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solv-int9710021.txt |@word sci:1 consider:2 results:2 leads:1 mild:1 2r4:1 2r3:1 2r2:4 2r1:1 whose:1 inverse:1 depend:2 ty:2 under:2 case:7 stud:1 erale:1 rise:1 3s0:2 fac:1 difference:10 deformations:1 condition:8 generalised:1 four:2 school:1 list:1 discrete:14 math:9 inconsistent:1 consistent:1 α2k:2 nonautonomous:2 painlev:18 odd:3 substitute:1 even:3 nonlinear:5 giving:1 section:8 version:7 poles:1 odes:3 above:1 sup:1 new:2 increasing:1 ordnung:1 full:1 degree:1 erieur:1 papageorgiou:2 drei:1 believed:2 les:2 equations:27 obtained:1 search:1 garnier:1 wherever:1 suggests:1 simultaneous:1 fourier:2 isomonodromic:1 scaled:4 univ:1 use:1 commun:1 substitutions:1 calculation:1 therefore:1 taken:2 australian:2 more:1 separated:1 becomes:1 award:1 announce:1 known:3 iii:1 must:1 ramani:4 account:1 valued:3 tokyo:1 recall:1 equation:28 three:1 following:3 give:2 process:1 preserving:1 νy:2 ia:1 council:1 arise:1 turn:1 s3:3 s2:4 4αn:1 six:1 how:1 fourth:5 significance:1 acta:2 ordinary:1 simplicity:1 continues:1 may:3 derived:1 movable:1 plane:1 meaningful:1 compatibility:9 constants:3 dynamical:1 maintain:1 inhomogeneity:1 sa:1 discussion:1 s0:14 hierarchy:10 pointed:1 ordre:3 paper:4 through:1 its:1 derive:3 solving:1 degrees:2 systems:1 wales:1 defining:1 deformation:2 s1:8 yh:1 them:1 pure:1 yn:5 propose:2 they:2 identically:1 singularity:1 discuss:1 eigenvalue:1 term:3 singul:1 university:2 2x:1 2y:1 each:1 found:3 isomonodromy:8 referred:1 homogeneous:1 differential:4 fixes:1 inhomogeneous:1 our:4 out:1 furthermore:1 rev:2 research:2 contained:1 egral:1 rational:1 ri:1 scalings:3 shows:1 8k:2 linear:9 singularities:1 kaup:2 possibility:1 base:1 subsequences:1 r4:5 r1:11 r2:6 r3:6 3r3:1 south:1 first:5 degr:1 dont:2 restrict:1 homogene:1 illustrate:1 endlich:1 given:1 introduction:1 system:6 their:2 calculations:1 recovered:1 collapse:1 postgraduate:1 continuous:1 newell:3 segur:2 authors:1 fuchs:2 second:8 strengthen:1 premier:1 spectrum:1 uniforme:1 clio:1 recover:1 viewed:1 realm:1 αn2:5 convenient:1 latter:1 uuxx:1 note:2 potential:1 take:1 renaming:1 mit:1 unless:1 though:1 4u2:1 plan:1 acknowledgements:1 laurent:1 considered:1 kh:3 order:16 points:1 6u2:1 hietarinta:1 lying:1 show:4 supported:1 joshi:3 solutions:4 trivial:1 find:2 based:1 parameters:1 erentielles:2 only:2 transcendental:1 integrable:10 oct:1 sur:2 do:1 notation:1 self:1 du:3 continuum:13 arxiv:1 expansions:1 ut:1 dpi:13 qn:2 annalen:1 set:1 sec:1 3c3:4 uux:1 ytt:1 ladik:3 simplest:1 conditions:8 αn:161 terms:1 utt:2 2m:1 p2m:2 wn:5 however:2 p2k:6 concentrate:1 solv:1 limits:5 reported:1 whole:1 otherwise:1 ci:1 2αn:15 moreover:1 due:1 pk:11 pi:13 pn:9 pl:6 define:1 arises:1 corresponding:1 confinement:1 c3:16 c2:11 c1:11 c0:10 c5:5 c4:23 p2:3 p0:15 p1:6 p6:1 p4:2 indefinitely:1 straight:1 expanded:2 examine:1 choices:1 