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solv-int9704009.txt |@word vessiot:2 ulam:5 london:1 belong:1 consider:2 show:1 llave:1 solvability:2 valuable:1 dv:2 underlying:1 relation:2 solutions:8 grateful:1 during:1 japan:1 satisfies:1 d2:4 dt:2 functionally:2 q1:1 chemical:2 q3:1 q2:1 const:1 thank:1 advanced:1 located:1 picard:2 edited:1 funct:1 complex:2 lattice:10 only:1 program:3 degrees:4 riken:2 easy:1 theorem:7 jacobi:1 integrable:1 moser:1 solvable:2 transformation:1 collaborators:1 do:1 non:15 his:2 above:1 dh:1 orthogonal:1 dependent:1 o:4 press:2 de:1 alamos:2 ηj:2 complete:1 course:1 amari:1 hands:1 hirosawa:1 lattices:4 singularity:2 condition:7 mod:1 easily:1 2v:1 induced:1 like:1 hamiltonian:8 µ2m:4 university:1 arxiv:1 t2:3 solution:2 µ2j:1 γ2m:8 vector:2 steps:1 integrals:4 follows:5 nonintegrability:2 2m:14 2n:1 fixed:1 reduced:1 proof:2 qn:3 homogeneous:2 application:1 differential:3 neighborhood:1 independent:2 continual:1 energy:4 sin2:2 algebraically:1 integrability:7 yoshida:2 tangential:2 nonhomogeneous:2 combining:1 discussions:1 t1:3 odd:1 special:5 theory:2 cambridge:1 dissertation:1 nonlinear:5 kowalevski:1 αt:4 analytic:1 frontier:1 univ:2 parallelogram:1 cφ:3 research:3 cell:1 written:1 does:3 poles:1 hill:2 morales:4 conjectured:1 formula:1 boundary:1 hold:1 ref:1 contrast:1 watson:1 meromorphic:2 ken:1 hypothesis:1 linear:1 degree:1 q0:1 equivalent:1 each:1 p2i:2 however:1 here:2 bednarek:1 qi:6 california:1 york:2 eigenvalues:1 solv:1 based:3 along:1 perturbative:1 equations:11 tion:1 additional:1 e2:3 obtained:3 remark:2 institute:3 freedom:5 study:1 impose:1 according:1 δqj:1 ξk:1 present:3 together:2 resonance:2 2k:3 other:1 first:5 mathematical:1 via:1 cn:3 apr:1 ηn:2 prof:9 integral:6 period:1 δpj:1 dimensional:2 pasta:3 because:2 references:1 determine:1 obtain:1 moreover:1 total:2 diff:2 between:1 given:6 rewritten:2 would:2 their:1 analogies:2 e1:4 support:1 initial:2 system:2 relations:1 oξ:1 explicitly:1 call:1 low:1 basic:1 dt2:3 variational:12 type:4 exponents:1 systems:7 function:4 corresponding:1 elliptic:5 form:3 branching:2 becomes:1 sufficient:1 cos:4 depend:1 2ik:1 known:1 cases:1 removed:1 hf:1 wako:1 he:3 case:7 ii:1 kind:2 thanks:1 tokyo:1 checking:1 crawford:2 equation:16 us:1 ziglin:4 international:1 note:1 fermi:3 three:1 whittaker:1 following:8 about:2 di:1 cγ2:1 jπ:8 decoupled:2 result:2 mechanics:2 existence:3 saitama:1 int:1 december:1 abstract:1 modern:1 thus:5 encouragement:1 general:1 high:1 vq:1 examine:1 sn2:2 periods:1 reports:1 sense:1 some:1 limit:2 science:1 check:3 physical:2 nk:1 author:1 eq:3 corresponds:1 holds:1 when:2 satisfying:1 clearly:1 fpu:8 k2:4 report:1 potential:1 criterion:1 neighbourhood:1 meeting:1 new:2 physica:1 guarantee:1 modulus:2 appreciates:1 sim:4 lam:10 towards:1 la:2 appl:1 normal:6 after:1 φ2m:9 doctoral:1 algebraic:3 ξj:7 plane:1 connected:2 anal:1 ξn:4 winkler:1 halphen:2 acknowledgements:1 symmetric:1 constants:1 matrix:1 workshop:1 dynamical:1 los:2 magnus:1 curve:2 nve:1 analysis:6 more:2 satisfied:1 fundamental:1 time:2 baldassarri:3 konishi:1 lett:1 researchers:1 dover:1
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solv-int9704011.txt |@word represent:2 since:13 minors:2 consider:11 secondly:1 rev:1 wi0:1 theoretical:1 results:3 afosr:1 proposition:23 computation:3 edu:1 consists:1 gk:3 restrictions:3 whose:6 preserves:3 maximally:1 depend:1 referring:1 i2:5 iii:2 funct:1 tr:2 neighbours:1 γn:1 th:1 umich:1 semenov:3 breach:1 tr2:2 conjecture:2 futhermore:1 g3:1 g2:12 orthogonal:8 institute:1 rise:1 conditions:1 choice:2 corollary:1 wishes:1 every:2 invent:3 entries:3 tridiagonal:2 emphasized:1 difference:3 matrices:14 condition:1 tri:2 dim:21 hamiltonian:12 irreducible:3 notes:1 list:1 solution:2 t0:9 t1:13 solved:2 vector:6 independence:2 ǫjk:1 eigenvalues:1 reyman:3 deleting:2 mo:2 upper:6 smaller:1 grateful:1 zk:2 codim:4 discover:1 tex:1 integrability:12 arizona:1 involution:6 concludes:1 xf1:3 dynamics:1 xf2:5 odd:1 αi0:4 substitute:1 linear:8 even:1 dissertation:1 what:3 nonlinear:2 developed:1 invertible:1 brackets:6 section:16 expressed:1 symes:3 looking:1 version:1 above:3 stabilizes:1 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solv-int9704013.txt |@word consider:1 remarkable:2 four:5 scalar:3 forget:1 present:1 th:1 under:2 case:3 belonging:1 string:13 far:1 continues:1 translations:1 geometrical:1 infiniteness:1 entries:1 matrices:3 annihilated:1 progression:1 presented:1 solution:1 vector:9 small:2 configurations:2 upper:6 consistent:1 sergeev:3 zero:6 pass:2 situated:2 subscripts:1 appear:1 sum:3 intersect:1 new:3 contrast:1 outgoing:1 equals:1 here:2 groups:1 others:1 directions:4 along:2 change:5 remark:1 incoming:2 involved:1 study:1 vectors:1 products:1 helps:1 apr:1 explained:2 logical:1 apply:2 total:3 unit:1 use:1 chelyabinsk:2 themselves:1 more:3 operators:19 particular:1 known:1 iii:1 must:1 recall:2 equation:12 work:4 paragraph:1 values:1 following:5 example:3 korepanov:4 arise:1 states:2 sphere:4 degenerate:3 allowed:1 tan:2 species:1 end:1 discussion:2 acts:1 nontrivial:4 fourth:1 instead:3 sin:9 modest:1 plane:8 horizontal:12 hedgehogs:2 lines:1 parameterized:1 cannot:2 playing:1 hedgehog:3 six:2 gauges:2 produces:1 essence:1 paper:7 through:3 looks:1 its:4 somewhere:2 fix:2 conjugation:1 absence:2 choose:1 main:1 non:1 combination:1 propose:1 legged:2 they:1 half:1 now:4 yu:1 possess:1 university:1 each:5 found:1 baxter:1 series:1 idea:1 static:2 begun:2 combining:1 quantum:1 our:2 special:2 really:2 matrix:20 space:1 sms:2 particles:2 cause:1 inevitably:1 linear:1 quite:2 imagine:3 put:1 8p:1 created:1 s123:6 place:1 degeneracy:1 first:1 already:1 number:3 construct:1 given:3 similarly:1 introduction:2 least:1 their:1 assumption:1 legs:3 acquire:1 determines:1 require:1 see:5 marriage:4 supposed:1 russia:1 explicit:2 zamolodchikov:1 say:1 7p:2 any:1 lie:1 studying:1 able:1 ideas:1 zoo:2 note:1 take:1 involving:1 formulae:1 pair:1 clear:1 section:8 fact:1 show:3 notations:1 purely:1 spaces:5 gauge:5 solutions:6 based:1 kagome:7 enough:1 only:4 going:1 factor:2 achieve:1 triangle:4 means:2 between:1 ones:1 words:1 invariant:1 stroganov:3 arxiv:1 twice:1 fixed:4 view:1 namely:2 result:1 acquires:1 said:1 