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solv-int9310001.txt |@word partial:2 gr:4 chain:1 funct:1 results:3 leads:1 generalize:2 expressions:2 inverse:1 const:2 tv:1 quasi:1 elliptic:4 degeneration:1 g1:2 g0:2 very:1 rise:1 trigonometric:3 difference:4 deformations:2 condition:1 hamiltonian:11 involution:4 occurrence:1 sin2:2 integrability:8 perspective:1 further:1 spectral:1 nonlinear:1 stands:1 section:1 celebrated:1 above:3 new:1 satisfy:1 equals:1 here:1 ansatz:1 address:1 equations:1 obtained:1 fwi:1 resulting:1 poisson:1 commun:3 whittaker:1 type:1 more:2 solitons:1 operators:3 known:1 iii:2 hamiltonians:3 quantized:1 science:1 values:2 9th:1 following:2 root:5 nearest:1 relativistic:6 permutations:1 dxj:1 needs:1 straightforward:1 discussion:1 pair:1 instead:1 parameter:3 sin:8 product:1 after:3 lax:3 italy:1 wave:1 constants:3 dynamical:1 light:1 schneider:1 explicit:2 representation:1 order:1 talk:1 september:1 years:1 held:1 including:1 uva:1 its:1 systems:16 covered:1 deformation:3 them:1 propose:1 material:1 half:1 now:1 netherlands:1 university:3 presented:1 2l:3 found:4 characterized:1 differential:1 ed:1 reduce:1 related:3 constitute:1 toda:5 quantum:1 our:1 eq:1 special:2 out:1 matrix:1 denotes:2 particles:2 acting:1 induced:1 math:6 hcm:4 free:1 standard:1 reason:1 ruijsenaars:4 interaction:2 transition:1 counterpart:1 turn:1 consequence:1 generalizations:1 βi:1 xj:16 xk:11 weierstraß:2 thereof:1 given:3 introduction:1 eqs:1 2ωr:1 system:11 πr:1 their:1 superintegrable:1 convention:1 gives:1 commutativity:1 kupershmidt:1 immediate:1 than:1 zero:1 preparation:1 ann:1 modern:1 generalization:2 seen:1 lie:2 wilson:1 lim:1 calogero:6 converges:1 εi:1 take:1 reparametrization:1 εj:8 formulas:3 olshanetsky:1 connected:1 dθj:1 remarks:1 class:1 soliton:1 torus:1 coincides:1 bracket:1 exp:2 discovered:1 relation:1 ground:1 sh2:1 parameters:3 inozemtsev:3 surveyed:1 factor:1 integrable:5 moser:6 oct:1 dn:2 reps:1 watson:1 lattices:1 evolution:1 course:1 arxiv:1 θj2:4 set:2 computer:1 terms:1 theoretic:1 eigenfunctions:2 αz:5 below:1 µr:4 state:1 between:1 limit:1 boundary:1 conditions:1 notice:1 recently:1 solv:2 multivariable:1 askey:1 cos:4 diejen:4 limits:2 equal:1 quantization:1 symplectic:1 σs:2 σr:6 cos2:1 ch:4 cn:2 cm:7 nonrelativistic:1 period:1 dimensional:2 polynomial:1 respect:1 been:7 int:2 reduction:1 workshop:1 asymptotics:1 algebras:1 θj:3 commutes:1 external:2 mail:1 case:2 novel:2 look:3 will:1 aid:1 iq:5 vj:3 according:1 ii:2 reads:1 id:1 verified:1 commuting:1 proved:1 finite:4 higher:1 singapore:1 i1:1 i0:1 upon:2 potentials:6 recent:1 lower:1 analysis:1 exponentials:1 model:2 dimension:1 usual:1 just:1 momenta:1 speed:1 yet:1 other:1 lett:1 theorem:3 corresponds:1 vε:1 world:1 particle:4 follows:1 integrals:3 become:1 pertaining:1 classical:3 some:3 cr:2 proofs:1 lead:1 chains:2 demonstrated:1 scientific:1 bn:2 expansion:1 although:1 o:5 neighbor:1 act:1 introduced:2 perelomov:1 cambridge:2 h0:4 h1:8 nonperiodic:1 references:1 ηr:1 amsterdam:4 van:4 additional:1 rcm:5 was:2 function:5 complete:4 form:4 governs:1 but:1 hn:2 hl:7 coupling:3 ωr:6 up:1 liouville:1 ui:2 uj:1 similar:1 detailed:1 associated:3 defined:1 flow:1 abstract:1 general:1 exist:1 periods:1 identities:1 again:1 functions:4 nl:1 generally:1 field:2 setting:2 papers:1 department:1 mathematics:1 nr:2 models:6 polynomials:1 generated:1 ago:1 bcn:3 factorized:1