aim:3 monodromy:1 property:6 rename:1 eral:1 vk:3 uxx:2 2ux:1 flaschka:1 im:1 vx:1 uxxx:1 different:1 same:1 complex:1 hierarchies:4 finite:1 higher:6 ablowitz:5 mappings:1 zweiter:1 well:2 analysis:2 stellen:1 gambier:2 arising:1 possesses:1 left:2 proposed:1 grammaticos:5 obtain:1 λk:1 scattering:3 previous:1 ease:1 yt:2 egrale:1 lett:4 sydney:1 transformation:1 identical:1 australia:2 possible:2 increases:1 using:1 follows:1 yields:5 translated:3 because:3 often:1 classical:2 some:1 identified:1 examples:1 diff:2 ourselves:1 nonzero:1 est:2 lead:3 refer:1 sixth:2 bn:7 expansion:2 substitution:1 akns:1 stage:1 comparison:1 extension:1 freedom:2 nijhoff:1 dependence:2 o:1 range:1 differentialgleichungen:1 h2:7 h3:2 into:4 h6:1 h7:1 h4:4 h5:2 down:1 linearization:1 en:2 references:1 next:4 nsw:1 additional:1 aren:1 transform:1 u2:2 restricts:1 appl:1 forward:1 was:1 hy:1 form:1 construction:1 okamoto:1 made:1 ux:3 versions:3 characteristic:1 lineare:1 up:2 below:2 limit:12 uk:2 problem:13 similar:1 called:3 uber:1 pii:2 associated:7 int:3 abstract:1 general:4 single:5 cresswell:1 adelaide:2 nh:3 satsuma:1 functions:1 compared:1 completeness:1 wesentlich:1 whereas:1 when:1 vanishes:1 department:1 mathematics:2 forcing:1 critiques:1 problems:1 deriving:1 variable:2 4u:2 fact:2 starting:1
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solv-int9710022.txt |@word represent:1 since:3 sci:3 consider:21 bull:1 focus:1 integration:11 leads:1 edu:2 consists:2 spaced:1 primes:1 disk:1 cases:1 whose:1 inverse:5 patches:1 technique:1 editors:3 finally:1 contours:1 elliptic:26 under:2 analogous:1 norm:2 divergent:1 6d1:4 g2:2 advantage:1 orthogonal:1 erale:1 rise:1 results:23 sons:1 bounding:1 fac:1 difference:1 exact:1 deformations:1 condition:2 entire:2 gov:1 riemann:1 notes:1 tokyo:1 solution:40 z10:3 integrated:2 large:33 solved:1 enclosing:2 small:23 relation:1 glued:1 noted:3 smaller:5 estimates:4 direct:6 painlev:45 evaluated:1 follow:1 rigorous:2 further:3 zw:2 iga:1 even:4 nonlinear:4 appear:2 d2:2 section:10 near:1 uniform:1 rescale:1 128e:2 poles:17 sur:3 above:10 scientists:1 obvious:1 originate:1 3g:1 method:2 3d:1 satisfy:7 full:1 simultaneously:1 excludes:1 spacing:2 equals:1 here:11 behaviour:13 exceptions:1 les:3 dover:1 separation:1 represented:1 path:24 along:5 standard:2 equations:32 z1:10 change:2 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solv-int9710023.txt |@word extrapolated:1 chaos:1 four:2 fortiori:1 whose:5 const:1 paris:5 segments:1 γu:1 under:11 worth:1 conjecture:10 rise:5 œuvres:1 every:5 summarized:1 overcomes:1 vast:1 school:2 investigator:1 solution:68 solid:2 10m:1 consistent:5 direct:6 second:19 rigorous:4 even:4 nonisolated:2 above:15 new:20 coefficient:7 here:11 reported:1 κz:1 path:5 logarithmic:6 obtained:3 property:83 suitably:1 study:4 changed:1 suitable:2 cancellation:1 york:7 classification:8 