tensor:1 state:5 closed:2 simplest:1 probably:1 boundary:1 conditions:1 doubly:2 ends:1 terms:1 vertical:6 however:2 solv:6 configuration:1 restrictions:1 cos:7 equal:4 april:1 sense:1 whole:1 point:3 corresponds:1 dimensional:5 pole:2 considering:2 described:2 transformations:1 three:2 been:1 immense:1 algebras:1 corresponding:3 both:3 else:1 angles:3 spin:12 those:5 applied:3 tetrahedron:9 rectangular:2 will:10 euclidean:1 while:3 property:1 equator:1 formulation:1 thus:2 them:1 iv:1 ii:1 technology:1 conserve:1 different:1 perform:3 belong:1 same:2 shifts:1 unity:1 resulting:2 finite:1 higher:1 independent:1 infinity:2 edges:14 infinite:4 lower:7 center:1 mangazeev:3 edge:2 model:8 left:1 spherical:3 just:3 bazhanov:1 rest:1 transforms:1 alternative:1 eigenstates:7 infinitely:2 regarded:1 seems:1 except:1 lattice:12 rˆole:1 east:2 remaining:1 momentum:1 dihedral:1 disappearance:1 posed:1 five:2 using:4 bit:2 intersection:1 like:3 particle:11 continue:1 yields:2 works:1 spins:7 mathematical:1 lenin:1 because:1 old:1 some:12 born:1 does:2 algebraization:1 step:1 about:2 terminology:1 considerations:1 perturbed:1 within:3 parameterizing:1 due:4 references:1 operator:11 proportional:1 tetrahedral:1 hep:1 transfer:8 there:2 way:2 oneparticle:1 sections:1 naturally:1 north:4 form:6 but:2 sophisticated:1 construction:4 made:6 up:5 us:9 below:1 limit:2 planes:3 similar:1 called:1 associated:4 entering:1 int:6 abstract:1 doesn:1 general:1 av:1 constructed:1 integrability:1 no:1 vanishes:1 multipliers:1 other:5 papers:3 conclusion:2 elements:1 vertex:4 a1:2 a3:2 a2:2 sides:1 independently:1 implies:1 auxiliary:4 assume:1 factors:1 having:2 weights:1 strings:6
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solv-int9704014.txt |@word darboux:4 sci:2 consider:2 moutard:12 vr:2 leads:1 sergey:1 6y:1 follow:1 expressions:1 2r0:2 inverse:1 calculate:1 paris:1 recurrence:2 elliptic:1 dressing:1 analogous:1 multilinear:7 kν:1 bτ:1 supported:1 r12:2 straightforward:2 erale:1 2rx:1 exact:1 condition:2 notations:1 eds:1 turns:5 solution:23 vector:3 permutability:4 noted:2 des:1 direct:1 literature:1 past:1 zero:1 equal:2 theory:1 bilinear:1 established:1 3y:7 appear:2 section:3 expressed:3 current:1 sur:1 above:1 new:3 etriques:1 3d:1 satisfy:1 newyork:1 nimmo:1 2kx:1 here:2 bi:2 les:1 represented:1 equations:5 change:2 aτ:1 obtained:2 rodionov:1 remark:1 study:1 allows:2 permutation:2 useful:2 apr:1 replace:1 apply:2 establish:2 linearly:2 use:1 ψy:1 takes:3 prove:6 remains:1 call:2 therefore:1 type:1 more:1 nauka:1 th:1 becomes:1 operators:1 under:3 berlin:1 uxx:1 particular:1 c0r:1 must:1 ramani:1 springer:2 dodd:1 equation:24 work:3 modified:2 mt:3 krasnoyarsk:2 obvious:2 following:6 example:2 proof:9 f1:3 f2:4 stated:1 lψ:1 verlag:1 ib:2 provide:1 holds:1 write:1 get:2 ryy:2 ordinary:1 parameter:1 sin:1 map:13 product:1 may:1 derived:1 diagram:1 applications:2 fi:3 compatibility:2 constants:5 short:1 imply:1 explicit:2 trilinear:5 su:1 rather:1 si:2 so:1 representation:4 order:2 over:1 di:1 years:1 paper:1 through:1 satisfies:5 τn:6 derive:2 group:1 thank:1 la:1 ln:38 matrices:1 2λn:1 τy:1 mail:1 fim:1 andreev:1 a0r:3 acklund:2 introduce:4 p12:4 a0m:1 now:4 yu:2 2u:3 fi1:2 equality:1 found:4 constraints:2 mikhailov:1 arxiv:1 ed:1 owing:1 eu:2 our:2 eq:1 special:2 out:6 shown:2 since:7 rx:3 ry:4 research:1 formula:5 rn:27 induction:2 ri:1 math:1 foundation:1 linear:6 given:9 besides:1 ri1:4 generate:1 definition:1 r0:42 r1:21 r2:7 r3:2 geometry:1 omit:1 multiparameter:1 1y:1 consequence:1 first:1 v1:1 xi:1 variables:2 xx:2 xy:32 relations:5 another:1 carry:1 differ:2 checked:2 publication:1 similarly:1 introduction:1 bologna:1 hydrodynamics:1 system:11 construct:1 too:1 calculations:2 articles:1 final:1 a31:4 statement:2 academy:1 exactly:1 part:1 x2:1 x3:1 x1:1 coefficients:1 see:4 k22:2 determined:2 russia:1 rewrite:2 θxy:1 θxx:1 say:1 manner:1 θxi:1 seek:1 any:1 jour:1 convenient:1 note:2 k2:11 k1:11 potential:12 take:1 analogs:1 salle:1 surfaces:1 shall:2 1rn:1 formulae:1 remarks:1 acknowledgements:1 yamilov:1 soliton:13 τxy:1 considered:1 ki:5 ko:1 physica:1 exp:9 hietarinta:1 kx:3 physics:1 set:1 show:2 12k:1 discovered:2 relation:2 solutions:19 trivial:1 find:3 based:1 knowledge:1 aψ:1 enough:1 should:1 lemma:6 only:1 integrable:2 means:6 express:1 fluid:1 a2ν:1 aim:7 du:1 aν:2 differential:3 vr1:1 multiplying:1 constructing:2 exists:1 computes:1 w2:1 discussions:1 theoretic:1 c2r:2 satisfying:1 tsarev:1 eorie:1 symmetric:9 written:2 classes:1 between:1 geometria:1 invariant:3 boundary:1 bi1:1 approach:1 terms:4 shabat:2 originated:1 matveev:1 however:1 le:1 solv:2 last:2 many:1 according:3 interesting:1 expression:2 ci:8 conclude:1 corresponds:3 dimensional:1 polynomial:1 respect:6 transformations:1 skew:9 infinit:1 ai1:41 three:1 been:1 ai2:13 int:2 bianchi:1 basic:2 topics:1 define:2 θi:3 corresponding:7 versa:1 sufficient:1 gap:2 θx:2 θy:2 fik:1 c2:5 c1:7 general:1 present:2 case:5 exponential:1 value:1 will:4 calcul:1 suppose:3 aik:10 aij:10 skewsymmetric:1 property:4 cons:1 vol:2 ki2:2 ki1:2 thus:3 surface:4 uxy:1 ik:6 ij:2 im:22 utt:1 ax:1 vx:2 vy:2 vanish:1 different:1 parte:1 grant:1 same:1 proved:1 finite:2 shan:1 independent:2 used:1 i1:12 kir:2 i2:5 hand:1 kij:2 purpose:1 kim:2 potentials:1 recent:1 suffices:3 center:1 nevertheless:1 analysis:1 obviously:2 being:1 grammaticos:1 obtain:9 transforms:2 λj:2 λi:6 λn:98 previous:1 bullough:3 sciences:1 ideal:1 other:1 lett:1 easy:6 theorem:8 transformation:22 bim:1 easily:1 sharipov:2 replaced:1 possible:2 vθ:1 using:2 aτ2:1 insert:1 acquainted:1 necessary:1 helpful:1 follows:5 ai:16 νa2:2 yields:2 arbitrary:7 multiplicative:1 c1r:4 acad:2 methods:2 classical:1 some:3 examples:1 b2:3 describing:1 lead:1 esimal:1 tools:1 vortex:1 does:1 assuming:3 equivalent:1 aj:3 ψx:1 substitution:1 relating:1 bx:2 properties:1 o:3 eica:18 ηn:3 into:3 c2σ:2 en:1 references:1 novosibirsk:1 pi1:6 elementary:1 k12:2 there:2 transform:1 ci1:4 way:1 was:2 function:24 form:12 but:2 volume:1 construction:1 russian:1 true:2 he:2 ux:2 wish:1 up:2 us:4 below:2 verification:1 iterated:3 ωn:5 problem:1 called:2 b1:3 pij:1 constant:1 computing:1 defined:3 coincides:2 abstract:1 describe:1 linearity:1 denote:4 exist:1 θn:2 formalism:1 commuting:1 check:1 constructed:1 again:1 functions:10 cim:2 no:1 lezioni:1 setting:4 solitons:2 theor:1 problems:1 a1:90 a0:9 a3:6 a2:40 cnr:1 implies:1 vice:1 assume:2 eom:1 rxy:4 rxx:2 hirota:2 once:1
