:4 pirani:3 leznov:2 le:1 group:3 how:1 interesting:4 solving:1 lj:3 coordinates:13 writing:2 forms:11 systems:2 constitutes:1 jacobi:1 derivative:1 gel:2 defining:3 setting:2 prolongations:3 non:4 h1:1 motivated:2 pseudopotential:1 thereby:1 wolfgang:1 acklund:5 mention:1 qr:2 they:3 now:4 nor:1 kirillov:3 2u:2 term:1 finite:2 equality:2 kersten:2 always:1 university:2 presented:1 diverging:1 mode:2 reasonable:2 each:7 found:2 identifies:1 higher:2 side:1 constraints:2 em:10 arxiv:1 ei:10 wα:2 ek:1 simplicity:1 series:1 ea:4 related:2 prolonged:1 constitute:1 society:1 extended:2 amsterdam:1 substantially:1 our:6 ew:6 pseudopotentials:4 eq:1 fu:2 rt:3 large:1 shown:2 matrix:2 space:5 restricted:3 since:5 rev:1 douglas:1 content:1 re:1 contained:1 write:1 denoted:1 rm:2 ref:2 ri:1 independence:2 shows:1 fiber:3 linear:8 frank:3 maintains:1 eck:2 albuquerque:1 free:1 quite:7 difficulty:2 ect:2 complicated:2 york:2 intermediate:2 subalgebras:1 dubna:1 beginning:1 generate:6 e2:8 created:1 determining:2 could:1 kon:1 voor:1 times:1 2πi:2 american:1 gordon:4 δij:1 netherlands:2 parallel:1 view:1 think:1 first:10 origin:1 intuition:1 already:1 roelofs:2 xb:4 xc:1 variables:11 xa:11 number:3 lond:1 restrict:1 multiplying:1 done:3 least:2 another:3 centrum:1 indices:1 angular:1 given:2 bracket:1 kluwer:1 jet:8 indicate:1 eqs:9 system:7 relations:3 zσ:2 their:8 assumption:1 twente:1 convention:1 siam:1 scheme:1 structures:2 gives:5 him:1 option:3 exactly:3 eliminates:1 sciences:1 part:4 too:1 somewhat:1 copy:1 than:2 coefficients:5 begins:1 john:2 third:2 gabor:1 isolation:1 second:3 listeners:1 classes:1 publ:1 were:3 radius:1 naturally:1 treated:1 remembers:1 published:1 symmetries:5 modern:1 generalization:1 say:1 inequivalent:3 need:1 seen:1 seem:1 gradings:1 any:4 emes:2 relatively:1 lie:4 built:1 depending:2 convenient:1 ideas:1 note:1 k2:11 ideal:7 contact:6 generalized:3 zu:2 techniques:1 bernd:1 kac:2 begin:2 akad:1 unless:1 investigations:1 who:2 chart:1 birkh:1 algebraic:1 petrov:2 meaning:1 multiply:1 commutation:1 kb:1 ka:1 calif:1 treats:1 prolongation:8 considered:1 kj:1 removed:1 phil:1 flow:3 kn:1 km:4 martini:2 countable:3 ext:1 hi:4 elie:1 sorts:1 wiskunde:1 zyy:2 physics:5 notion:1 fact:2 quantity:1 precise:1 saying:1 show:3 reductions:1 discovered:1 spaces:6 relation:1 solutions:11 wahlquist:5 trivial:1 find:1 q0:7 believe:1 commutators:10 homomorphic:2 should:1 only:9 explicitly:1 believing:1 integrate:1 integrable:1 circle:2 local:3 hopf:1 hope:2 sur:1 dn:4 do:1 his:1 subspaces:1 cons:1 dependent:3 syst:2 express:1 db:3 dc:1 da:5 next:1 ones:1 dz:11 negative:1 dx:25 dy:24 combinations:3 dw:4 dt:2 du:3 geometric:1 dp:2 dq:1 closure:1 evolution:5 resolve:2 covering:2 fields:9 differential:6 twice:1 involutive:2 double:1 qi:1 qj:1 qm:1 carrier:1 qn:4 krasil:2 set:10 art:1 ser:1 physically:1 j0:2 j1:3 module:3 j3:1 see:1 computer:1 geometrically:1 terms:4 janet:1 αr:2 wa:11 ways:1 below:1 yet:3 symmetric:2 smallest:1 identification:3 zakharov:1 closed:2 simplest:3 progress:2 neither:1 equiv:1 approach:9 knowing:1 notice:1 wc:2 shabat:1 vertical:5 complementary:1 adjoint:1 however:8 jm:1 reproduces:1 ji:1 jj:2 jk:2 solv:1 amer:1 both:3 cos:2 parentheses:1 2n:1 pdx:1 many:3 taking:1 jn:2 presentations:1 conference:1 etc:4 connection:2 les:2 pde:30 holonomic:1 acceptable:1 unm:2 otherwise:1 ck:1 among:2 ch:1 co:4 cn:1 point:3 simple:4 seems:3 berkeley:1 dimensional:4 cx:1 simply:1 izvestija:1 lagrange:3 respect:1 li:1 cu:2 math:11 considering:1 better:1 ensures:1 described:5 transformations:4 basis:3 addition:1 locally:1 three:3 been:3 basel:1 defined:7 faithfully:1 describes:3 maintenance:1 xaa:2 algebras:10 pn:2 universal:2 choose:2 conte:1 direction:2 corresponding:1 unidentified:1 solitons:1 estabrook:7 bull:2 resultant:1 spin:1 those:7 c4:1 case:5 look:2 partielles:1 value:2 transformation:2 will:9 dept:1 while:1 suppose:1 ought:1 behavior:1 aij:3 situation:1 study:1 procedure:1 k1:2 studied:3 a25:2 mexico:1 vol:2 ned:1 them:3 uxy:3 ii:1 characterize:1 dual:1 df:1 return:1 vanish:2 finds:1 different:4 fibers:4 generic:1 lett:1 same:2 tells:1 nδ:1 complex:1 emphasize:1 largest:1 resulting:4 several:2 subalgebra:4 grows:2 difficult:1 independent:11 used:3 paths:1 mathematicae:4 hoenselaers:6 pick:1 upon:2 effect:1 flows:3 hand:2 pubs:1 action:1 viewing:1 levels:1 uses:1 auser:1 student:1 potentials:1 infinite:9 interested:1 ablowitz:1 identity:2 eigenvectors:1 task:2 center:1 expression:1 ua:1 no:6 well:2 analysis:2 obviously:1 academic:2 directly:1 without:1 solve:1 components:3 coordinate:4 dimension:2 researchers:1 usual:3 fand:2 manifold:1 graded:1 just:3 less:1 being:2 applicandae:1 ottcher:1 press:2 transforms:1 integer:1 useful:1 scattering:2 guides:1 boccara:1 villars:1 adr:2 eriv:1 generator:1 infinitely:1 thinking:1 onward:1 character:1 except:2 cc:3 k0:5 maintaining:1 moody:1 remaining:3 momentum:1 take:2 applic:3 eigenvalue:1 repetitions:1 sums:1 possible:4 spanned:1 integrations:1 testa:1 finding:2 quest:1 ej:2 vacuum:2 ye1:1 using:5 unique:2 mod:1 desire:1 theor:2 like:2 alternatively:2 reduces:2 ees:1 loses:1 separately:1 ai:3 integrals:1 james:1 denis:1 weiner:1 reduced:1 replacement:2 mathematical:3 reidel:1 right:1 methods:2 subideal:2 some:9 back:1 ideals:2 linearly:5 growth:7 nonetheless:2 choosing:2 diff:1 proper:1 kdv:1 provided:1 describing:1 lead:3 affects:1 centre:1 integration:4 providence:1 does:1 eliminate:1 provides:2 assuming:1 trautman:3 demonstrated:1 refer:1 pr:2 object:1 l0:1 power:1 performed:1 equivalent:4 continuing:1 bu:2 step:1 polynomials:1 although:1 downward:1 gauthier:1 integers:1 about:1 carried:1 a0:1 dependence:4 o:1 pz:1 important:4 act:1 referred:1 slightly:1 other:2 minoru:1 computational:1 h2:1 into:4 within:8 integral:1 functional:2 j2:1 ut:2 en:3 references:1 determine:3 einstein:1 proportional:1 reducing:1 lifts:1 van:2 additional:2 area:1 there:2 transform:2 board:1 dropping:1 way:1 labelling:2 was:2 assumes:1 toeplitz:5 function:2 considerably:1 form:12 szeg:1 removes:1 but:5 hj:1 repeated:1 construction:1 ec:1 larger:1 encoded:1 segur:1 highest:1 partially:1 vectorfield:1 made:2 rogers:1 versions:1 uu:1 coordinatize:1 us:14 theoretical:1 dordrecht:1 ωk:4 un:1 iterated:1 coverings:1 problem:5 define:3 similar:1 ab:4 constant:2 ad:24 af:1 int:1 countably:1 ak:5 describe:4 dga:1 general:6 ar:1 exist:1 shchik:2 formulation:1 operation:2 mciver:2 defines:1 functions:4 faithful:2 variety:3 when:6 multipliers:3 field:9 conditions:3 details:1 appending:1 mathematics:2 out:1 finley:5 nice:1 conclude:1 elements:3 generates:1 ru:1 problems:2 bundle:3 much:2 a1:12 commutator:4 generated:8 a2:12 log:3 variable:2 astronomy:1 needed:1 structure:5 gibbon:1 longer:1 informatica:1 required:1 pseudo:1 eom:1 lift:2 came:1 requires:4 original:2 xbc:1