explained:1 plenum:2 rρ:1 derivatives:4 would:1 negative:9 noting:1 call:3 therefore:15 type:12 until:1 zeroes:2 solitons:2 odinger:2 hold:2 must:19 springer:1 work:7 lipschitz:1 petersen:6 example:29 indicated:1 ingenuity:1 preserving:1 generically:1 involve:2 indicates:4 guarantee:1 boussinesq:1 provide:1 how:4 nontrivial:1 answer:1 ordinary:8 description:5 arcs:1 after:6 movable:47 demanding:2 hence:5 parallel:2 types:2 third:5 enter:1 order:21 interpretation:1 over:2 vary:1 satisfied:1 london:1 thesis:1 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solv-int9710024.txt |@word consider:4 remarkable:1 scd:1 magnetic:1 results:1 four:2 pearce:1 generalize:1 c2:1 consists:2 research:1 compact:1 whose:4 certainly:1 depend:2 referring:1 removal:1 quasi:1 present:1 th:2 under:3 x02:1 nodes:1 include:2 applied:1 supported:2 amplitudes:1 kcb:1 far:1 difference:3 matrices:19 condition:6 sklyanin:1 list:1 solution:21 solved:1 postdoctoral:1 bd:1 strongly:1 ewha:2 sin2:49 mussardo:1 fold:1 integrability:3 further:1 odd:5 linear:5 even:6 what:1 plays:1 brien:1 iterating:1 trivial:1 section:1 above:9 new:4 satisfy:4 condensed:1 respectively:1 bsri:1 here:2 cos2:17 sinh:14 represented:1 const:1 sine:3 equations:9 change:2 obtained:8 wdc:4 ctp:1 conformal:4 study:1 studied:1 suggests:1 periodic:1 hexagon:8 9i:1 control:1 via:2 useful:1 family:2 extra:3 redefining:1 b348:1 takes:2 covariant:1 positive:1 contains:1 nucl:3 therefore:1 type:2 bethe:1 more:1 introducing:1 formally:2 becomes:2 known:5 nepomechie:1 cases:2 iii:2 x01:1 k00:2 k01:1 ρc:4 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solv-int9710025.txt |@word 1st:1 represent:2 r1t:2 homomorphism:1 consider:3 remarkable:2 similarity:1 pairing:2 varying:1 results:7 integration:1 four:7 eds:1 scalar:1 commute:2 follow:1 expressions:7 research:1 contributions:1 c1:6 gi:2 compact:2 whose:2 preserves:2 weierstrass:7 depend:3 analytic:3 asymptotics:1 paris:1 assigning:1 concerned:1 equivalence:4 tr:6 tq:1 intensive:1 finally:5 uniquely:2 those:2 elliptic:2 under:9 phil:1 te:1 presentation:2 regrets:1 r16:1 p2:21 belonging:1 g4:2 g3:2 g2:5 g1:5 orthogonal:1 induce:1 choice:7 isomorphism:10 ramified:3 inequivalent:2 ma:1 exact:1 mumford:1 vast:1 preserve:1 leads:5 lam:1 encodes:1 riemann:8 level:6 positions:3 integrating:1 list:3 solution:4 pullback:2 involution:14 vector:12 annihilates:2 relation:21 proof:1 attracting:2 abbreviated:1 unexpected:1 φu2:10 φu1:25 summarizing:1 consistent:5 direct:5 hs:10 sign:11 matrices:2 fold:1 integrability:2 alent:1 insertion:2 further:2 odd:5 ues:2 canonical:2 spectral:5 will:4 what:2 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solv-int9710026.txt |@word represent:5 consider:3 pointing:2 osp:2 results:1 gx:1 leads:3 scalar:2 computation:1 edu:1 follow:2 remarkably:1 equivalences:1 const:2 chain:1 bivector:2 superspace:4 equivalence:1 nonlocal:7 tn:12 