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solv-int9704015.txt |@word represent:1 minors:7 consider:1 chain:1 nauchn:1 desirable:1 scalar:1 commute:2 consists:4 remarkably:1 row:4 compact:1 inverse:2 april:1 z1r:1 young:15 finally:2 tm:1 manifolds:6 th:7 under:1 ta:7 case:2 giambelli:1 sons:1 entries:1 difference:5 matrices:14 condition:3 presented:1 turns:1 notes:1 sklyanin:2 itep:2 solution:8 try:1 discrete:7 vector:1 τˆi:1 eigenvalues:1 barbara:1 zi:1 mi:2 sign:1 imply:1 laced:1 gm:4 zr:1 canonical:1 bilinear:17 what:1 appear:2 chicago:4 sum:1 celebrated:1 expressed:1 subspaces:1 new:1 increasing:1 method:5 coefficient:1 respectively:1 here:2 understanding:1 objects:1 ansatz:3 groups:1 along:3 equations:18 z1:1 z2:1 box:1 arrive:1 zr2:1 institute:6 involved:1 vectors:2 allows:2 loop:1 hospitality:1 auxillary:1 useful:2 br:1 family:1 extra:1 apr:1 namely:1 claredon:1 apply:1 univ:1 linearly:1 franck:2 reflected:1 usa:2 commun:1 contains:1 next:1 linear:2 therefore:1 ip:3 taken:1 associated:1 type:3 theoretical:2 diagrams:10 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solv-int9704016.txt |@word neighbors:1 concept:1 partial:1 consider:4 chain:1 results:1 illustrated:1 eds:1 code:1 comments:1 computation:3 edu:3 c1:8 inverse:1 technique:1 βc2:1 languages:2 charge:1 program:2 those:1 under:4 analogous:1 include:1 case:1 stud:2 outside:3 splitting:1 anonymous:1 prof:1 discretizations:2 difference:3 leads:1 school:1 hamiltonian:1 list:4 solution:5 enon:1 large:1 discrete:5 vector:1 prevent:1 work:1 force:1 occurrence:1 consistent:1 literature:1 sign:1 integrability:11 dynamics:1 implemented:3 substitute:1 theory:1 spectral:1 aim:1 nonlinear:13 appear:1 brackets:5 trivial:1 section:3 3w:2 analogously:3 networks:1 above:2 new:1 method:5 contrast:1 modify:1 here:3 equations:11 change:3 ragnisco:1 shift:4 study:2 studied:1 allows:2 ignoring:1 resulting:1 golden:1 equivalence:5 spatially:1 apr:1 requiring:2 replace:3 logarithmic:1 deconinck:1 total:1 circumvent:1 unit:1 derivatives:4 use:6 proceed:2 would:2 positive:2 contains:1 suppl:1 next:2 few:1 call:1 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solv-int9705001.txt |@word consider:1 remarkable:1 localizes:1 sca:6 four:4 grateful:1 antichiral:1 expressions:1 nwo:1 localized:1 certainly:1 superspace:5 tp:1 finally:1 tk:4 th:5 under:1 include:1 applied:5 conjecture:1 advantage:1 far:1 rise:3 putting:1 school:1 immediately:2 hamiltonian:38 turns:1 t2:15 t3:6 t1:3 manifestly:1 superalgebras:1 inspection:1 dfpd:1 work:1 consistent:1 direct:2 second:40 φdd:2 even:3 what:2 nonlinear:1 appear:1 invertible:1 brackets:11 d2:1 section:5 consistently:2 version:2 above:1 krivonos:7 new:12 acknowledgments:1 contrast:1 coefficient:1 full:1 dψj:2 dψd:6 here:3 strong:1 equations:21 z1:2 z2:1 knowledge:1 obtained:6 search:3 studied:1 allows:2 resulting:1 poisson:7 hospitality:1 studies:1 quotient:1 via:5 useful:1 extra:1 prefer:1 brought:1 addressed:1 apply:3 derivatives:2 would:1 commun:1 covariant:3 positive:1 contains:1 ψj:1 nucl:1 therefore:2 those:1 simpler:2 type:2 theoretical:1 ψd:1 more:3 operators:5 validity:1 correspondingly:2 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solv-int9705002.txt |@word results:6 expressions:2 seemed:1 relationships:1 whose:2 simplify:1 young:1 tl:2 under:2 x00:1 ingredient:1 p2:1 supported:1 bilinear:2 entries:3 redefinition:1 difference:1 matrices:3 look:1 solves:1 did:1 turns:1 solution:4 try:1 discrete:15 noted:2 zn:3 ekvac:1 japanese:1 sign:2 jump:1 painlev:9 rigorous:1 further:3 even:2 index:1 what:3 plays:1 funkcial:1 brackets:1 section:1 expressed:5 version:4 above:5 scientists:1 3c:1 obvious:1 acknowledgments:1 satisfy:1 led:1 degree:2 exchange:1 respectively:1 modify:1 here:4 papageorgiou:1 sinh:2 right:1 equations:7 change:1 depended:1 obtained:6 8z:1 search:1 shift:1 study:3 studied:1 suggests:1 products:2 usually:1 symmetrical:1 suitable:1 changes:1 followed:1 classification:1 hermite:5 linearly:2 derivatives:1 use:2 working:1 next:4 few:1 therefore:1 means:1 type:2 more:8 comparison:1 started:1 clue:1 normalized:1 particular:1 known:6 cases:3 must:1 ramani:6 include:1 science:2 equation:11 work:1 det:1 xhn:1 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solv-int9705003.txt |@word partial:1 consider:5 rev:3 results:5 four:2 scalar:1 grateful:1 consists:1 inverse:5 const:1 calculate:1 paris:1 tp:3 c6:1 c5:1 p2:9 orthogonal:2 2rg:1 dell:1 geometrical:1 matrices:2 deformations:1 condition:2 leads:1 iλx:1 riemann:8 presented:4 bn:1 carmo:1 t2:3 solution:16 moldova:2 large:1 discrete:1 vector:4 wronskian:1 sin2:1 ωab:1 generalisations:2 second:4 further:1 dynamics:1 theory:7 spectral:3 what:1 nonlinear:5 plays:2 specification:2 dr2:1 geodetic:1 sur:1 abx:7 new:1 method:3 satisfy:2 b2x:2 here:4 diagonal:2 behaviour:1 tangent:1 separation:1 others:1 consideration:1 along:2 equations:38 change:1 ctt:1 institute:1 study:4 studied:2 allows:2 hospitality:1 3ux:1 r010:3 ξk:1 departement:1 via:2 useful:3 family:1 p3:2 des:1 kobayashi:1 derivatives:1 ψx:2 ψy:1 projector:2 covariant:2 teor:1 few:1 approach:1 type:4 more:2 separated:1 introducing:1 immersion:1 solitons:3 mathem:1 factor:1 odinger:15 curvature:8 basically:1 particular:6 known:3 caz:2 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solv-int9705004.txt |@word homomorphism:1 consider:23 funct:1 rev:2 particular:1 dynamic:1 trigonometric:3 hαi:1 commute:1 consists:2 l13:1 whose:1 preserves:2 const:1 submanifold:1 kinetic:2 ty:1 paris:2 bx2:1 tr:19 young:3 tm:2 restriction:1 petersburg:2 elliptic:7 dressing:4 tr1:6 unit:2 di1:1 case:10 belonging:1 r12:11 r13:2 advantage:1 p3:3 frequencies:2 pages:1 rise:4 springer:4 choice:1 reinterpret:2 every:2 entries:3 word:1 emphasized:1 matrices:22 condition:3 groups:1 dim:1 din:1 immediately:2 hamiltonian:48 turns:1 notes:1 developing:1 t2:1 solution:1 t0:1 t1:1 magnet:3 involution:14 vector:4 science:1 anal:1 mn:5 zi:2 zk:2 det:3 α2j:5 direct:1 groupes:1 integrability:1 arnold:2 2q2:2 quite:1 canonical:12 spectral:27 will:1 what:1 filtration:2 invertible:1 brackets:13 