|
solv-int9512005.txt |@word sci:1 consider:6 results:1 leads:5 grateful:1 expressions:1 inverse:2 petersburg:2 th:4 under:1 te:8 conjecture:1 supported:1 straightforward:2 choice:1 interpreting:1 difference:3 matrices:2 condition:2 school:1 solution:4 leave:1 discrete:14 math:1 eigenvalues:1 programme:1 villa:1 zero:3 zx:1 linear:4 bilinear:3 plays:1 xσ:1 section:1 axes:1 maillet:5 current:1 version:1 above:1 new:1 method:2 3d:2 satisfy:2 respectively:1 spacing:1 here:1 others:1 represented:1 sine:1 equations:6 interpret:1 obtained:3 institute:1 vectors:2 suggests:1 permutation:4 action:1 suitable:1 substitution:3 private:1 b224:1 linearly:1 takes:1 nijhoff:3 positive:1 contains:1 suppl:1 next:1 vol:3 nucl:1 associated:9 type:1 historically:1 more:1 fontanka:1 operators:1 curvature:3 particular:2 known:1 chiral:1 valued:2 equation:34 work:1 theories:1 values:1 following:14 dec:1 stimulating:1 proof:2 claim:1 korepanov:11 solved:1 december:1 permutations:2 smirnov:1 pushed:1 numbers:1 sense:1 exclude:1 enslapp:4 rescaling:1 g1:1 discussion:1 holds:2 write:1 how:2 ens:1 3dimensional:1 massive:1 fr:1 algebra:2 may:1 derived:2 mapping:5 lax:1 italy:1 associ:1 dynamical:6 correspond:1 st:2 sect:4 definitions:1 order:1 help:1 hierarchy:2 interpreted:3 held:1 paper:1 through:5 statistical:2 japan:1 satisfies:2 steklov:1 group:2 xl:4 singular:1 exact:1 solving:1 coordinates:3 absence:1 systems:5 mail:1 1dimensional:1 them:2 conversations:1 introduce:3 repulsive:1 identically:1 multidimensional:1 now:5 yu:1 2πr1:1 2r:1 2d:1 universit:1 baxter:5 el:3 arxiv:1 ek:3 ej:12 ee:2 series:1 idea:1 related:6 inhomogeneous:2 toda:3 quantum:7 shown:1 rw:1 matrix:1 involution:5 since:1 rev:2 wholly:1 content:1 zap:1 rational:1 ri:2 rj:11 limλ:1 theory:3 standard:1 completely:1 e4:2 e1:13 e3:13 e2:12 r6:2 interaction:1 r1:14 r2:14 r3:19 gordon:1 bkp:3 βj:3 first:5 xj:6 xk:5 symmetry:1 variables:3 xz:1 relations:2 another:2 open:1 maple:1 ser:1 given:1 rewritten:2 introduction:1 lapp:1 system:7 construct:2 their:1 intermediate:1 identity:7 calculations:1 potts:1 gives:1 abovementioned:1 continuous:6 nauch:1 x2:6 x3:4 x1:4 pomi:1 coefficients:2 18b:1 kind:2 imply:1 str:12 were:1 russia:1 jpn:1 rewrite:1 ann:1 generalization:2 cumbersome:1 any:3 latter:2 physique:1 note:2 generalized:1 heisenberg:2 formulas:1 cnrs:1 acquire:1 electric:6 gλ:3 algebraic:1 connected:2 letter:1 formulae:4 ura:1 considered:4 partition:1 yang:4 exp:1 physics:2 notion:1 fact:1 particularly:1 show:2 λrj:1 discovered:1 miwa:6 relation:5 solutions:12 substituting:1 analogue:1 networks:6 egion:1 parameters:4 specified:1 varenna:1 should:3 only:1 integrable:15 local:13 triangle:14 dependent:1 de:4 international:1 du:1 dq:1 differential:5 summary:1 fixed:2 body:1 set:5 constructing:1 j2:2 see:1 computer:1 lyon:3 satisfying:2 exponent:1 symmetric:3 enough:1 identification:2 simplest:2 fermi:1 αj:3 europe:1 recently:1 matveev:1 however:1 solv:2 ja:1 both:1 last:1 x2j:2 many:1 ir2:1 ybe:14 context:2 whole:1 comment:1 affine:1 dimensional:9 respect:3 described:3 transformations:1 three:6 been:4 int:2 define:7 corresponding:9 commutes:1 quantities:1 subspace:1 gap:1 c1:1 case:1 tetrahedron:4 ǫn:2 while:1 replaced:1 au:1 studied:1 century:1 iq:1 thus:2 non:2 quantize:1 itself:1 id:2 verified:1 author:1 make:1 same:1 clearly:1 complex:2 proved:1 finite:1 composition:2 independent:1 used:1 laboratoire:1 numerical:1 enrico:1 infinite:2 expand:1 well:1 analysis:2 academic:1 coordinate:4 model:15 dimension:1 φijk:1 usual:1 being:3 obtain:2 underlying:1 identify:1 using:1 scattering:2 multiples:1 alpes:1 preprint:1 parametrization:1 lattice:6 lett:3 easy:1 theorem:6 annecy:1 solvable:1 transformation:12 real:1 involutions:1 eorique:1 press:1 integer:1 generated:3 reshetikhin:1 like:1 follows:2 reduces:3 steps:1 reduced:1 gauge:1 mathematical:1 acad:1 lectures:1 kashaev:2 some:6 somehow:1 b1:2 b2:2 b3:2 proper:2 delivered:1 est:1 dimensions:2 comments:1 unit:1 proc:2 savoie:1 faddeev:3 power:1 equivalent:2 bj:2 qˆ:3 relating:1 central:1 prove:2 discussed:1 ξj:1 o:1 act:1 eight:1 introduced:3 exactly:1 soc:1 communication:1 into:1 numerically:1 functional:2 hermitian:1 references:1 sov:1 operator:10 france:1 log:1 there:1 italie:1 way:2 forward:1 sections:1 function:9 form:8 analyse:1 gaussian:1 delta:1 he:1 up:1 us:1 resultants:1 limit:10 verification:1 problem:2 similar:2 called:1 mechanics:1 interval:1 constant:1 defined:5 certain:1 abstract:1 aj:5 conserved:1 pˆ:1 formalism:1 check:1 constructed:4 functions:4 integrability:1 no:1 resistances:1 multipliers:1 field:3 role:1 branch:1 massless:1 star:14 calculating:1 models:9 time:1 vertex:1 semin:1 a1:7 bolzmann:1 a3:7 a2:6 ising:8 variable:1 sides:1 acknowlegements:1 implies:1 auxiliary:1 space:3 together:1 weights:1 hirota:6 n1:2 n2:2 n3:2
|