δhn:10 finally:2 dressing:3 worth:5 subtleties:1 conjecture:1 straightforward:6 very:2 rise:2 wave:1 matrices:1 nijenhuis:2 entire:1 hamiltonian:19 notes:1 t2:2 t3:2 t0:5 t1:11 try:2 manifestly:1 becker:2 inspection:1 noted:1 akns:12 consistent:1 direct:2 zero:8 further:1 odd:3 expressions:1 linear:9 spectral:3 nonlinear:2 appear:3 dφd:5 chicago:2 giving:1 section:9 d3:1 reminiscent:1 above:1 new:3 method:6 coefficient:1 led:2 ibid:1 respectively:3 henrik:1 here:11 understanding:3 desired:1 identifications:1 groups:1 address:1 sine:1 equations:24 obtained:7 study:2 allows:2 ignoring:1 suggests:2 published:2 genuinely:1 useful:2 texts:1 rσ:1 should:1 conventional:4 would:11 sake:1 super:1 coupled:1 ψt:1 next:1 distinct:1 few:3 noting:2 ψn:4 opposed:1 ψa:1 ψd:10 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solv-int9710027.txt |@word allowed:1 consider:7 chain:3 illustrates:1 crucial:1 global:1 results:2 bubble:3 leads:6 facilities:1 governs:1 selection:1 fig2:1 fig3:1 2n2:1 consists:6 follow:1 dϕ2:2 fig8:1 devoted:1 whose:2 fronts:4 inverse:2 const:2 calculate:1 paris:1 tt:3 γk:5 finally:3 monotonically:3 those:4 th:3 under:6 presentation:1 applied:1 belonging:1 supported:1 string:1 straightforward:1 very:4 rise:3 springer:1 splitting:2 chooses:1 lecture:1 redefinition:1 difference:2 exact:3 deformations:38 condition:1 look:5 fig6:1 iλx:2 obvious:1 presented:4 notes:1 developing:1 solution:10 tubes:1 ax:3 discrete:1 convenience:1 adjust:1 math:7 refer:1 glued:2 noted:3 upper:3 revolution:44 sinh2:3 det:6 fig1:1 sin2:1 l2l:2 sign:1 jump:3 second:4 dynamics:7 kx2:1 linear:6 even:1 established:1 nonlinear:6 appear:1 fr2:2 section:9 http:27 near:1 uniform:1 poles:1 sur:1 above:2 capital:1 new:4 increasing:4 method:7 contrast:3 raton:1 satisfy:1 wavefunctions:4 respectively:4 preserves:1 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solv-int9710028.txt |@word neighbors:1 represent:6 consider:12 chain:40 similarity:3 magnetic:3 results:8 four:4 gf:32 scalar:6 commute:1 generalize:1 gb:22 grateful:1 θf:6 follow:1 expressions:4 denotes:1 contributions:20 cases:1 analiz:1 dξ:3 inverse:2 depend:1 calculate:16 bogoliubov:1 tu:1 tr:21 finally:2 critical:1 petersburg:6 th:2 under:2 worth:1 up1:2 p2:49 very:2 αrj:1 springer:2 cyclone:1 fab:3 emphasized:1 difference:3 matrices:20 deformations:1 leads:2 tro:1 presented:1 anisotropy:1 t2:2 t1:2 large:3 solved:3 equalities:1 vector:1 tognetti:3 zf:32 kalinin:1 sin2:2 direct:4 zb:25 sign:4 zero:2 correlator:10 invariant:2 odd:1 columns:1 canonical:4 bilinear:1 transverse:1 nonlinear:2 diag:12 section:10 analogously:5 expressed:1 above:1 new:14 d1:1 method:3 coefficient:4 respectively:1 component:1 answers:10 diagonal:15 quasimomenta:2 eides:1 ansatz:4 sinh:1 represented:9 equations:9 change:9 obtained:12 remark:1 antisymmetric:1 institute:3 involved:1 studied:1 products:4 