section:7 selected:1 expressed:2 consequent:1 henceforth:1 birkhoff:1 version:1 poles:11 subspaces:6 new:11 construction:3 change:1 method:11 completion:1 soviet:1 q0:1 multipole:1 respectively:1 here:24 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solv-int9705007.txt |@word consider:10 rev:2 global:3 datum:1 results:3 leads:10 consists:2 expressions:3 γz:2 γx:8 depend:5 paris:5 disposal:1 description:3 simplify:1 29b:1 29a:1 superficially:1 finally:6 does:8 those:1 th:1 under:5 logarithm:2 g5:4 linearising:1 straightforward:2 far:2 p0:1 induce:1 choice:1 every:4 difference:4 matrices:2 condition:49 four:2 presented:4 did:1 turns:7 list:7 solution:19 discrete:28 relation:3 upr:1 programme:1 zn:4 century:1 go:1 second:30 zx:2 further:2 zw:1 odd:3 ode:3 quite:1 canonical:4 even:6 established:1 what:4 nonlinear:1 stands:1 incompatible:2 exactly:1 3w:1 xxvii:1 19th:1 poles:2 above:4 capital:1 new:2 3a:1 method:5 coefficient:1 full:2 led:2 degree:3 choose:3 here:5 understanding:1 inverse:1 possibility:1 address:1 consideration:1 along:2 standard:3 equations:24 appears:3 logarithmic:4 knowledge:1 obtained:4 remark:1 ǫx:1 suitably:1 receive:1 study:4 studied:2 subcase:1 resulting:2 usually:1 implement:2 history:1 makes:1 involves:1 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solv-int9705008.txt |@word partial:1 consider:8 results:6 consists:4 whose:6 inverse:5 deterministic:1 recurrence:3 uniqueness:2 stochastic:1 include:1 γf:1 orthogonal:1 springer:1 choice:3 every:1 difference:1 exact:1 condition:2 solution:31 t0:1 try:1 convenience:1 dit:1 anal:1 originally:1 neighborhood:6 sign:1 approximation:6 fold:3 second:16 nonhomogeneous:1 canonical:1 aim:1 what:1 nonlinear:2 invertible:1 section:2 expressed:1 poles:1 above:8 new:2 method:26 full:1 xfn:3 respectively:2 pushing:1 prescribe:1 here:2 understanding:1 behaviour:1 focused:1 ansatz:2 separation:2 others:2 alone:1 xγ:7 standard:1 equations:13 box:1 great:1 krall:1 institute:1 adomian:9 resulting:1 usually:1 succesive:3 f0:8 technique:1 useful:2 compare:1 apply:2 tools:1 derivatives:1 use:2 give:3 few:3 therefore:1 taken:1 volterra:9 until:1 more:4 clever:1 becomes:1 clue:2 berlin:1 known:6 cases:3 account:4 science:1 equation:43 work:1 values:2 following:2 trans:1 example:3 beautiful:1 f1:10 f2:1 degenerate:1 stated:2 process:1 pieces:1 numbers:2 want:1 sense:1 sought:1 verlag:1 goal:1 rather:2 get:7 write:2 how:1 ordinary:2 singular:3 may:1 variant:2 dx2:1 applications:1 fk:10 fn:7 fo:1 light:1 explicit:1 so:1 order:16 adamian:1 help:1 jν:1 indeed:3 satisfied:1 existence:1 satisfies:1 its:7 lf:3 complicate:1 chosen:1 bringing:1 ll:1 solving:7 better:1 parts:1 choose:6 derivative:3 defining:1 non:5 good:1 obtaining:2 accumulate:1 now:5 nor:1 easily:5 february:1 2q:1 found:4 side:4 2k:1 homogeneous:11 arxiv:1 formulate:1 series:5 hypergeometric:8 reduce:1 related:1 our:5 eq:9 special:7 out:1 shown:1 frontier:1 since:2 crucial:1 looking:2 transforming:1 contained:2 constants:1 induction:3 math:2 complicates:1 linear:10 quite:2 reason:1 term:5 starts:1 consequence:1 first:8 origin:1 xk:2 romania:1 initial:8 xn:2 xf:9 relations:1 xq:2 given:7 dxx:1 rewritten:1 introduction:1 unknown:1 construct:2 tell:1 recovered:1 tool:1 part:11 x2:6 x1:8 than:2 wide:1 supposes:1 iteration:2 zero:2 matter:1 supposed:1 minus:1 sees:1 generality:1 rewrite:2 manner:1 seen:1 clearly:1 convenient:1 able:1 concerns:1 take:13 finding:2 green:1 formulas:1 shall:5 who:1 most:5 involving:1 but:3 extremely:1 class:1 dordrecht:1 coincides:1 points:2 exp:1 grama:1 left:3 physics:5 show:2 fink:1 relation:5 solutions:13 d2:2 find:18 principal:2 parameters:2 should:1 only:1 integrable:1 means:1 df:6 simplest:2 cannot:3 dx:20 dy:6 dt:9 dp:1 conditions:3 differential:14 prescribing:1 view:1 decides:1 see:1 decided:1 sec:1 result:1 recently:1 eigenfunctions:1 definite:1 written:1 difficulties:1 identification:1 closed:1 αf:1 boundary:2 approach:4 terms:2 sole:1 however:1 2αx:1 solv:1 amer:1 come:1 improve:1 last:2 many:7 taking:2 according:1 picard:3 reobtain:1 finds:1 ck:10 kamke:1 cn:1 point:11 xν:1 constant:1 indefinite:1 locally:1 been:3 int:1 treat:2 interest:1 define:1 obtained:6 corresponding:1 sufficient:1 writting:1 observe:1 c2:8 c1:8 present:1 case:3 unify:1 look:4 value:3 will:1 suppose:1 behavior:3 thus:2 them:2 make:3 same:3 complex:2 propose:1 modification:2 reminder:2 finite:1 independent:3 used:2 hand:3 moving:1 identity:1 lower:1 no:1 well:2 concrete:2 without:1 solve:5 arising:1 usual:1 comment:2 proposed:2 being:2 obtain:7 atomic:1 kluwer:1 seems:1 other:2 transformed:1 solvable:1 euler:1 generalized:1 leipzig:1 around:1 represents:2 decomposed:1 possible:1 using:3 unique:1 formal:3 loss:1 modifications:2 necessary:2 reduces:1 works:1 bucharest:1 because:2 old:1 methods:1 deal:2 some:1 back:1 examples:1 proceeding:1 integration:4 does:1 decomposition:12 bessel:11 core:1 slight:1 equivalent:3 confluent:3 illustration:1 cochran:3 polynomials:8 although:2 bx:1 properties:1 stage:1 about:1 extension:1 o:1 regular:3 consequently:1 mathematical:2 soc:1 differentialgleichungen:1 into:9 integral:13 right:2 references:1 operator:8 classical:6 there:1 transform:3 start:1 appl:1 way:4 was:1 function:7 form:25 gauss:2 highest:1 true:1 aqk:2 applying:1 smooth:2 us:4 theoretical:1 below:1 problem:5 piece:1 called:1 ordered:3 defined:2 abstract:1 general:12 aq:8 engineering:1 formulation:1 defines:1 functions:15 variety:2 when:2 application:1 interested:1 department:1 nq:1 conclusion:2 separate:1 preceding:1 problems:8 variation:2 includes:1 chance:1 important:1 pseudo:4 starting:2