solv-int9512006.txt |@word argyres:1 magnetic:1 results:2 scalar:1 commute:1 generalize:1 yankielowicz:1 compact:1 inverse:1 lerche:1 charge:5 funk:2 elliptic:3 under:1 presentation:1 ingredient:1 v11:1 string:1 very:5 zachos:2 witten:1 every:1 exact:1 deformations:5 riemann:3 z12:9 large:1 solved:1 3b:1 anal:2 refer:2 unexpected:1 tel:2 renormalized:1 mussardo:1 sign:2 surrounding:1 invaded:1 cft:8 obey:1 appear:1 d2:6 section:4 expressed:1 version:1 above:7 new:2 3a:1 method:5 satisfy:1 degree:1 here:3 ranges:1 reported:1 explore:1 address:2 path:1 along:2 equations:1 z1:4 z2:14 z3:1 obtained:2 search:1 institute:1 study:1 studied:1 slq:1 action:2 resonance:3 fateev:2 changes:1 br:1 requiring:1 should:2 virasoro:2 takes:1 commun:2 negative:1 few:1 nucl:4 therefore:6 taken:1 compactly:1 theoretical:2 today:1 more:2 untwisted:6 israel:1 duality:1 started:1 becomes:2 operators:5 stanishkov:1 particular:6 known:2 nepomechie:2 account:1 integrating:1 ashkin:1 avoiding:1 equation:2 work:2 iα0:2 theories:2 taup:1 values:4 mp:1 following:5 closing:1 example:2 proof:1 tau:1 calculation:2 states:1 sphere:4 minimum:1 sense:2 counting:2 simple:2 end:1 discussion:5 write:1 maps:1 pure:1 parameter:1 map:1 product:1 algebra:9 may:3 plane:1 z23:1 meaningful:1 constants:1 short:1 sectors:1 sp:6 st:1 ones:1 correlation:1 representation:1 order:1 over:1 years:1 paper:1 statistical:1 shake:1 mentioned:1 existence:1 still:1 lsz:1 its:1 before:1 sλ:6 group:5 personal:1 affine:2 aviv:2 choose:1 cotta:1 mail:2 main:1 deformation:1 cft1:1 them:2 propose:1 primary:4 scaling:1 mention:1 mezincescu:2 they:1 1b:1 now:1 day:1 teller:1 possess:1 2t:2 university:2 2g:1 2a:2 2b:2 found:2 constraints:1 weight:2 series:4 energy:1 revised:1 used:2 extended:1 expect:1 quantum:9 our:4 special:2 out:2 category:1 living:1 matrix:4 space:2 restricted:1 rep:1 rev:2 denotes:1 particles:1 investigation:1 reader:2 ref:1 reg:3 math:4 theory:9 8b:1 8a:1 diagonal:1 free:1 quite:1 completely:1 costas:1 8p:2 generate:1 revolutionary:1 fixed:4 area:1 turn:1 βg:2 massive:3 generalizations:1 first:1 symmetry:4 subtlety:1 number:2 martellini:2 open:1 given:5 perturbation:1 introduction:1 twisted:5 relations:2 1a:1 their:3 perturbations:3 seiberg:1 statement:1 ramusino:1 hyperelliptic:1 klemm:1 assumption:1 favorable:1 authors:2 appearence:1 completes:1 determines:1 double:1 integrability:3 project:1 determined:1 spoiled:1 minus:1 vx2:1 7b:1 7a:1 zamolodchikov:4 argument:2 b398:1 seek:1 any:1 solitons:1 lie:1 built:1 depending:1 able:1 ideas:1 note:1 analogy:1 kac:1 added:1 electric:1 opposite:1 vnm:4 sl:2 most:1 beta:1 sheets:1 pair:1 monodromies:4 extremely:1 commutation:1 z31:1 considered:4 cover:1 points:2 physics:6 fact:2 laws:1 sector:11 hyper:3 phenomenon:1 γnm:1 infrared:1 fletcher:1 trivial:6 finally:1 knowledge:1 topological:1 yerphi:1 bernard:1 only:3 explicitly:1 factor:1 integrable:19 local:3 dn:1 do:1 means:1 lukyanov:2 cannot:2 dz:6 dx:1 despite:1 during:1 fields:8 arxiv:1 expansions:1 rinaldi:1 cycles:1 modulo:1 constructing:1 cuts:1 p2g:2 maximum:1 relative:3 see:1 result:1 acquires:1 surfaces:8 preparation:1 tensor:1 review:1 written:1 various:2 conditions:3 notice:3 terms:1 punctured:1 however:4 vanishing:1 concentrate:1 armenia:1 solv:2 last:1 many:2 equal:1 etc:1 genus:3 finds:1 among:3 relevant:5 point:5 reasons:1 corresponds:1 dimensional:1 simply:1 polynomial:1 respect:1 considering:1 described:1 basis:1 due:1 been:9 pmin:3 defined:4 much:1 interpret:1 basic:2 algebras:3 lett:6 6a:1 6b:1 corresponding:3 quantities:1 gas:1 present:1 case:2 examine:1 will:2 while:2 monodromy:1 conformal:6 bonora:2 aa:4 unitary:4 almost:3 sotkov:1 non:7 surface:2 il:1 mod:1 currents:4 sensitive:1 generic:2 make:1 same:1 arguments:1 φk:2 higher:2 development:1 investigated:1 flows:1 v1:3 infinite:2 felder:1 center:1 charges:9 studies:1 well:1 analysis:1 model:7 arising:1 dimension:1 usual:2 stringent:1 graded:1 proposed:1 vαβ:1 obtain:1 rest:1 underlying:1 faraggi:1 alternative:1 hess:12 scattering:2 adv:1 rapid:1 discuss:1 appeared:1 interested:1 developments:1 iπ:1 guarantees:1 5a:2 momentum:1 5b:2 aspects:2 iα:2 progressed:1 vγ:1 background:1 press:1 using:1 usually:1 moody:1 ˆba:8 continue:2 indication:1 either:1 5c:1 yerevan:2 mathematical:1 parity:1 namely:1 some:2 suppl:1 moreover:2 slice:1 lead:1 shall:2 comments:1 proc:1 minimal:6 mode:1 ba:1 problems:1 equivalent:1 expansion:1 plb:1 although:1 exciting:1 hilbert:2 asymptotic:2 central:1 novikov:3 fairlie:1 discussed:2 o:3 act:1 perturbed:5 cambridge:1 letter:3 communication:1 into:2 copies:1 references:1 determine:2 sov:1 operator:3 additional:1 hes:5 there:6 appl:2 bosons:2 way:1 was:1 braiding:1 function:1 hard:1 complete:1 form:5 but:2 construction:2 related:1 longer:1 places:1 leclair:2 2πi:5 up:2 krichever:3 problem:1 similar:3 mechanics:1 ac:1 constant:4 int:3 abstract:1 am:1 direction:1 denote:3 twist:1 conserved:6 formalism:1 constructed:4 functions:1 nm:6 no:2 when:3 field:9 other:1 nuyts:1 papers:2 department:2 massless:3 briefly:1 models:25 symbol:1 vertex:1 15a:1 meaning:2 15b:1 a4:1 astronomy:1 russo:1 structure:2 independently:1 coupling:3 coulomb:1 knizhnik:1 requires:1 ryder:1 weights:5 time:1 4d:1 4b:2 4c:2 4a:3
|
solv-int9512007.txt |@word consider:3 funct:1 desirable:1 results:3 leads:2 eds:2 proposition:4 computation:3 follow:1 expressions:2 gl:5 whose:1 inverse:2 const:3 tu:1 tr:6 γk:47 finally:1 γm:1 under:2 tr0:1 subtleties:1 belonging:1 zhang:1 ieice:1 every:4 summarized:1 discretizations:6 difference:11 matrices:16 condition:3 obvious:1 hamiltonian:14 turns:2 notes:1 solution:3 deals:1 solved:1 interpolating:3 small:2 anal:1 inspection:3 unversity:1 upper:2 lecture:1 direct:2 approximation:2 second:3 perspective:1 further:3 odd:1 bilinear:2 nonlinear:2 appear:3 brackets:2 diag:1 sum:1 analogously:1 version:1 fuchssteiner:1 above:1 new:4 consisting:2 mem:1 respectively:2 even:1 here:6 papageorgiou:1 tangent:1 groups:1 represented:2 depend:3 along:1 equations:15 implicit:7 change:2 obtained:1 remark:2 shift:1 leaves:1 changed:1 leaving:2 exemplifies:1 periodic:15 poisson:13 advantages:1 uniquely:2 formulated:2 family:1 highly:1 brought:1 use:1 asymptotic:1 would:2 prove:8 remains:1 positive:2 contains:1 negative:2 live:1 call:1 opposed:1 m2:1 means:1 volterra:5 type:3 more:3 fractions:1 sharing:1 formally:1 successful:1 becomes:1 operators:1 particular:6 cases:9 hold:1 producing:2 must:4 springer:1 valued:1 cas:1 recall:1 equation:29 modified:2 values:2 capel:1 following:13 example:1 proof:10 beautiful:1 give:3 relativistic:2 want:1 conversely:3 simple:2 dk:2 