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solv-int9711001.txt |@word consider:1 osp:16 results:3 gx:4 leads:3 roy:1 generalize:2 go:1 follow:1 row:2 whose:1 superspace:10 tn:3 under:1 must:1 tb:2 belonging:9 straightforward:4 very:1 wave:6 puzzles:1 matrices:9 condition:17 bxx:1 solves:1 hamiltonian:6 turns:1 notes:1 differential:1 becker:2 superalgebras:1 cfm:1 second:8 further:2 linear:12 spectral:1 what:1 stands:1 section:8 brief:1 dχ2:2 consistently:1 dχ1:2 manin:1 method:4 contrast:1 satisfy:1 ibid:2 respectively:1 component:12 here:7 identifications:2 operating:1 address:1 standard:2 equations:7 appears:2 obtained:1 study:3 studied:1 allows:1 suggests:2 resulting:1 published:1 suitable:1 emerge:1 useful:5 santa:1 analyzing:1 catarina:1 apply:1 readily:1 conventional:1 would:7 remains:1 super:1 eφ:3 physics:3 next:3 therefore:3 more:1 becomes:3 curvature:47 berlin:1 correspondingly:1 particular:1 known:6 fermionic:3 dex:2 springer:1 equation:14 work:1 theories:2 obvious:1 lχ:3 give:1 arise:1 guarantee:1 provide:2 discussion:1 how:5 fourth:2 dg:3 parameter:1 description:1 algebra:6 may:2 derived:2 lax:6 coming:1 representations:12 sx:1 natural:1 dynamical:5 four:1 explicit:4 correspond:1 element:1 so:1 automatically:1 fundamental:6 sl:3 sc:1 representation:22 bleuler:1 order:1 belong:2 hierarchy:42 pointed:1 years:1 scheunert:1 course:1 paper:1 through:1 da1:1 da2:1 mentioned:1 brunelli:4 derive:2 thank:1 ln:2 interesting:3 solving:1 boson:1 differently:1 mail:1 them:1 cep:1 now:6 discuss:1 nor:1 easily:3 2ex:1 university:1 hepth:1 2g:1 each:1 found:1 2n:1 reetz:1 aratyn:3 square:1 ed:1 energy:1 hard:1 reduce:4 related:4 extended:1 ex:8 our:1 beyond:1 eq:16 frappat:1 out:3 shown:3 matrix:7 furthermore:3 since:1 at0:1 lecture:1 issue:1 math:7 shows:2 theory:2 dictionary:1 fisica:1 departamento:1 quite:4 completely:1 publ:1 irreducible:1 zimerman:1 derivation:1 universidade:1 starts:1 ufsc:1 turn:3 adjoint:1 first:10 already:3 features:4 symmetry:4 variables:2 bars:1 supersymmetrization:2 another:2 illustrate:1 given:8 necessarily:1 similarly:1 introduction:2 eqs:9 system:2 construct:5 their:1 structures:2 gives:2 way:3 exactly:1 kupershmidt:1 nahm:1 part:1 completes:1 skdv:11 showed:1 zero:47 submitted:1 determined:1 enables:1 generalization:2 say:1 rittenberg:2 clearly:1 lie:8 rochester:2 check:1 note:9 gφ:1 generalized:1 kac:1 systems:2 nothing:2 pais:1 petry:1 sciarrino:1 clear:3 kx:1 normally:1 exx:3 particularly:2 show:5 reductions:1 supported:2 sorba:1 relation:2 ashok:1 fg02:1 2bx:1 explain:1 than:1 only:2 integrable:8 oct:1 do:1 notation:1 familiar:1 de:10 db:1 obtain:5 geometric:1 evolution:7 stb:21 qx:1 arxiv:1 yield:1 view:1 redefine:1 constructing:4 imposing:1 j0:4 j1:3 namely:5 discussions:1 jx:1 nonstandard:2 techniques:1 brazil:2 federal:1 review:2 written:2 between:2 drawn:1 neither:1 before:2 conditions:9 terms:11 nature:1 attention:1 transpose:1 