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solv-int9705009.txt |@word gd:6 represent:9 concept:2 partial:4 consider:13 chain:4 directions:1 global:5 trisecant:1 invent:1 leads:6 eds:2 scalar:35 disc:8 generalize:1 grateful:1 consists:8 gn:2 expressions:4 disk:1 gi:3 compact:10 inverse:2 depend:5 paris:1 tt:2 technique:3 nonlocal:2 kα:4 tj:2 γn:2 dressing:7 analogous:2 include:1 applied:1 belonging:2 fay:1 string:1 g1:13 g0:15 very:6 rise:10 dell:2 choice:9 every:1 difficult:2 nontrivially:1 difference:6 matrices:2 condition:5 look:2 discovered:1 riemann:1 presented:2 positions:1 tokyo:1 t2:20 solution:4 excessive:1 t1:21 try:1 discrete:24 convenience:1 vector:1 subscript:2 indices:9 anal:1 hospitality:1 neighborhood:1 const:1 meromorphic:1 consistent:2 onecomponent:1 zero:13 bilocal:1 further:3 dynamics:15 substitute:1 linear:20 bilinear:24 index:13 nonlinear:2 developed:1 d2:1 section:16 expressed:1 orthogonaux:1 version:3 poles:2 d0:7 above:1 obvious:1 consisting:6 contrast:1 coefficient:1 devoted:2 condensed:1 full:4 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solv-int9705010.txt |@word represent:1 λa1:1 consider:1 cj:3 hierarchy:4 novikov:1 splitting:3 identity:1 scattering:1 paper:1 relation:1 modified:1 differentiation:1 substituting:2 expressions:4 denotes:1 d2:1 λn:8 principal:1 whose:1 inverse:1 group:4 symmetry:1 density:1 fix:1 solving:1 functions:4 should:1 quadratures:4 being:1 finally:1 powers:2 under:1 integrable:4 transformation:2 real:2 applied:1 matem:1 above:5 means:2 results:1 possible:1 introduce:1 choice:1 dx:10 press:1 using:1 now:3 densities:2 prime:1 reveal:1 dubrovin:1 equality:1 hereafter:1 always:1 reduces:1 differential:7 make:1 yield:2 integrated:1 solved:1 academic:1 yields:5 2a:5 arbitrary:5 become:1 stationary:9 2j:1 view:1 mathematical:1 reidel:1 arxiv:1 methods:1 some:3 idea:2 solution:2 facts:1 integrability:3 street:1 c1:2 choosing:1 respect:4 our:2 kdv:14 ode:1 special:1 provided:2 what:2 nonlinear:1 λj:2 kiev:2 integro:2 subsequent:1 furthermore:1 integration:1 its:2 transforming:1 acting:1 determined:1 provides:1 between:1 new:3 get:2 approach:1 method:2 rj:1 york:2 inserting:2 full:1 terms:1 olver:1 recurrence:1 2c:1 however:1 here:2 standard:2 admits:1 applications:1 ansatz:1 groups:2 solv:1 based:1 come:1 change:1 takes:1 ukraine:1 v0:11 about:1 arrive:1 last:2 a0:2 institute:1 determining:3 study:1 rdx:2 recognized:1 enabling:1 turn:1 admit:1 unknown:1 action:1 makes:1 recursion:2 zhdanov:2 considerations:1 ci:1 via:1 cn:8 family:2 follows:3 u1:1 variables:1 integrations:1 transform:1 restrict:1 nothing:2 ηu:1 2v0:1 references:1 solve:1 operator:9 guesses:1 establish:1 fj:1 ηx:1 derivatives:1 use:1 additional:1 second:1 equations:8 springer:1 initial:5 question:1 u0:5 relations:4 u2:3 their:1 constants:2 show:1 siam:1 vj:3 more:2 function:3 inefficient:1 form:4 given:1 operators:1 math:1 else:2 repeated:1 segur:1 repeatedly:1 mail:1 cases:1 c0:5 than:3 coefficients:1 case:2 account:1 nauk:1 ux:1 integrating:4 recall:1 equation:31 see:3 easier:1 will:5 infinitesimal:4 suppose:1 rewritten:1 uj:6 following:6 making:1 gives:1 ua:1 example:1 def:4 f0:3 f1:1 f2:1 symmetries:2 uspekhi:1 generality:1 af:1 int:1 abstract:1 aj:4 dx2:2 vn:5 vx:1 conserved:3 taking:1 avj:1 need:1 evidently:2 lie:6 containing:1 end:1 recursive:1 no:1 suggest:1 latter:1 recurrent:2 connection:1 note:1 application:2 conditions:1 criterion:1 details:2 solitons:1 mathematics:1 ordinary:2 parameter:5 higher:4 ξx:1 independent:1 matveev:1 philadelphia:1 may:1 av0:1 ξu:1 polynomials:1 riccati:7 simplify:1 ra0:1 variable:1 invariance:1 structure:2 say:1 third:1 λv1:1 dordrecht:1 whole:2 into:5 kh:1 coincides:1 yielding:1 analysis:1 order:1 equivalently:1 so:1 easily:1 ibragimov:1 first:3 physics:1 having:2 fact:1
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solv-int9705011.txt |@word consider:1 remarkable:1 results:3 integration:2 computation:2 expressions:1 inverse:2 const:1 paris:1 under:3 hermann:1 case:1 very:1 choice:1 matrices:1 dubrovin:1 solution:10 vector:1 shows:1 integrability:3 street:1 iσ1:2 dψ2:2 dψ1:1 theory:3 will:4 what:1 trivial:1 erieurs:1 above:3 new:5 method:3 satisfy:2 here:1 les:1 ansatz:1 groups:2 equations:16 obtained:2 remark:1 institute:1 studied:1 drk:2 zhdanov:2 via:1 establish:1 use:1 next:1 call:2 ibragimov:1 means:2 introducing:1 solitons:2 operators:1 odinger:2 particular:1 springer:1 valued:3 integrating:1 equation:21 infinitesimal:1 following:4 fulfill:2 def:1 give:3 cartan:2 tan:1 lamb:1 s2:1 s1:4 s0:1 how:1 syst:1 ordinary:3 parameter:1 may:1 wiley:1 dx2:2 applications:2 lax:1 constants:2 sk:2 si:5 sn:2 order:1 elie:1 holds:2 help:1 hierarchy:7 dv:12 paper:2 mentioned:1 its:3 derive:1 solving:2 mail:1 wellknown:1 easier:1 them:1 good:1 they:1 eigenvalue:1 2v:5 dirac:9 university:1 higher:3 2k:2 differential:5 idea:1 2hv:1 quantum:1 our:1 kiev:2 furthermore:1 since:1 denotes:1 acting:1 reader:1 integrated:1 math:1 rk:4 linear:1 york:4 asi:1 beginning:1 definition:1 derivation:1 r2:2 determining:2 hence:3 first:2 there:1 symmetry:7 miura:1 variables:1 number:1 restrict:1 equating:1 given:2 necessarily:1 manakov:1 system:11 relations:2 academy:1 exactly:1 x0:1 than:2 vxxx:1 accordance:1 see:3 determined:1 powers:1 symmetries:6 generality:1 rewrite:1 matem:1 any:1 emes:1 lie:11 latter:1 note:2 sciences:1 potential:2 allerton:1 formulae:4 nothing:1 class:3 soliton:1 tpa:1 dordrecht:1 kh:1 looked:2 ext:1 physics:1 fact:1 show:1 relation:1 solutions:3 d2:6 d3:1 lemma:3 coefficients:4 integrate:1 integrable:5 dh:1 get:1 df:1 dg:1 between:1 dx:34 dy:2 combinations:1 du:1 arxiv:1 yield:3 nauk:1 leur:1 common:1 fixed:1 clausthal:1 set:1 exists:1 namely:1 eliminating:1 satisfying:1 commutation:1 doebner:1 bureau:1 simplest:1 approach:1 matveev:1 however:1 jr:1 key:1 solv:1 last:1 nikitin:1 connection:1 mann:1 ck:1 ci:3 cn:1 conclude:2 simple:2 mkdv:13 dependent:1 constant:2 ct:1 due:2 pk:8 pn:2 ukraine:2 else:1 6v:2 olver:1 c2:9 c1:11 present:1 applied:1 look:1 tanh:1 aim:1 technical:1 suppose:1 familiar:1 procedure:1 thus:2 4c1:1 reads:1 vt:1 vx:1 recursion:1 recurrent:2 complex:3 pauli:1 difficult:1 hand:1 infinite:1 identity:1 schr:2 2gv:1 no:1 well:1 without:2 components:2 possesses:1 usual:1 using:2 scattering:2 preprint:1 zakharov:1 quadratures:7 setting:1 transformed:1 theorem:1 transformation:2 real:3 iλ:4 press:1 immediately:1 loss:1 follows:1 admitted:1 remind:1 yields:3 arbitrary:4 works:1 stationary:11 mathematical:1 reidel:1 classical:1 some:2 consultants:1 uspekhi:1 kdv:1 fushchych:2 provided:1 2c1:3 inserting:3 equivalent:1 novikov:2 consequently:1 into:3 within:3 pair:1 references:1 operator:6 initial:2 u1:2 u2:2 inasmuch:1 function:10 form:7 repeatedly:1 made:1 applying:1 smooth:1 us:1 ui:1 demonstrate:1 problem:2 ua:1 mechanics:1 proved:1 computing:1 int:1 recognize:1 abstract:1 general:4 functions:6 variety:1 composing:1 priori:1 details:1 papers:1 mathematics:1 pitaevski:1 conclusion:1 elements:1 polynomials:2 commutator:1 variable:2 matrix:5 4v:2