needs:1 end:13 rather:2 holds:1 how:1 hαk:26 ordinary:1 parameter:3 priori:1 map:8 product:1 proc:1 algebra:3 may:11 suppose:1 oscillators:1 after:1 inessential:1 orbits:1 applications:1 levi:1 lax:19 multiplication:1 representations:1 compatibility:3 dynamical:2 third:1 interpolated:4 computations:1 light:1 schneider:1 explicit:1 deutsche:1 so:9 representation:5 first:9 order:1 restriction:1 recurrent:9 interpretation:5 hierarchy:1 indeed:4 over:2 spectral:1 soc:1 years:2 paper:2 through:3 differs:1 existence:1 its:3 derive:1 group:7 maps:4 πkj:3 continued:4 unity:2 conjugation:2 li:1 h2:11 lt:2 drawback:1 systems:22 mail:1 hidden:1 main:1 defining:4 setting:1 non:2 combination:3 lambert:1 framework:1 they:1 now:2 yu:6 easily:1 term:7 several:1 dirac:1 sufficiently:2 ussr:1 each:2 found:6 side:4 associative:1 baxter:1 arxiv:1 invoked:1 ek:34 simplicity:1 series:2 related:1 applicable:2 moser:3 toda:5 our:3 neighbourhood:5 out:1 matrix:30 discrete:27 gradient:1 lagrangian:1 chaos:1 research:1 particles:1 replacing:2 izv:1 reader:2 formula:8 rn:3 ref:1 correct:2 math:9 linear:2 coef:3 derived:1 diagonal:2 free:1 standard:1 admits:7 completely:3 complicated:1 yuri:1 subalgebras:1 ruijsenaars:1 generate:1 definition:2 via:1 itoh:2 excluding:6 motion:1 turn:4 hence:1 generalizations:1 βj:2 βk:105 origin:1 there:6 someday:1 variables:3 number:2 rank:1 twisted:2 done:1 least:4 precisely:1 open:13 given:5 checked:1 rewritten:1 introduction:1 eqs:1 system:24 construct:1 their:2 appl:1 calculations:2 justified:1 dfg:1 scheme:4 relations:13 fraction:4 continuous:6 serve:6 recurrences:2 coefficients:3 was:6 approximations:1 see:4 winternitz:1 future:1 yang:1 letters:6 were:3 lotka:1 enables:1 powers:2 symmetries:2 rewrite:2 argument:1 generalization:1 factorizations:2 close:1 seen:1 seem:1 any:3 solitons:1 complete:2 lie:1 εx:1 depending:1 calogero:2 potential:1 take:6 coincide:2 analogs:2 subscripts:5 convinces:3 antoniou:1 trace:1 shall:8 trφ:1 algebraic:1 regular:5 germany:1 ht:19 successive:2 pair:2 numerous:1 soliton:1 laurent:2 observation:1 considered:4 kj:1 clear:1 flow:8 bracket:6 principle:2 exp:1 physics:10 section:2 fact:5 nlp:1 oevel:1 reductions:2 supported:1 recipe:1 notations:1 bring:1 spaces:1 relation:5 solutions:3 find:2 based:1 explain:1 should:2 jan:1 only:11 explicitly:1 postfach:1 factor:11 integrable:18 constant:7 hamiltonians:1 hope:3 do:2 dm:4 dj:1 subspaces:1 get:13 de:1 dc:2 famous:1 ones:1 suris:8 report:2 lattices:28 admissible:1 αk:22 evolution:6 approach:3 differential:1 factorization:5 method:1 financially:1 qd:1 pang:1 view:1 hλ:2 set:6 computed:1 exists:1 hη:2 namely:4 recently:1 analog:2 subject:1 satisfying:4 expert:1 nondegenerate:1 pattern:2 representatives:1 symmetric:2 enough:3 oishi:1 simplest:3 invariant:3 boundary:1 conditions:1 notice:3 terms:6 attention:1 however:1 veselov:2 jm:5 key:1 solv:2 amer:1 come:1 received:1 last:13 taking:1 equal:7 etc:1 admit:2 symplectic:2 context:1 attributes:1 expression:5 combinatoric:1 sake:1 hvk:6 ch:1 point:1 appeared:1 corresponds:1 cd:2 dimensional:3 respect:5 peakons:1 cp:1 kp:3 nijhoff:3 described:1 basis:1 suppressed:1 skew:1 three:2 kuznetsov:1 defined:8 reduction:3 workshop:1 algebras:2 abstract:1 define:1 field:1 describe:1 families:1 finishes:2 both:5 quantities:9 formed:2 subspace:1 gen:2 general:8 present:4 case:33 intriguing:1 value:6 will:3 while:3 proves:4 replaced:1 applies:1 bogoyavlensky:18 loop:3 garnier:1 vj:1 vk:50 them:1 according:1 dη:2 containing:1 author:1 belong:6 same:4 stimulated:1 complex:2 hierarchies:3 finite:5 subalgebra:2 tedious:2 literature:1 upon:1 flows:2 hand:4 moment:3 uni:1 infinite:7 a2k:2 reference:1 subgroups:2 lower:2 suffices:2 well:3 tsujimoto:1 without:1 solve:1 sets:2 position:1 model:3 unities:1 just:2 less:1 being:1 hγk:33 resp:4 obtain:2 underlying:2 tilde:1 λj:2 λm:4 previous:2 visualization:1 haj:1 hak:39 preprint:1 hint:1 seems:1 lattice:29 belongs:2 lett:4 easy:1 theorem:13 gave:1 deift:1 read:1 admitting:2 integer:1 unique:2 formal:1 theor:1 like:2 semi:1 identifying:1 systematically:3 follows:2 serves:2 collect:1 integrals:1 ha1:1 ha2:1 conclusion:1 reduced:1 right:6 leningrad:1 classical:2 sequence:1 some:11 examples:2 moreover:2 kdv:1 provided:1 avoid:1 centre:1 does:3 decomposition:1 provides:1 assuming:2 prog:1 chains:1 equivalent:16 continuing:1 bi:1 ragnisco:2 actual:3 extension:1 most:1 dd1:4 commun:2 dependence:1 o:6 covariant:2 extensions:1 introduced:2 automatically:1 discretization:6 computational:1 statements:6 previously:1 into:3 multiply:1 square:1 references:1 neumann:1 log:3 strictly:1 initial:2 quadratic:2 way:3 mappings:3 sections:1 function:11 elsewhere:1 form:19 triangular:4 but:2 construction:3 repeatedly:1 counterparts:1 hc:2 ha:1 considerable:1 compute:4 algorithm:1 consist:1 versions:3 2πi:1 ut:3 ωt:2 us:2 discretized:1 below:2 demonstrate:1 problem:7 called:1 definitions:3 proved:1 int:3 certain:4 ak:176 aj:5 denote:1 conserved:1 enable:1 exist:1 formulation:3 corresponding:10 dε:1 defines:5 nh:9 again:9 functions:9 integrability:3 no:2 mathematik:1 tomei:1 bremen:3 application:2 other:2 role:1 special:2 papers:1 techn:1 nice:2 generates:3 hirota:1 problems:1 polynomials:1 recent:2 included:1 generalized:2 structure:5 independently:1 implies:7 auxiliary:1 using:4 vinet:1 space:3 orbit:1 time:32 dϕ:4 starting:2 original:1 once:2
|