however:8 comm:1 universitario:1 solv:1 connection:3 among:1 unclear:1 point:4 reasons:1 corresponds:1 dimensional:19 superstring:1 cx:1 stanciu:1 proved:1 gxx:1 mathieu:1 described:4 addition:2 been:1 reduction:1 basic:1 algebras:7 define:9 generating:1 relations:1 supersymmetric:3 systematic:2 derivative:1 present:1 case:3 hughes:1 unlike:1 will:5 redefinitions:1 thus:3 surprisingly:1 balantekin:2 itself:1 superconformal:1 different:1 grant:1 things:1 formulations:1 same:5 any:5 hierarchies:1 several:1 higher:18 used:1 hand:1 potentials:13 dgx:1 expand:1 recent:2 variety:1 well:2 analysis:5 components:3 consistency:3 model:1 arising:1 dimension:1 graded:14 profs:1 das:6 dφ1:21 dφ0:30 previous:3 kluwer:1 readers:1 guaranteed:1 gj1:1 lett:5 easy:3 represents:1 supercovariant:1 superfield:3 five:1 know:1 mod:2 like:1 systematically:2 follows:1 reduces:5 become:1 works:1 lends:1 mathematical:1 because:1 methods:1 some:1 examples:2 proper:1 provided:4 describing:1 dimensions:1 lead:2 superfields:1 does:2 provides:3 refer:1 br:1 bx:2 properties:2 about:2 usa:1 o:1 consequently:1 block:7 puzzle:1 nsf:1 reducible:1 acad:1 references:1 determine:2 operator:3 bosonic:2 additional:2 there:4 start:1 lot:1 was:4 naturally:7 function:6 form:5 construction:1 cnpq:1 trying:1 wish:1 us:11 problem:2 associated:10 ad:1 int:2 eφ1:2 abstract:1 describe:2 general:1 formulation:26 ax:1 campus:1 again:4 functions:1 compared:2 puzzling:5 no:2 wavefunction:1 when:1 detail:2 field:1 other:6 details:1 jcb:1 department:2 conclusion:2 briefly:2 elements:3 a10:1 models:7 radul:1 a1:19 a0:20 a2:3 a8:1 astronomy:1 structure:6 fsc:1 dφ:8 dχ:5 together:1 equivalently:1 fact:4 time:7 starting:3 once:2
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solv-int9711002.txt |@word since:1 partial:1 consider:1 unhatted:1 moutard:3 gx:1 scalar:1 proposition:9 during:1 go:1 sci:1 expressions:3 compact:2 γx:2 paris:2 tn:4 finally:2 spain:1 th:3 aux:2 te:1 presentation:1 ingredient:1 case:5 conjecture:1 ginn:1 string:1 far:2 erale:2 bilinear:1 results:3 bihamiltonian:2 manin:11 αxx:1 condition:3 school:1 obvious:1 hamiltonian:1 die:1 dψ0:6 solution:16 t0:5 leave:1 discrete:1 vector:2 indices:2 eigenvalues:1 hospitality:1 permutability:1 der:2 explicite:1 wronskian:1 sturm:1 jacobians:1 cosh:1 matrices:1 second:1 quelques:1 further:1 odd:7 dψ2:1 dψ1:1 theory:4 even:15 index:1 nonlinear:5 appear:1 giving:3 deeply:1 expressed:1 current:1 version:4 sur:4 above:6 krivonos:1 new:16 method:3 body:4 1997b:4 1997a:5 wronskians:1 relationships:1 nimmo:4 here:3 objects:2 china:1 sciuto:1 dψx:2 represented:1 path:1 sine:12 equations:17 appears:1 differential:3 obtained:6 publisher:1 remark:5 kanno:3 technical:1 study:2 periodic:1 mulase:2 studies:2 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solv-int9711003.txt |@word proposition:15 secondly:1 partial:2 consider:4 skip:1 equalities:1 