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solv-int9705012.txt |@word proposition:12 sci:2 consider:5 rev:3 results:9 eds:3 scalar:7 gd:20 expressions:3 gl:4 gk:1 gj:4 gi:8 compact:2 preserves:4 inverse:8 depend:4 analytic:1 integral:3 re:9 paris:1 concerned:2 departing:3 tn:18 finally:2 tm:5 those:3 th:12 te:1 applied:2 conjecture:1 g3:4 g2:3 g1:2 very:2 rise:1 dokl:1 wave:12 corollary:1 p1:1 got:1 resonant:1 gℓ:7 condition:10 dim:2 school:1 obvious:1 riemann:1 solves:4 hamiltonian:2 bn:21 t4:1 t2:9 solution:46 t1:5 large:1 vector:2 recall:2 anal:2 ωij:2 commented:1 t31:1 dealing:1 consistent:1 requirements:2 direct:3 literature:1 zero:7 concludes:1 further:1 dynamics:1 gm:5 linear:34 spectral:6 established:1 fℓ:3 appear:1 invertible:4 t2n:2 diag:1 sum:1 expressed:6 consequent:1 3k:2 ˆb:15 localized:2 above:5 new:9 method:4 ˆn:6 3d:1 coefficient:3 devoted:1 exponentials:1 degree:4 deduces:1 nimmo:2 even:1 here:7 water:1 desired:2 objects:1 china:1 galilean:3 groups:1 situation:1 quite:1 equations:21 appears:7 contraction:1 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solv-int9705013.txt |@word sci:1 consider:2 ceases:1 varying:1 results:3 four:4 eds:3 ginzburg:2 restated:1 consists:1 lebedev:1 causes:1 devoted:1 inverse:1 patches:1 show:1 tn:25 quasi:4 tm:3 those:5 th:3 under:1 exposition:1 eikonal:1 rel:1 straightforward:1 orthogonal:1 very:2 implicitly:2 ηij:2 dokl:1 wave:2 difference:2 exact:2 condition:2 notations:1 twistorial:11 dubrovin:4 riemann:21 hamiltonian:23 turns:2 notes:4 t2:2 t3:1 t1:2 leave:1 solved:1 vector:4 phase:4 science:1 small:1 gauge:1 shows:1 petersburg:1 l95:1 neighborhood:2 grateful:1 l98:1 approximation:1 integrability:4 evaluated:1 rigorous:1 further:3 implemented:1 canonical:23 established:1 what:1 nonlinear:5 reformulated:1 invertible:1 brackets:2 giving:1 section:4 reminiscent:1 version:1 above:8 kyoto:4 new:2 method:11 3d:2 satisfy:7 compact:2 full:1 notions:1 respectively:2 hitchin:3 here:1 tangent:2 others:1 concluding:1 quite:1 equations:29 change:3 obtained:1 institute:2 shift:1 vectors:1 suggests:2 resulting:1 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solv-int9705014.txt |@word homomorphism:1 consider:3 equalities:1 ptd:8 leads:1 eds:1 grateful:1 edu:1 go:3 oevel:2 inverse:1 depend:5 calculate:3 tu:1 tn:2 δhl:1 tj:5 tk:1 ti:19 zhang:1 far:1 exact:1 condition:1 hamiltonian:3 ref:1 notes:1 t2:6 t3:1 t0:4 t1:2 discrete:9 vector:19 rj:1 application:1 modified:4 second:2 dordrecht:1 korteweg:1 chen:2 further:2 theory:5 established:1 what:3 nonlinear:12 sub:1 expressed:1 hereditary:1 current:1 experiment:1 fuchssteiner:5 above:3 new:9 order:1 consisting:2 coefficient:9 lee:2 degree:13 respectively:1 here:5 galilean:1 address:1 equations:33 obtained:2 institute:1 shift:1 commonly:2 resulting:2 usually:1 conveniently:1 studies:1 identification:1 family:1 p60:1 explained:1 virasoro:14 kγ:3 use:1 would:2 prove:4 visit:1 chief:1 tm:4 call:2 kl1:8 kl2:2 memory:1 conservation:1 associated:1 type:4 von:1 more:9 fokas:1 operators:1 under:1 curvature:1 particular:1 known:2 must:1 keeping:1 ma:6 integrating:1 science:1 equation:20 ρl:37 itself:1 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solv-int9705015.txt |@word homomorphism:6 consider:5 particular:6 focus:1 gy:2 leads:1 eds:1 commute:1 go:2 oevel:4 expressions:1 research:1 causes:1 inverse:1 depend:4 calculate:2 must:1 tj:2 th:2 under:6 include:1 case:4 belonging:1 broadly:1 zhang:1 very:3 rise:1 results:2 every:2 exact:1 condition:1 presented:7 notes:1 t2:2 applicable:1 t1:4 discrete:6 vector:29 math:10 recall:1 relation:1 dealing:1 discover:1 modified:22 integrability:3 korteweg:1 chen:2 further:4 linear:2 spectral:3 what:2 nonlinear:11 plays:1 appear:1 ak3:11 ak2:7 section:6 hereditary:3 birk:1 fuchssteiner:11 above:6 new:13 method:2 satisfy:2 lee:2 degree:3 respectively:3 realizations:2 here:11 china:1 galilean:1 groups:1 active:1 equations:52 change:1 obtained:3 aky:4 institute:1 shift:1 later:1 aki:1 resulting:1 published:1 usually:1 suitable:1 studies:1 uniquely:1 φkl:1 cij:2 tools:1 subalgebras:1 virasoro:23 use:1 tn1:6 would:1 tn2:5 visit:1 next:3 noting:2 kl1:6 kl2:2 memory:1 taken:1 candidates:1 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solv-int9705016.txt |@word represent:1 sci:1 consider:1 remarkable:2 similarity:2 depends:1 varying:2 results:3 leads:1 scalar:3 supplement:1 consists:2 expressions:1 gl:2 whose:2 inverse:4 depend:1 ceases:1 tr:2 singularit:1 tn:2 kα:6 tj:8 those:1 elliptic:4 ti:56 include:1 p2:1 random:2 string:1 straightforward:1 outside:2 very:1 witten:9 govern:1 inherited:1 difference:1 matrices:4 deformations:9 condition:1 dubrovin:1 riemann:3 hamiltonian:5 turns:4 xyz:2 sklyanin:2 list:1 solution:6 t1:2 solved:1 vector:2 minimal:1 universal:1 small:3 eigenvalues:5 noted:1 des:1 lecture:2 ekvac:1 nonautonomous:1 direct:1 approximation:1 fold:1 integrability:2 dynamics:11 ode:2 canonical:1 schlesinger:9 nonlinear:2 const:12 reformulated:1 diag:1 section:2 selected:1 version:1 poles:2 sur:1 above:9 new:5 method:1 filled:1 3d:1 coefficient:1 ibid:1 here:5 hδs:1 ansatz:4 separation:1 situation:5 consideration:2 equations:21 logarithmic:1 obtained:3 interscience:1 technical:1 garnier:2 leaving:1 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solv-int9705017.txt |@word partial:1 consider:5 chain:7 rx:2 varying:1 results:5 scalar:1 generalize:1 sci:1 expressions:2 inverse:2 const:8 aji:22 paris:1 tu:1 finally:1 investigation:3 preserved:1 under:10 analogous:2 applied:1 abelian:1 orthogonal:1 far:1 quadruples:4 ηij:2 wave:10 2ry:1 2rx:1 emphasized:1 iut:1 generalised:3 dubrovin:2 riemann:12 presented:1 turns:3 solution:2 ri:4 pullback:1 discrete:2 vector:1 rj:3 science:1 indices:4 round:1 enjoy:1 des:2 direct:2 second:8 further:2 canonical:1 spectral:5 what:2 nonlinear:1 iterating:1 dr1:6 section:2 dr2:6 analogously:1 rescale:1 sur:3 above:1 new:5 net:1 congruences:5 hb1:1 bn:4 exercise:1 satisfy:10 respectively:1 promising:2 component:7 here:2 behaviour:1 les:2 tangent:1 address:1 represented:2 consideration:1 method:1 equations:36 change:2 knowledge:1 obtained:7 sending:1 remark:2 institute:1 shift:1 