solv-int9512008.txt |@word proposition:4 sci:3 consider:1 chain:1 similarity:1 pairing:1 pseudodifferential:1 results:1 invent:1 eds:6 ge:1 commute:3 generalize:1 douglas:1 houches:1 edu:1 intricate:1 oevel:1 denotes:2 3m:2 whose:2 preserves:1 inverse:1 const:1 gq:1 aug:1 γs:3 dickey:2 tr:13 ts:8 tl:26 tm:16 tj:1 those:1 th:27 under:4 semenov:3 presentation:1 mehta:2 p2:8 random:1 proved:1 string:8 orthogonal:4 bilinear:1 multi:13 eckmann:1 witten:2 lecture:2 difference:1 matrices:5 gurion:2 χd:2 school:2 basics:1 mo:1 soluble:1 tra:4 turns:4 notes:3 sklyanin:1 t2:1 solution:4 t1:19 large:1 discrete:12 vector:3 section:2 indices:1 relation:2 reyman:1 hospitality:1 equation:7 upper:3 zn:10 wronskian:5 takhtajan:2 direct:1 et1:2 zero:3 deutscher:1 mitter:1 further:2 linear:2 subscripts:2 what:2 nonlinear:7 appear:1 chicago:2 annali:1 sum:1 brief:1 expressed:7 find:3 symes:2 above:2 fractional:1 expresses:1 b448:1 order:4 method:1 viii:1 pioneering:1 full:4 notions:3 wronskians:1 respectively:2 realizations:3 proc:1 here:5 canonically:2 les:1 groups:1 sheva:1 ratio:2 equations:11 box:1 shansky:3 arrive:2 institute:1 experience:1 poisson:8 published:1 action:1 complicated:2 manakov:1 via:5 useful:1 diffeomorphisms:1 f1:1 belongs:1 klebanov:1 conditions:3 remnant:1 qnn:3 virasoro:2 derivatives:1 use:2 takes:2 usa:1 commun:7 ψs:1 h0:9 contains:3 suppl:1 next:1 few:1 nucl:10 ψi:11 ψn:10 zemba:1 ψm:9 dijkgraaf:1 themselves:1 type:2 kostant:2 tk:4 nauka:1 israel:1 γm:1 definition:2 initial:3 operators:12 dressing:8 curvature:2 site:2 eξ:2 particular:1 known:4 morozov:4 cases:1 bessis:1 account:1 language:1 φdφ:3 recall:4 originally:1 work:1 det:4 london:2 theories:4 remain:1 marshakov:2 following:13 dec:2 tian:1 example:1 claim:1 freiburg:1 νq:1 haine:1 december:1 preserving:1 lψ:1 dependence:1 high:1 indicates:1 dxm:4 assumptions:1 cartan:2 employs:1 verlinde:2 verlag:1 information:1 b405:1 end:1 provide:2 discussion:1 acts:1 chadha:1 leznov:1 how:1 pura:1 pure:1 instead:1 ordinary:1 g12:1 quart:1 sato:3 express:1 mat:2 algebra:16 may:2 after:1 singularities:1 orbits:1 isospectral:3 constraint:6 applications:1 plane:1 lax:27 fj:1 derives:1 arch:2 compatibility:1 ooguri:1 realized:1 short:3 natural:2 effective:1 rα:3 hepth:1 ueno:1 explicit:5 st:1 darboux:12 kacmoody:1 so:3 fundamental:1 sl:3 sc:1 representation:3 acknowledges:2 playing:1 talk:1 superscript:1 words:1 correlation:1 hierarchy:22 pointed:1 years:1 xi:1 through:4 statistical:2 differs:1 satisfies:2 still:1 its:13 refs:7 before:1 tˆm:1 group:1 xl:1 ln:12 interesting:1 heron:1 lk:6 conjugation:2 writing:1 forms:1 lt:1 parts:2 systems:6 constitutes:1 martinec:3 jacobi:1 mail:3 main:4 defining:1 deformation:1 lx:2 ly:1 non:6 motivated:1 schoutens:1 acklund:13 noticing:1 introduce:2 functional:2 qr:2 they:2 oxford:1 now:6 yu:4 hall:1 developments:1 possess:2 easily:1 term:2 dirac:1 name:2 φl:1 university:4 hamiltonian:9 hermitian:1 fs:1 φm:3 each:2 inherent:1 tˆ1:8 constraints:4 subset:3 ann:1 differential:18 formulate:1 nanopoulos:1 there:2 energy:4 physica:1 related:1 t3:1 constitute:1 operator:32 toda:8 used:3 interplay:2 quantum:6 our:3 eq:8 out:5 shown:1 matrix:33 space:6 res:2 furthermore:2 since:4 rev:1 detailed:1 research:1 particles:1 attracted:1 mα:3 stud:1 denoted:1 formula:3 rn:12 ref:4 math:21 shows:1 shiota:1 foundation:1 theory:10 reformulated:1 tsarigradsko:1 kulish:1 diagonal:2 free:5 standard:2 romans:1 completely:2 ntm:1 ψdo:6 approach:1 subalgebras:2 publ:1 generate:1 parametrized:1 perform:1 svetlana:2 takasaki:1 times:1 motion:2 turn:3 place:1 massive:1 δij:1 consequence:1 qn:6 eqs:8 first:4 xk:1 already:2 features:1 symmetry:5 admissible:1 number:2 thereof:1 exact:1 employing:1 aratyn:8 another:3 precisely:2 lacki:1 illustrate:1 given:5 fk:1 similarly:2 introduction:2 adjoint:8 system:14 relations:2 their:5 intermediate:1 seiberg:1 listed:1 statement:1 realization:1 normalization:2 stora:1 perfectly:1 structures:5 ranging:1 originating:1 moscow:1 exactly:3 park:1 α2m:1 part:5 b339:1 than:1 coefficients:9 cheng:1 λr:2 ben:2 qs:4 accordance:1 sections:1 require:1 second:7 warner:1 1l:8 nonlocally:1 ktk:1 providing:1 solely:2 distinguished:1 perturbative:2 springer:6 lowest:1 symmetries:8 substantiated:1 outstanding:1 b253:1 topics:1 modern:1 matem:1 generalization:3 lin:1 need:2 elsevier:1 constrained:9 any:5 solitons:3 ray:1 lie:4 wilson:2 petviashvili:2 convenient:1 latter:7 able:1 gravity:2 inv:3 note:1 instance:1 absorbed:1 generalized:11 pm:1 δnm:1 new:1 kerner:1 kac:2 spectral:1 play:1 towards:1 trace:1 shall:1 object:1 satisfy:2 most:1 involving:1 connected:1 successive:5 acknowledgements:1 class:3 yamilov:1 soliton:5 pohlmeyer:1 especially:1 ψk:7 orlov:3 brackets:1 flow:6 schweiger:1 km:9 lλ:1 lχ:1 proceedings:1 kp:25 ckp:10 exp:9 mechanical:1 χm:6 χl:3 physics:11 notion:2 fact:4 semiinfinite:1 particularly:1 akhiezer:1 pope:1 show:2 reductions:4 supported:2 gerasimov:1 notations:4 purely:5 session:1 gauge:1 solutions:4 substituting:2 nlk:1 label:1 indicate:1 current:1 based:2 parameters:5 much:1 yen:1 only:3 obeys:1 black:1 ambiguity:1 prof:2 integrable:23 circle:2 moser:1 dl:4 dm:7 dj:2 dk:1 get:3 de:1 db:16 itoyama:1 b361:1 ganchev:1 legitimate:1 dx:4 rˆoles:1 fateev:1 represented:1 areas:1 evolution:10 kadomtsev:2 densities:1 fields:4 arxiv:1 grav:1 gaum:1 contain:1 bao:1 fixed:2 qm:1 valid:2 bulgaria:2 coefficient:1 set:4 ser:1 exists:1 physically:1 turbulent:1 j1:1 plausible:1 see:8 bare:2 result:3 w1:6 w0:3 terms:13 contour:1 subject:5 cappelli:1 αs:9 satisfying:2 eigenfunctions:7 dmq:1 b367:1 nuclear:2 bitnet:2 justifies:1 µs:2 partition:4 various:3 membrane:1 limit:1 αm:14 preserve:1 adv:2 matveev:1 recently:1 shabat:1 wn:9 attention:2 wk:6 wj:6 wi:1 however:2 gratefully:1 wu:2 trugenberger:1 solv:3 problem:1 originates:1 last:2 han:1 many:1 taking:1 contract:1 etc:1 connection:2 context:1 b434:1 expression:4 finds:1 among:2 ci:2 relevant:2 gorsky:1 appeared:2 vast:1 uic:1 crum:1 dimensional:9 superstring:1 boson:1 spans:1 polynomial:3 moreover:3 bouwknegt:1 lect:2 pq:7 described:1 transformations:14 spanned:1 lattice:9 addition:1 zimerman:1 due:2 b428:1 ai:1 beer:1 workshop:1 interest:2 basic:2 transformed:6 ph:2 algebras:5 pn:1 ak:3 choose:1 obtained:4 generating:2 zamolodchikov:3 supersymmetric:2 itzykson:2 coincides:1 mavromatos:1 chapline:1 pacheva:6 bull:1 general:2 xiong:4 present:3 case:8 explicitly:1 negev:1 p1:9 processes:1 karabali:1 appearance:1 chap:1 value:1 will:4 tˆs:6 irrespective:1 property:1 conformal:2 procedure:1 dλ:4 bonora:6 planar:1 heng:1 endowed:1 vj:3 chau:1 thus:1 vm:2 reads:3 itself:1 il:4 dual:2 zhang:1 acquires:2 generalizes:1 different:4 φs:1 shaw:1 grant:1 generic:2 suggest:1 same:7 clearly:1 shifts:1 complex:1 φd:2 ince:1 φi:15 hierarchies:16 