global:6 eds:1 commute:8 computation:1 edu:1 follow:1 depend:2 advantage:1 iii:1 equivalence:1 tr:37 finally:2 dressing:2 include:1 belonging:1 wjm:1 string:10 straightforward:1 very:1 implicitly:1 rise:1 seemingly:1 corollary:3 wishes:1 every:2 entries:1 matrices:2 deformations:7 condition:3 presented:2 t2:2 solution:2 t1:2 solved:1 convenience:1 vector:5 indices:2 mi:55 consistent:1 second:4 chen:1 linear:4 what:2 invertible:1 ak1:3 celebrated:1 poles:2 above:4 new:2 contrast:1 lee:1 degree:1 got:1 modify:1 equals:3 here:6 objects:2 equations:19 change:1 obtained:3 remark:2 involved:3 study:1 larger:1 changes:1 isomonodromic:4 replace:1 total:3 virasoro:1 derivatives:4 use:3 prove:3 distinct:2 positive:5 contains:1 negative:7 symbolizes:1 explicitly:2 call:2 therefore:4 totality:1 expanding:1 themselves:2 type:2 more:5 rk1:4 fokas:1 operators:7 ti:2 virtue:1 particular:1 known:2 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solv-int9711004.txt |@word bogoliubov:1 xinxiang:1 consider:1 chain:6 correlation:1 inami:1 σnz:4 obtain:1 σnx:4 sites:1 eds:1 statistical:2 follow:1 expressions:2 scattering:2 find:2 verlag:1 q1:9 inverse:2 based:1 thank:1 recover:1 ln:11 interesting:1 guaranteed:2 w2:9 should:2 forms:1 only:1 does:1 systems:4 σny:4 integrable:4 hamiltonians:1 nucl:4 discuss:2 ingredient:1 mn:7 foerster:1 ig2:2 g3:3 g2:1 g1:3 advances:1 de:1 trigonometric:1 σ1z:5 σ1y:3 σ1x:3 zuber:1 they:1 prof:2 press:1 using:1 nov:1 now:2 matrices:6 combined:1 condition:4 mod:3 theor:1 like:1 alez:2 hamiltonian:1 approach:1 university:2 sklyanin:3 guo:1 izergin:1 2e:4 xy:5 2a:4 follows:2 found:1 notes:1 qism:1 view:1 baxter:4 heisenberg:1 arxiv:1 houches:1 exists:1 vega:1 σ2z:2 lecture:1 σ2x:2 σ2y:2 some:1 w12:2 up:1 integrability:5 w4:7 w3:7 expect:2 b2:2 quantum:4 terms:1 constraints:2 jy:9 spectral:1 said:1 xing:1 matrix:2 furthermore:1 a12:4 extensively:1 boundaries:1 kun:1 version:1 above:1 between:1 prog:1 limit:1 boundary:11 conditions:7 method:3 shows:1 satisfy:1 faddeev:1 after:1 recently:1 theory:2 jz:9 problems:1 equivalent:2 l1:2 however:1 completely:2 les:1 references:1 shi:1 solv:1 depend:1 publ:1 equations:8 fring:1 e2:2 both:2 cos:1 ref:4 central:1 σn:39 institute:1 sinica:1 taking:1 studied:1 konno:1 wu:1 example:1 compatible:2 fiz:1 periodic:5 ghoshal:2 transfer:1 teor:1 qn:9 cambridge:1 useful:1 a21:4 guan:1 xyz:2 snu:2 dimensional:3 remarks:1 ju1:1 done:1 construct:3 operator:1 open:11 wang:2 zhou:1 given:7 karowski:1 would:1 chi:1 eqs:3 there:3 system:4 been:4 defined:1 linear:1 nepomechie:1 ψn:6 1d:3 lot:1 m2:1 calcula:1 theoretical:1 sogo:2 relations:1 corresponding:1 elsewhere:1 form:1 xxz:2 operators:1 ruiz:2 c2:4 hold:1 spin:6 stora:1 those:1 auxiliary:1 case:4 springer:1 jx:9 holland:1 whether:1 equation:7 work:1 imply:1 theories:1 will:1 w32:2 yang:5 henan:2 aij:7 following:3 problem:1 kulish:1 called:3 proof:1 mechanics:2 