study:1 vectors:2 akj:3 aki:11 periodic:22 bol:1 generale:1 akl:2 βij:21 hn2:2 uniquely:1 appropriately:1 family:1 extra:1 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solv-int9706004.txt |@word proposition:5 ajs:1 partial:1 consider:12 funct:1 alg:2 results:2 leads:2 eds:1 ferreira:1 commute:1 consists:5 sci:1 expressions:1 nwo:1 gr:20 compact:1 inverse:1 depend:2 dickey:9 utwente:2 tn:16 tkn:1 tj:1 manifolds:1 th:12 ti:24 multilinear:1 applied:1 fax:1 string:1 straightforward:1 orthogonal:8 geometrical:4 corollary:2 p1:2 coprime:4 multicomponent:1 condition:17 generalised:1 dim:1 hamiltonian:4 solution:11 t1:1 leave:1 vector:13 math:16 anal:1 unifying:1 solutions:12 lw1:1 zk:1 direct:2 zero:4 concludes:2 further:1 dynamics:1 substitute:1 even:2 index:1 what:1 nonlinear:2 appear:2 section:6 resume:1 foregoing:1 version:1 subspaces:6 obvious:1 consisting:1 satisfy:5 deduces:3 respectively:5 l1:56 component:1 here:4 ihes:1 groups:1 melnikov:1 equations:20 box:1 sending:2 remark:1 studied:1 allows:1 action:1 proof:14 uniquely:1 formulated:1 useful:2 projection:4 claim:1 private:1 modifying:1 viz:1 apply:2 univ:1 denotes:2 virasoro:1 derivatives:1 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solv-int9706005.txt |@word partial:1 funct:1 leads:5 scalar:2 follow:1 expressions:2 compact:1 inverse:1 ario:1 tr:5 tn:1 charge:1 present:1 under:1 worth:1 p2:1 straightforward:2 far:1 choice:2 matrices:1 entire:1 dubrovin:1 riemann:3 hamiltonian:11 turns:1 large:1 involution:3 anal:1 cfm:1 consistent:1 second:5 incidentally:1 dynamics:2 even:1 nonlinear:3 sub:1 suspect:1 fractional:2 new:2 acknowledgments:1 coefficient:1 component:1 here:5 water:2 separation:1 address:1 equations:21 obtained:10 study:2 studied:2 hospitality:1 suitable:1 santa:1 catarina:1 would:2 prove:1 distinct:1 finally:1 few:2 noting:1 call:1 therefore:1 mckean:1 type:1 operators:2 curvature:1 rigid:1 particular:2 known:3 must:3 nutku:3 equation:6 work:2 following:1 example:1 beautiful:1 give:3 expanding:2 share:2 degenerate:1 rescaling:1 information:1 write:6 how:2 nontrivial:3 parameter:1 description:8 may:1 wiley:1 derived:1 residues:1 lax:20 fg:1 wave:1 natural:1 dynamical:2 succeeded:1 correspond:2 so:1 allow:1 sc:1 representation:3 order:5 hierarchy:3 indeed:3 over:1 years:1 rubtsov:1 paper:1 through:2 2v:7 satisfies:1 roots:1 brunelli:3 thank:1 acknowledge:1 ln:3 interesting:2 systems:8 mail:1 deformation:1 them:1 framework:1 they:6 cep:1 singularity:1 now:1 yu:2 represents:1 term:1 2q:3 invariants:2 university:1 2m:4 universit:1 2h:6 differential:1 energy:1 reduce:2 expect:1 our:1 beyond:1 eq:1 special:2 out:1 shown:1 benney:1 matrix:3 space:1 res:2 furthermore:1 since:3 rev:1 ref:2 math:4 shows:2 linear:2 ısica:2 diagonal:2 departamento:2 quite:2 admits:1 york:1 members:1 generate:1 definition:2 derivation:1 universidade:1 hyperbolic:1 ufsc:2 hence:1 first:3 separable:2 radical:1 variables:1 waves:1 number:1 done:1 another:3 given:2 rewritten:1 similarly:1 leading:2 system:22 relations:1 their:1 appl:1 structures:3 gives:3 shallow:2 zeroth:2 whitham:1 part:1 representing:1 peculiar:1 see:1 were:1 opolis:1 powers:3 symmetries:1 derivative:1 generalization:1 yielding:1 manner:1 any:4 rochester:2 zero:1 florian:1 pursued:1 note:7 potential:2 finding:1 trace:1 sets:7 pleasure:1 phase:1 class:1 orlov:1 flow:1 physica:1 physics:1 fact:6 laws:1 particularly:1 show:5 supported:2 relation:4 inconsistent:1 ashok:1 d0:3 d1:4 completion:1 parameters:1 only:1 explicitly:1 de:4 dx:7 during:1 densities:10 nicely:1 arxiv:1 hydrodynamic:1 contain:1 satisfy:2 set:3 physically:1 namely:2 nonstandard:2 best:1 clarifies:1 brazil:2 federal:1 irrotational:1 written:3 various:1 closed:3 between:4 terms:1 uux:2 missing:1 restricting:1 however:7 reproduces:1 solv:2 uχ:2 both:4 last:1 taking:2 expression:1 cn:3 simple:3 corresponds:1 whatever:1 polynomial:1 respect:3 described:2 been:2 describes:3 interest:1 define:1 generating:8 corresponding:1 quantities:2 gas:11 systematic:1 olver:3 surveys:1 those:1 case:1 value:1 will:1 property:1 vt:5 vx:7 grant:1 recursion:6 same:3 campus:1 emphasize:1 going:1 several:1 higher:2 literature:1 trivially:1 infinite:6 normalization:1 off:1 charges:15 no:1 well:7 analysis:1 dispersionless:5 consistency:1 model:1 proposed:1 das:1 obtain:4 identify:1 immediately:1 yet:2 impetus:1 density:1 zakharov:1 alternate:2 easy:5 gave:1 around:3 easily:2 possible:1 period:1 vγ:3 integer:1 enriquez:1 like:3 δv:1 follows:3 δu:1 specific:1 continue:1 either:1 δh:2 arbitrary:1 become:1 because:1 proper:1 provided:1 dimensions:1 lead:1 extensively:1 does:1 nitions:1 equivalent:2 bi:1 expansion:2 br:1 found:1 2n:2 pγ:1 about:1 a1:3 usa:1 novikov:1 quasilinear:1 discussed:1 consequently:3 h2:1 h0:1 h1:1 functional:1 nsf:1 references:1 sov:1 operator:4 elastic:3 there:2 u2:8 conservation:1 notices:1 was:5 naturally:3 function:6 medium:3 form:9 jun:1 but:1 hn:29 russian:1 cnpq:1 ux:8 ut:6 uv:4 us:3 un:1 limit:1 problem:1 associated:4 int:3 recognize:1 abstract:1 general:3 conserved:26 formalism:1 identities:1 check:4 functions:8 polytropic:10 when:1 ny:1 department:2 elements:1 problems:1 manin:2 a0:3 important:2 astronomy:1 structure:5 fsc:1 implies:1 using:3 4u:1 equivalently:1 4d:1
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solv-int9706006.txt |@word neighbors:1 partial:2 consider:14 remarkable:1 t2i:2 pseudodifferential:10 invent:1 leads:2 eds:2 commute:2 during:1 consists:2 homomorphism:1 expressions:2 nwo:1 cases:1 gr:30 preserves:4 inverse:1 calculate:2 reformulate:2 iii:1 tt:1 equivalence:1 nonlinear:1 charge:22 tm:3 tj:6 tk:16 th:4 auv:1 tg:6 analogous:2 must:2 ta:4 applied:1 straightforward:8 orthogonal:6 transitively:4 conditions:1 wave:20 corollary:8 isomorphism:6 putting:1 entries:1 matrices:3 dim:3 level:1 bn:1 turns:6 t4:2 t5:3 t2:4 t3:3 d2:2 t1:7 involution:5 convenience:3 vector:24 math:11 ǫjk:1 small:1 eigenvalues:1 hospitality:1 der:1 ǫji:1 ten:2 submodules:1 sℓ:1 det:1 direct:2 sign:1 go:1 second:8 folowing:1 zx:3 eλj:10 concludes:1 further:5 dynamics:1 odd:16 eigenspaces:5 victor:1 bilinear:24 t2k:3 gl:6 stands:1 invertible:5 ψn:1 diag:5 section:8 expressed:3 d3:2 rescale:1 version:2 δq0:30 subspaces:8 basic:1 replaced:1 row:2 consisting:3 ek1:2 ordp:1 coefficient:5 