solv-int9310002.txt |@word consider:3 yasuhiro:1 similarity:2 directions:1 focus:1 gn:10 expressions:1 row:2 whose:5 inverse:2 remarkable:1 paris:2 finally:1 th:2 ramani:7 very:1 results:1 putting:2 entries:3 difference:2 solution:13 leave:1 discrete:30 wronskian:1 10b:2 10a:2 direct:1 painlev:21 bilinear:5 nonlinear:1 funkcial:1 section:2 brief:1 expressed:9 reminiscent:1 version:2 3n:12 above:1 new:4 method:4 nakamura:1 satisfy:1 led:1 respectively:3 here:1 papageorgiou:3 active:1 equations:14 obtained:1 institute:1 study:1 hiroshima:1 minsk:1 followed:1 hermite:1 vii:1 plenum:1 would:1 prove:3 next:3 usp:1 means:1 type:2 more:2 introducing:1 ecole:1 fokas:1 2w3:1 particular:5 known:2 cases:1 me:1 tokyo:4 science:1 equation:13 values:4 evolved:1 following:5 example:2 proof:1 give:2 sense:1 holds:1 feature:2 how:1 pura:1 criterion:2 answer:1 acta:1 ordinary:2 parameter:1 mat:2 may:2 derived:3 dx2:1 levi:1 faculty:2 horizontal:1 fn:12 occurence:1 third:1 grant:1 bunkyo:1 cannot:1 so:1 six:1 closely:1 indeed:2 pointed:1 vary:1 paper:1 through:3 mentioned:1 japan:5 satisfies:9 its:3 before:3 τn:75 derive:1 interesting:1 forms:4 offers:1 systems:3 jacobi:5 weber:1 eventually:1 them:1 auto:1 acklund:1 introduce:2 singularity:1 now:2 possess:2 easily:2 2q:1 40a:1 university:4 applied:2 2f:1 2b:1 each:3 universit:1 side:2 xǫ:1 domain:1 doing:1 series:2 reduce:1 operator:1 toda:6 expect:2 quantum:2 aids:1 eq:34 special:10 out:2 shown:8 kazakov:1 rev:3 research:3 investigation:1 rational:1 math:4 theory:1 york:2 put:1 asi:1 obtention:1 derivation:3 ministry:1 dubbed:1 int:1 hence:3 first:2 variables:1 construct:1 given:6 rewritten:6 similarly:1 introduction:1 eqs:7 relations:2 their:1 constants:1 alfred:1 airy:8 recovered:1 gives:2 ekvac:1 2an:14 explanation:1 continuous:5 segur:1 completes:1 kenji:1 second:1 submitted:1 winternitz:1 were:3 denominators:1 etage:1 ann:2 kajiwara:1 kitaev:1 close:1 seen:1 seek:1 linked:1 gravity:2 note:3 sciences:2 concerns:1 take:1 analogy:2 cnrs:1 molecule:6 riccati:1 most:1 letter:2 nothing:3 class:1 appear:1 considered:1 clear:2 partition:1 lpn:1 kp:1 ohta:1 principle:1 ku:2 hietarinta:1 physics:1 fact:5 dover:1 show:4 reductions:1 supported:1 notations:1 relation:1 solutions:17 substituting:1 analogue:3 d2:2 find:1 based:1 proposed:1 parameters:3 should:1 analytic:1 only:2 explicitly:1 transcendental:1 parabolic:1 integrable:5 oct:1 get:1 dependent:3 dd:1 between:2 ones:2 dx:18 meguro:1 dpv:1 evolution:1 determinants:4 continuum:1 arxiv:1 yield:1 nauk:1 common:1 αn:1 exists:1 culture:1 see:2 result:3 eliminating:2 existence:2 terms:8 forthcoming:1 techniques:1 satisfying:1 written:1 simplest:1 subscript:1 approach:2 discovery:1 publishers:1 notice:1 recently:1 vertical:1 wn:23 analogues:2 however:2 solv:1 2pn:1 both:3 essentially:1 taking:2 equal:1 tour:1 pde:1 expression:1 unn:3 afterwards:1 point:2 simple:1 dimensional:1 concluding:2 mkdv:1 equivalent:2 been:1 xai:1 reduction:1 interest:1 basil:1 pi:1 pn:8 komaba:1 pl:2 choose:1 determinant:6 25a:1 fund:1 confinement:1 present:3 case:5 periwal:1 transformation:2 intimately:1 while:1 ǫw:1 property:1 cylinder:1 jpn:2 vn:10 encountered:1 ii:2 itself:1 leaving:1 education:1 author:1 same:3 palaiseau:1 ince:1 several:1 pan:6 higher:1 again:1 hand:2 purpose:1 ablowitz:1 identity:7 well:1 gambier:1 model:1 2gn:1 just:1 being:1 grammaticos:6 obtain:5 integer:1 hongo:1 alternative:1 scattering:2 ucker:2 adding:1 regarded:1 lattice:1 other:2 nato:1 lett:8 5e:1 remaining:1 nuov:1 possible:1 increases:1 using:3 unique:1 40b:1 like:1 semi:1 reduces:3 polytechnique:1 arbitrary:3 become:1 reduced:1 mathematical:2 right:2 methods:1 some:3 okamoto:1 defined:1 does:2 assuming:1 bessel:1 2xw:1 scientific:1 kyoto:2 bn:10 expansion:1 br:1 2n:112 constraint:1 column:2 nijhoff:2 discussed:1 ezin:1 soc:2 transcendents:2 into:2 wn2:3 remarks:1 because:1 references:1 elementary:2 france:2 log:1 there:1 transform:1 appl:1 way:1 ed:1 forward:1 was:6 function:19 form:1 2vn:1 but:4 expected:1 russian:1 removed:1 applying:2 casorati:7 us:6 un:2 limit:2 problem:1 similar:1 laplace:1 pii:4 ai:11 abstract:1 general:3 engineering:2 exist:3 numerators:1 formalism:1 satsuma:2 functions:6 cim:1 integrability:1 wxx:1 setting:1 department:3 mathematics:1 really:1 intend:2 important:1 variable:2 sides:1 structure:2 hirota:3 cpt:1
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