finite:3 subalgebra:3 composition:1 higher:5 independent:3 φi0:2 extended:1 horozov:1 singapore:2 upon:2 effect:1 flows:7 hand:2 v0:1 purpose:1 potentials:1 infinite:9 changing:1 invariance:1 identity:3 recent:1 b396:1 lower:3 nn:2 well:1 analysis:2 todorov:1 coordinate:1 model:11 self:1 usual:1 summer:2 resx:1 zhao:1 graded:2 ibid:6 being:2 sofia:1 obtain:3 underlying:2 identify:3 transforms:1 resl:1 world:3 alternative:2 functionally:1 nissimov:6 ˆb1:1 ˆb0:1 preprint:1 bullough:1 application:3 zakharov:1 parametrization:3 simple:2 rˆole:1 conjugated:3 lett:19 natl:1 constant:1 mod:8 plasma:2 transformation:3 scientific:2 take:1 alvarez:1 eigenfunction:12 alternatively:1 akademischer:1 comparing:1 admitting:1 cf:1 background:1 press:1 using:11 sakita:2 moody:1 radul:2 theor:2 pertinent:1 like:6 particle:1 identifying:1 follows:7 reiman:1 mironov:2 b347:1 specific:4 δm:1 steps:2 integrals:1 arbitrary:2 acad:1 kiritsis:1 salle:1 traced:1 methods:1 namely:1 lectures:2 shen:1 phenomena:1 back:1 γss:1 dold:1 trends:1 b0:10 b1:5 uspekhi:1 kdv:1 b373:2 yamagishi:2 vol:1 describing:1 dimensions:2 lead:1 broad:1 van:1 b348:1 everything:1 defined:3 provides:1 yields:3 inrne:1 closely:1 polyakov:1 demonstrated:1 faddeev:4 bg:1 ba:8 power:1 intimate:1 bl:3 bm:5 equivalent:4 bi:5 bj:4 bk:4 step:6 2m:3 qnm:3 relating:1 between:3 reports:2 schulman:1 comparison:1 pα:3 quant:1 extension:1 algebraic:1 novikov:1 gα:2 compatible:2 plus:1 bgu:3 ti:1 introduced:1 sept:1 other:1 perelomov:1 soc:1 letters:2 final:1 previously:2 material:1 into:3 within:4 integral:1 isomorphic:1 nsf:1 appropriate:2 zuber:3 references:1 sov:1 elementary:1 factor:1 gomez:1 xxxix:1 hep:24 additional:9 area:1 vafa:1 support:2 twodimensional:1 u1:1 u2:1 dm1:1 quadratic:1 low:1 way:2 series:1 infinitedimensional:1 was:3 naturally:2 function:15 dνα:1 form:15 makeenko:1 some:1 δkl:1 sequel:1 tˆ2:1 triangular:2 volume:1 serie:1 repeated:1 hn:11 hl:1 a10:1 fg02:1 adler:5 applying:1 emil:2 versions:1 olshanetsky:1 smooth:1 us:6 theoretical:2 krichever:1 discretized:1 below:3 ui:2 coadjoint:1 more:5 similar:1 called:7 peterson:1 continuum:8 mechanics:1 ac:2 taylor:1 associated:6 int:8 pseudo:13 abstract:1 describe:3 condition:1 bulgarian:1 deep:1 denote:3 tˆ:3 single:1 associates:1 exist:1 rule:1 interchanged:1 formulation:1 corresponding:3 rαα:1 formalism:4 commuting:1 reexpress:1 again:2 functions:14 nm:7 integrability:4 variety:2 extract:1 whereas:3 detail:2 illinois:1 rewriting:1 field:9 bracket:8 role:1 swieca:1 branch:1 papers:1 department:3 mathematics:1 austauschdienst:1 pitaevski:1 diagonals:1 a14:1 elements:7 superposition:1 models:15 resembles:1 polynomials:1 expressing:1 a0:4 qσ:1 important:5 a7:3 a6:2 ellis:1 needed:1 structure:4 watanabe:1 ghost:1 lm:13 implies:2 coupling:4 dφ:1 bakas:2 baker:1 factors:3 holes:1 together:1 equivalently:1 a8:2 correspondingly:1 χi:7 time:5 appl:2 orders:1
|
solv-int9601001.txt |@word funct:3 results:5 invent:3 illustrated:1 commute:1 particularly:1 dunod:1 inverse:1 depend:1 paris:1 show:3 tr:38 δhn:7 quasi:1 δhk:3 tk:14 under:2 semenov:6 up3:1 p2:3 straightforward:1 rise:1 p0:1 dokl:1 wave:4 balancing:1 manin:8 tri:4 dynamiques:1 riemann:16 hamiltonian:46 did:1 t7:1 notes:2 t5:1 t3:1 δh1:1 t1:1 try:1 involution:1 anal:3 equation:33 des:1 10b:1 takhtajan:1 10a:1 past:1 second:8 follow:1 chen:2 theory:2 residue:1 what:1 nonlinear:5 stands:1 brackets:7 section:5 symes:1 new:4 method:1 3d:1 coefficient:1 lee:1 degree:4 respectively:3 inviscid:1 here:2 behaviour:2 enℓ:15 free:1 groups:2 address:1 equations:29 implicit:1 obtained:11 shansky:6 instituto:1 singapore:2 study:2 studied:3 allows:1 poisson:10 studies:2 useful:1 although:1 9a:1 namely:1 explained:1 texts:1 apply:1 unit:1 use:7 would:1 commun:1 contains:1 negative:1 next:1 comparing:1 call:1 therefore:3 usp:1 mckean:1 kostant:4 duals:2 formally:1 sokolov:2 operators:2 tℓ:5 berlin:2 particular:1 known:2 ward:1 must:1 nutku:3 springer:3 decouples:1 setup:1 work:1 modified:2 london:1 three:7 following:2 making:1 example:4 deg:6 compare:1 degenerate:1 give:1 organized:1 performed:1 want:1 sense:2 yang:1 end:1 mo:1 enk:27 enm:3 write:4 how:1 nontrivial:1 env:2 ordinary:1 frenkel:1 product:1 algebra:7 after:4 derived:1 orbits:1 74a:1 lax:21 waves:2 representations:2 truly:2 δhm:1 quasiclassical:1 dynamical:1 third:8 whenever:1 sp:1 yielding:1 en2:4 so:7 representation:13 order:6 breaking:2 interpretation:1 parmentier:2 hierarchy:22 paper:3 through:4 satisfies:2 its:3 brunelli:3 derive:2 thank:1 interesting:5 li:1 forms:2 systems:5 jacobi:3 olver:4 main:1 them:2 introduce:2 functional:1 cep:1 now:7 yu:4 oevel:2 kirillov:3 easily:1 term:2 dikii:1 dirac:1 difficult:1 characterized:1 baxter:1 differential:2 directly:3 related:3 our:4 ev:5 eq:3 out:3 shown:2 benney:6 matrix:9 res:3 since:4 investigation:2 ra:1 rb:1 formula:1 math:17 sympletic:1 linear:4 associate:1 8b:2 8a:2 ısica:2 departamento:1 mapping:1 tian:6 atica:1 york:2 subalgebras:1 reyman:2 e2:2 derivation:1 applications:1 could:2 transition:1 nonnegative:2 int:2 u20:2 assumed:1 qn:2 onto:1 first:14 already:1 frech:1 variables:2 number:3 clear:1 long:2 another:1 illustrate:1 dispersive:4 given:13 introduction:1 leading:1 system:11 least:1 appl:4 structures:18 gives:4 recursively:1 incompressible:1 kupershmidt:5 whitham:1 part:1 natural:1 coefficients:1 approximation:1 succeeded:1 holds:1 eqe:1 zero:1 kth:2 contrasted:1 powers:1 projections:1 derivative:2 rewrite:1 matem:1 generalization:1 any:3 lie:7 lin:1 responsible:1 note:2 instance:2 without:1 take:1 even:1 exactly:2 scripta:1 trace:4 though:1 magri:4 algebraic:2 pair:1 acknowledgements:1 class:2 soliton:2 laurent:7 wiley:1 considered:2 calculated:1 flow:1 physica:2 bracket:10 fact:1 laws:1 lebedev:8 dickey:3 supported:1 purely:1 solutions:4 ashok:1 d2:8 d3:6 d1:7 q0:3 finally:2 written:5 topological:1 should:1 jan:1 only:2 integrable:7 hamiltonians:3 hopf:1 do:2 his:1 get:7 de:3 fluid:1 da:1 ones:3 dx:15 dy:3 liu:1 evolution:1 arxiv:1 qe:1 identify:1 valid:1 view:1 endowed:1 set:2 ser:1 up:4 observed:1 depends:1 result:2 