degree:1 q0:4 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solv-int9707002.txt |@word minors:1 consider:5 remarkable:1 results:1 functionen:1 gc:1 mnm:1 computation:1 consists:1 compact:1 hold:2 depend:1 kγ:3 kα:35 γn:11 elliptic:14 under:2 degeneration:1 p2:3 labels:1 kτ:10 entries:1 matrices:1 condition:5 notations:1 riemann:4 hamiltonian:4 sklyanin:1 solution:2 try:1 involution:5 vector:1 indices:1 eigenvalues:5 anal:1 configurations:5 zl:3 upper:9 ze:1 direct:2 tex:1 surrounding:1 second:5 estimated:1 odd:3 selfadjointness:2 canonical:2 spectral:6 index:1 nonlinear:1 appear:1 section:3 sheeted:3 3h:4 above:4 new:1 acknowledgments:1 satisfy:2 even:4 here:2 desired:1 sinh:1 address:1 equations:5 z1:1 z2:1 obtained:4 involved:1 study:1 vectors:2 glg:1 ekx:1 action:4 useful:1 classification:1 requiring:1 talon:1 total:1 use:1 would:2 prove:6 distinct:8 finally:3 next:3 few:1 call:1 therefore:15 taken:1 associated:2 mckean:5 type:1 more:2 th:2 billey:1 becomes:2 odinger:4 curvature:1 berlin:1 appendix:1 normalized:1 known:1 cases:3 eζ:1 iτ:1 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solv-int9707003.txt |@word sco:1 looped:2 partial:3 consider:13 chain:5 zhang:1 crucial:1 global:5 rod:5 trigonometric:1 gg:3 commute:1 computation:4 parameterization:2 intricate:1 perturbations:1 expressions:1 iu2:5 coleman:2 compact:2 whose:4 preserves:4 inverse:6 sogo:2 calculate:3 dieudonn:1 paris:1 concerned:1 equivalence:1 ind0:2 zreg:4 quasi:30 critical:11 manifolds:1 elliptic:11 under:1 hermann:1 tg:12 include:2 worth:1 applied:1 conjecture:2 string:3 notations:1 kτ:2 very:6 decreases:1 u2s:1 conditions:1 geometrical:4 rotational:1 ga:1 difference:1 exact:5 strang:1 condition:29 dim:1 tokyo:2 riemann:1 hamiltonian:3 did:2 proc:1 t4:1 t5:2 t2:4 solution:9 occurs:2 large:9 discrete:1 vector:9 phase:1 min:1 section:4 indices:1 gauge:4 anal:1 ict:1 commented:1 des:1 force:3 grateful:1 periodicity:3 folds:1 kc2:1 direct:2 go:2 zero:5 fiber:7 tangential:3 concludes:1 dynamics:4 acid:1 odd:1 theory:21 even:17 employ:1 rewritten:2 nonlinear:6 plays:3 appear:8 t2n:17 theories:1 sun:1 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solv-int9707006.txt |@word consider:3 chain:7 illustrated:3 computation:1 consists:1 whose:1 graph:1 concerned:1 quasi:2 case:5 g0:3 far:1 wave:19 novel:1 mixing:1 exact:3 condition:4 hamiltonian:2 convenience:1 eigenvalues:1 noted:2 concluded:1 grateful:1 second:5 further:1 canonical:1 even:3 nonlinear:3 plays:1 appear:7 ishiwata:3 sum:2 anniversary:1 expressed:4 version:1 above:2 new:1 method:1 body:14 outgoing:1 full:1 respectively:3 component:1 here:5 reported:1 ansatz:1 investigating:1 appears:2 incoming:1 parameters:1 study:3 resonance:1 captions:1 total:2 unit:1 eψ:1 γk2:9 contains:1 negative:1 next:1 noting:1 bethe:1 diagrams:4 more:2 initial:7 operators:3 odinger:4 normalized:1 must:2 ma:1 quantized:1 equation:2 obvious:1 thin:1 following:1 my:1 impose:1 figure:1 calculation:4 relativistic:2 purposes:1 saito:1 states:5 collision:7 performed:1 occur:1 rather:3 discussion:1 holds:1 recovers:1 sate:1 ordinary:2 parameter:1 after:1 diagram:6 applications:1 waves:1 law:1 revealed:1 shigeki:1 types:1 third:1 computations:2 cannot:1 green:1 representation:1 order:1 words:1 interpreted:3 through:1 argued:1 japan:2 its:2 before:1 solitary:4 thank:1 somewhere:1 masses:5 boson:1 fig:10 constitutes:1 might:1 non:7 yj:1 introduce:1 mention:1 they:1 transparent:1 term:3 classified:1 realistic:1 theory:2 found:2 2n:4 ei:6 cyclotomic:1 series:1 energy:5 hard:2 toda:1 expect:1 quantum:14 transitions:1 special:1 matrix:2 space:2 furthermore:1 since:3 rev:3 particles:12 collisions:1 mediated:1 dxdy:2 conjectured:1 denoted:1 ref:4 occurs:2 attentions:1 earlier:1 linear:2 free:3 completely:2 φdx:2 care:1 transition:2 times:1 hence:2 first:4 exotic:1 xi:1 symmetry:1 succeeds:1 number:1 thick:1 precisely:1 given:11 perturbation:3 similarly:2 unknown:1 interact:1 system:31 relations:3 intermediate:1 scheme:2 final:1 exactly:2 constituent:1 believe:1 than:3 kind:1 showed:1 transferred:1 determined:2 were:1 perturbative:7 fashion:2 argument:2 generalization:2 need:2 any:1 converges:1 k3:9 k2:43 k1:59 take:1 converged:1 calculus:3 spectral:1 though:3 most:3 letter:4 phase:3 soliton:2 considered:2 kj:2 calculated:6 later:1 kn:9 graphs:2 yang:1 principle:1 velocity:4 fact:1 discovered:1 ki:2 iǫ:3 relation:5 analogue:1 trivial:1 principal:1 ratio:11 dp2:2 dp1:2 should:7 only:4 factor:2 quasimomentum:1 integrable:12 goes:1 means:1 express:1 ones:1 dx:1 exchanges:1 momentums:5 dr:1 fields:1 arxiv:1 consisting:3 investigate:2 fixed:1 clarified:1 p21:1 p22:1 discussions:1 recently:2 quantizing:1 commutation:1 propagates:1 kj2:1 state:12 between:1 neither:1 attention:1 terms:2 ikx:1 however:2 incident:1 solv:1 configuration:2 cos:2 x2i:1 region:2 equal:1 onishi:1 comment:1 30th:1 point:1 corresponds:2 dimensional:4 polynomial:1 commutative:1 due:6 int:1 expected:1 pk:2 trices:1 commutes:1 quantities:1 essentially:2 last:1 p2:6 p3:4 p1:9 value:1 eigenstate:1 will:15 while:2 situation:2 property:1 loop:5 inherits:1 coupled:1 ki2:1 thus:6 itself:1 ic:5 different:4 pay:1 same:4 parts:1 modification:3 higher:1 used:1 reversion:1 upon:2 hand:1 infinite:1 schr:4 reflection:1 k22:1 model:2 drawing:1 obtain:2 integer:2 scattering:1 regarded:1 alternate:1 except:1 lattice:1 lett:1 mod:1 transformation:3 momentum:22 emphasis:1 advances:1 vacuum:1 using:2 helpful:1 appearing:1 like:3 particle:11 follows:1 velocities:2 reduced:1 old:2 classical:11 creation:1 proper:1 rapidity:1 scale:1 ehime:1 cφ:1 does:5 prof:2 core:2 ration:1 properties:4 stage:1 y2j:1 extension:1 obeys:1 matsutani:4 h0:2 three:9 appropriate:2 references:1 operator:1 bosonic:1 k12:1 deal:1 elastic:2 transfer:1 there:5 long:1 start:1 accordingly:2 conservation:3 was:3 function:18 newtonian:1 jul:1 line:2 partially:1 compute:1 2πn:2 ωk:3 problem:1 called:1 mechanics:1 sometimes:1 proved:1 defined:1 certain:2 abstract:1 am:1 general:6 conserved:1 physical:1 beyond:1 when:1 virtual:1 field:1 other:3 role:1 becomes:3 picture:1 repeat:1 kinds:2 generates:1 time:2 variation:1 meaning:1 important:1 thacker:4 structure:1 acknowledgment:1 pseudo:1 4n:4 mass:10 remarked:1
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