discussions:1 nonstandard:3 analog:1 brazil:1 satisfying:1 behind:2 various:1 between:1 limit:3 before:1 approach:7 quadri:1 notice:1 terms:5 uux:3 relative:1 nature:1 however:5 comm:2 huang:2 solv:2 coadjoint:1 endows:1 water:1 taking:1 etc:1 expression:1 relevant:1 point:3 simple:1 corresponds:2 polynomial:7 respect:2 lect:2 due:1 been:1 defined:1 reduction:1 dropping:1 slowly:1 pi:7 define:2 corresponding:1 observe:2 systematic:1 mail:1 general:2 present:1 case:2 p3:2 multi:1 p7:1 p5:1 will:7 ǫv:2 situation:1 di:1 property:2 coupled:1 vol:1 vi:7 thus:3 non:1 surface:1 itself:1 vt:1 dual:3 uxxx:1 containing:1 recursion:2 make:2 check:1 paulo:2 parts:1 souriau:1 higher:2 independent:1 used:2 dǫ:1 see:2 trivially:1 flows:2 v0:3 constraining:1 infinite:4 identity:3 charges:4 whole:1 well:3 burgers:1 dispersionless:32 usual:1 gelfand:3 das:5 obtain:9 shape:1 drinfeld:2 using:6 alternative:1 resa:2 scattering:1 conclusions:2 conclude:1 belongs:1 lett:4 theorem:1 mod:2 scientific:2 generalized:12 9b:1 possible:1 know:1 integer:1 unique:1 helpful:1 like:3 follows:4 reduces:1 δu:9 yields:2 arbitrary:1 methods:1 classical:3 sequence:1 kdv:20 describing:1 δen:2 extensively:1 comments:1 conservative:1 minimal:1 faddeev:1 ba:1 power:1 bi:1 bv:1 ragnisco:2 br:1 substitution:1 about:1 world:2 constraint:1 discussed:1 dependence:1 o:5 compatible:5 whence:1 associative:2 introduced:2 consequently:1 soc:1 h3:2 h1:2 h7:1 h5:2 linearization:1 en:58 references:2 δun:7 sov:3 operator:3 additional:1 u4:1 there:1 u0:26 u3:6 u2:11 much:2 way:3 was:10 hx:1 form:11 hp:1 ht:1 hn:4 hm:3 cnpq:1 highest:1 dissipative:1 adler:2 bypassing:1 algebras:1 ux:6 ut:4 uv:1 6uux:1 maximum:1 us:12 krichever:2 un:5 ui:1 uh:1 problem:4 called:7 ab:2 associated:1 ai:6 abstract:2 contribute:2 am:1 ao:2 denote:2 conserved:4 formalism:1 commuting:1 universidade:1 again:1 functions:1 integrability:1 when:1 graduate:1 other:3 solitons:1 mathematics:1 elements:1 a10:1 models:3 polynomials:3 deriving:1 important:2 a9:1 variable:1 structure:20 implies:1 assume:1 pseudo:1 time:1 4d:1
|
solv-int9601002.txt |@word represent:1 partial:1 consider:7 similarity:1 leads:1 commute:1 generalize:1 expressions:1 gl:2 gi:2 devoted:2 λij:24 inverse:4 alvarez:1 those:1 under:3 analogous:2 te:1 fax:1 amplitudes:4 rise:1 dokl:1 wave:39 resonant:13 exact:1 deformations:2 condition:5 solves:4 hamiltonian:1 turns:1 solution:24 large:2 solved:1 vector:10 indices:1 anal:1 zm:1 mli:2 zi:10 zj:2 zk:15 direct:3 painlev:2 further:3 dynamics:1 what:3 nonlinear:8 appear:2 invertible:10 ˆbj:1 section:7 interactions:2 expressed:3 ˆb:1 version:1 pershan:1 above:1 new:5 method:3 3d:1 satisfy:8 λik:4 full:2 respectively:2 realizations:1 component:1 here:2 leo:1 behaviour:1 desired:3 objects:1 free:2 path:1 equations:31 z1:18 z2:18 z3:18 obtained:3 study:1 vectors:4 allows:4 trial:1 sji:1 action:2 suitable:1 changes:1 santini:1 apply:1 derivatives:7 use:1 takes:2 distinct:3 positive:1 contains:2 negative:1 next:2 call:1 therefore:3 taken:1 means:1 e2:2 type:3 more:4 thus:3 operators:11 dressing:2 interaction:16 everywhere:2 virtue:1 particular:1 known:1 cases:1 hold:2 must:3 valued:2 ma:5 integrating:1 equation:8 work:1 det:2 remain:1 obvious:1 following:6 arrive:1 could:1 proof:2 tau:2 give:4 numbers:4 kijk:1 conversely:1 end:1 s3:1 s2:1 s1:1 six:1 write:1 how:2 sik:1 sij:5 cicyt:1 product:1 description:2 τij:2 derived:1 lump:4 hence:1 levi:1 plane:21 lax:6 waves:4 fi:9 fj:2 choice:2 data:2 compatibility:6 imply:2 light:1 explicit:2 mji:1 mjk:1 sk:2 darboux:11 so:5 martina:2 allow:1 acknowledges:1 order:2 davey:3 holds:2 deform:2 indeed:2 over:5 paper:3 existence:1 satisfies:2 cole:1 its:4 before:2 fis:1 group:2 xl:4 chosen:3 interesting:1 jim:1 coordinates:1 systems:4 derivative:2 main:1 defining:2 deformation:5 them:3 pji:3 pjk:2 acklund:4 introduce:3 scaling:1 motivates:2 they:2 instead:1 multidimensional:1 now:4 dielectric:1 easily:3 finite:1 equality:1 name:1 81a:1 simplified:1 characterized:1 constraints:8 homogeneous:1 differential:1 ei:8 ek:2 ej:7 series:1 energy:1 idea:1 related:1 our:7 eq:8 es:1 really:1 shown:3 matrix:1 space:16 rep:1 rev:3 acting:1 dsi:1 math:6 linear:29 found:1 kaup:5 ısica:1 departamento:1 completely:1 e1:2 e3:2 care:1 definition:1 pairs:2 qj:8 haberman:1 βi:46 impose:1 int:1 concrete:1 δij:1 universidad:1 consequence:2 adjoint:4 βj:7 first:4 xi:3 symmetry:5 variables:2 rank:8 ℓk:7 ℓi:1 done:1 relations:1 another:3 pˆ:1 given:22 asymptotic:1 introduction:1 eqs:28 system:17 construct:6 their:2 1d:1 scheme:2 gives:4 s31:1 s32:1 optical:1 x2:3 x3:3 x1:3 than:1 coefficients:2 cyclic:11 require:2 namely:3 limiting:1 winternitz:1 µkj:11 µki:15 were:1 treated:1 pre:4 motivation:1 symmetries:3 ann:2 argument:1 kitaev:1 correspond:2 say:2 manner:1 need:7 constrained:1 seek:1 any:4 mik:1 mij:4 bers:1 zero:2 depending:1 lumps:1 potential:1 take:6 play:1 shall:2 rarefied:1 connected:1 qˆk:1 pair:4 constructed:4 considered:6 parametric:1 into:1 request:1 coppi:1 part:1 exp:16 physics:2 fact:4 show:4 reductions:2 solutions:54 βk:2 pkj:10 trivial:2 find:2 principal:1 parameters:2 contraction:1 jan:1 only:4 summarizing:2 integrate:2 integrable:1 adequate:1 local:1 hopf:1 do:4 notation:2 get:1 de:1 fluid:1 gen:3 evolution:2 exhibiting:1 determinants:5 approach:1 arxiv:1 qi:4 qk:13 fixed:1 moduli:1 set:7 see:5 result:2 βˆj:1 βˆi:6 subject:6 satisfying:1 damping:1 λkj:4 functionals:5 grammian:4 written:1 closed:1 between:1 αi:6 invariant:1 αj:1 conditions:9 notice:3 terms:6 amplitude:1 however:1 vanishing:1 ji:6 solv:1 dress:1 solu:1 both:1 prescription:2 taking:3 hϕ:5 fulfilled:1 context:1 proyecto:1 expression:1 comes:1 among:1 shabat:1 relevant:1 point:3 simple:1 dimensional:7 simply:1 associated:7 ucm:1 kp:2 described:1 transformations:5 three:27 ai:19 reduction:4 aijk:2 µji:3 µjk:1 algebras:1 define:10 determinant:1 corresponding:2 observe:4 func:1 plasmas:1 denote:1 spain:1 case:4 exponential:1 mlj:2 ski:1 expanded:1 value:1 will:2 while:1 suppose:2 orica:1 rosenbluth:1 studied:2 played:2 soliani:1 tions:1 non:4 ii:3 characterize:1 itself:1 dual:2 loosing:1 vanish:1 different:4 sjk:1 perform:1 complex:10 defines:1 independent:2 extended:2 flows:1 hand:1 πij:4 πik:1 infinite:1 ablowitz:1 identity:1 prescribed:1 modes:1 nevertheless:3 well:3 analysis:2 s23:1 s21:1 solve:1 firstly:1 arising:2 posses:1 just:2 obtain:6 immediately:1 scattering:6 stewartson:3 previous:4 zakharov:3 conclude:1 parametrization:1 bloembergen:1 rˆole:3 lett:4 easy:2 theorem:9 mod:1 plasma:2 transformation:14 skj:1 real:1 read:1 evaluate:2 spatial:1 possible:2 vacuum:2 press:1 using:3 moreover:1 disadvantage:1 follows:6 reiman:1 arbitrary:2 become:1 ˆbi:3 mathematical:1 right:6 madrid:1 phenomena:2 understood:2 elements:1 respect:2 solving:3 dimensions:4 sudan:1 does:1 provides:1 adjoints:1 s13:1 s12:1 δi:3 bi:42 bj:20 bk:6 although:2 substitution:1 imaginary:2 hilbert:4 proceed:1 extension:1 ϕij:2 compatible:5 considerations:1 previously:1 image:1 functional:1 because:1 references:1 determine:1 sov:1 operator:11 pˆij:6 support:1 there:3 mkj:2 mki:2 appl:1 inner:1 was:6 naturally:1 function:4 medium:1 form:3 some:7 differences:2 but:6 hi:2 characteristic:1 up:1 us:6 a209:1 manuel:2 problem:10 pij:50 pik:12 constant:3 armstrong:1 defined:6 certain:1 abstract:1 aj:4 general:6 dirac:1 initial:3 physica:2 πjk:1 families:3 commuting:1 check:3 physical:1 again:1 functions:22 no:1 dressed:1 when:5 plugged:1 nas:5 other:1 special:2 papers:1 1bj:1 out:1 applications:1 francisco:1 complutense:1 µij:13 a1:1 a3:1 a2:1 implies:2 assume:1 values:7 required:1 packets:1 time:1 starting:1 once:1
|
solv-int9601003.txt |@word limited:1 lakshmanan:2 consider:2 funct:1 rev:2 leads:3 eds:1 ηi1:1 partial:1 gh:1 inverse:1 providence:2 shanghai:2 tn:1 δhn:5 finally:2 th:6 under:1 worth:1 applied:4 ηin:1 rise:1 every:1 exact:1 hamiltonian:29 induction:1 t2:2 solution:2 δh1:2 t1:2 leave:1 involution:1 vector:2 small:4 anal:1 second:2 further:4 dynamics:1 even:1 established:2 what:1 nonlinear:3 stands:1 hereditary:7 version:1 fuchssteiner:4 above:5 new:4 method:3 ˆn:2 respectively:1 component:1 here:2 china:3 groups:1 equations:25 obtained:1 bibliopolis:1 remark:2 institute:1 study:3 vectors:2 allows:1 resulting:4 suitable:1 scales:2 manna:1 texts:1 would:2 distinct:1 negative:1 noting:2 call:1 therefore:4 themselves:1 more:5 engender:1 becomes:1 operators:3 holm:1 cases:1 springer:1 ma:3 science:2 equation:34 2ux:1 ms:4 following:6 example:5 f1:2 want:1 evidently:1 provide:2 discussion:1 means:1 write:1 answer:1 acta:1 parameter:1 description:1 may:4 wiley:1 space:2 applications:3 waves:4 constants:3 natural:1 clarkson:1 cannot:1 so:1 suggest:1 order:7 typical:3 hierarchy:15 symbols:1 mentioned:1 satisfies:1 still:1 its:2 thank:1 acknowledge:1 interesting:3 actually:1 absence:1 choose:2 xyy:1 olver:1 gel:1 non:1 greater:1 yyy:1 acklund:1 introduce:1 effects:1 they:4 now:2 discuss:2 possess:2 easily:1 hereafter:1 tonian:1 university:1 presented:1 each:1 acoustic:1 universit:1 differential:5 financial:1 ed:1 idea:1 constitute:3 society:1 our:2 operation:1 δh0:9 special:1 out:2 solved:1 gradient:3 hyman:1 δi0:4 denotes:1 rn:1 ref:4 correct:1 math:6 foundation:2 theory:3 kaup:1 standard:1 york:2 besides:1 generate:1 pairs:1 sinica:1 motion:2 american:1 hence:1 think:1 first:7 humboldt:1 symmetry:1 miura:1 variables:1 number:1 transform:1 xx:2 another:1 ηtn:4 given:2 perturbation:32 rewritten:1 similarly:1 system:1 construct:1 appl:2 fn:2 show:1 siam:2 structures:2 gives:1 ηt1:4 exactly:1 segur:1 authors:2 than:2 coefficients:1 kind:3 namely:1 determined:1 stratified:1 amplitude:1 powers:1 symmetries:2 generalization:2 kepler:1 conjugate:1 any:1 lie:2 εx:2 depending:1 note:4 instance:2 k1:1 εn:6 εi:7 take:1 lectures:1 multiple:2 philadelphia:1 shall:2 magri:2 systems:6 algebraic:2 germany:1 fore:1 letter:2 pair:2 herman:1 soliton:8 don:1 especially:1 considered:3 physica:1 ks:4 part:1 kraenkel:1 physics:1 fact:1 oevel:2 disturbances:1 contemporary:1 solutions:4 find:2 slow:1 appended:1 haven:2 jan:1 analytic:1 only:1 geometric:1 integrable:11 get:2 ones:1 dx:2 ds:5 alexander:1 approach:1 arxiv:1 expansions:1 acknowledgments:1 investigate:1 common:1 discussing:1 computed:1 exists:1 utn:1 national:1 see:8 result:1 discussions:1 subject:1 fand:1 marmo:1 boundary:1 conditions:1 confusion:1 however:5 ji:1 solv:1 informatik:1 many:3 according:1 propagation:1 eta:1 whole:3 comes:1 among:1 point:2 dimensional:1 cs:5 moreover:3 fruitful:1 described:2 due:1 been:3 int:1 reduction:1 describes:1 kronecker:1 fudan:1 ls:5 referee:1 corresponding:2 cotangent:1 sufficient:1 precision:1 gen:2 present:1 case:6 multi:1 schmidt:1 unlike:1 contexts:1 dorfman:1 value:1 aim:1 balance:1 mistake:1 changed:1 von:1 thus:3 reads:2 casati:1 uxxx:1 technology:1 recursion:1 make:2 matsuno:1 same:1 φn:3 higher:2 independent:2 forced:4 i1:2 effect:2 ion:1 infinite:1 uˆ:4 ablowitz:1 paderborn:2 well:1 analysis:2 concrete:2 position:1 possesses:3 usual:1 proposed:2 obtain:1 valuable:1 scattering:1 fokas:1 disturbance:1 kluwer:1 infinitely:3 conclude:1 lattice:1 internal:1 lett:1 easy:1 plasma:1 real:1 around:2 read:1 know:2 ams:1 mod:2 like:3 exploiting:1 yields:1 arbitrary:1 jˆ:6 works:1 reduced:1 therein:1 because:2 methods:2 some:5 examples:1 kdv:24 dimensions:2 broad:1 comments:1 tma:1 provides:1 problems:1 equivalent:2 bi:14 expansion:5 bs:5 montero:1 integers:1 pereira:1 o:4 unidirectional:1 mathematical:1 presence:1 ηn:11 h0:6 h1:2 ηk:2 ηj:9 ηi:25 nayfeh:1 references:2 operator:13 ηx:5 commission:1 support:1 there:4 approximate:3 long:1 ut1:1 inner:1 lot:1 function:2 complete:1 form:1 2ηi:1 basic:1 but:1 hn:6 compute:1 ux:4 6uux:1 us:4 naples:1 dordrecht:1 problem:2 called:1 detailed:1 constant:1 defined:3 abstract:1 aj:2 doesn:1 general:4 exist:2 dλ:3 formulation:2 physical:1 functions:3 integrability:1 mathematik:1 when:2 detail:1 graduate:1 other:1 details:1 solitons:1 mathematics:5 pedroni:1 xxy:1 symbol:1 asterisk:1 bundle:2 helpful:1 a1:3 a0:2 hydromagnetic:1 variable:3 structure:15 coupling:4 4u:1 time:1 starting:1 original:2
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.