beijing:1 a22:4 xxxix:1 proved:1 w1:9 rewrite:1 int:4 abstract:1 zamolodchikov:1 tions:1 discussions:1 conserved:1 mezincescu:1 north:1 formalism:2 gonz:2 constructed:1 result:1 motion:2 lengthy:1 hubbard:1 make:1 responsible:1 same:1 pp:2 write:1 field:3 other:2 dt:15 pauli:2 quantities:1 department:1 finite:1 parameter:1 sin:1 oberle:1 province:1 w42:1 investigated:1 a11:5 mat:1 see:2 normal:1 models:1 consistency:1 variant:1 functions:1 hand:1 wadati:2 a2:2 lax:13 letter:2 pair:6 replacement:1 constants:1 recent:1 natural:1 reflection:5 ke:1 considered:1 interval:1 explicit:1 korepin:2 cherednik:2 academia:1 so:2 sn:1 time:1 w22:1 representation:3 model:7 physics:3 order:1 fact:1
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solv-int9711005.txt |@word dewitt:1 partial:1 leads:2 φ1x:1 llm:9 edu:2 preserves:1 inverse:1 superspace:2 tw:2 equivalence:6 finally:1 preserved:1 under:5 applied:2 straightforward:2 geometrical:4 summarized:1 manin:4 hamiltonian:14 solution:4 t1:1 vector:2 superalgebras:1 originally:1 nthu:1 sign:1 second:1 odd:5 canonical:8 even:5 θlm:7 plays:1 section:1 expressed:2 dbt:6 above:1 new:4 method:1 satisfy:1 respectively:5 component:1 here:2 explore:1 tangent:2 address:2 represented:2 equations:2 change:1 obtained:2 remark:1 kanno:5 remarks:2 rests:1 vectors:1 poisson:1 permutation:2 action:2 chang:1 quotient:1 via:1 2φd:2 apply:1 univ:1 would:1 commun:4 suppl:1 next:1 comparing:1 ψi:3 therefore:1 taken:1 type:1 theoretical:1 more:1 sokolov:2 operators:3 4ad:1 particular:1 iii:2 science:2 equation:7 work:1 ik:13 dxdθ:2 mr:30 following:4 council:2 give:1 calculation:2 preserving:2 organized:1 contradicts:1 want:1 sense:1 darboux:3 s2:16 s1:23 get:1 map:5 product:4 algebra:1 after:1 derived:4 lax:12 φ2x:1 natural:1 si:6 interpretation:3 hierarchy:25 inami:5 over:1 paper:2 mentioned:1 satisfies:2 its:4 du:9 thank:1 ln:3 solving:1 choose:1 derivative:1 them:1 acklund:2 introduce:1 framework:1 they:3 nov:1 now:2 discuss:4 possess:1 2u:7 february:1 university:2 presented:1 2d:2 l2:1 referred:1 differential:1 fr:1 related:1 our:1 eq:2 out:1 shown:4 matrix:1 space:3 furthermore:1 since:2 rev:1 denoted:1 ref:5 math:10 fiber:1 theory:7 pairs:1 linearized:2 thing:1 chiao:1 hence:4 features:1 miura:1 variables:1 simplified:1 another:6 given:3 similarly:2 introduction:1 adjoint:3 construct:1 echet:1 structures:5 tu2:1 supermanifolds:1 gives:2 hua:1 relationship:3 acquire:1 kupershmidt:4 tsing:1 2ax:3 skdv:25 showed:4 cyclic:2 str:3 treated:1 minus:1 generalization:1 ming:1 gradings:1 hsien:1 any:1 viewed:1 lie:2 wilson:4 form:3 petviashvili:1 mr2:1 note:1 sciences:1 pair:2 nctu:1 calculated:1 sometimes:1 kw:3 physics:1 fact:1 oevel:1 show:4 supported:1 notations:1 gauge:28 substituting:1 superalgebra:1 find:1 based:1 just:1 superalgebraic:1 should:1 only:4 coefficients:1 do:1 viewpoint:6 means:1 df:1 dd:1 de:1 da:4 words:1 dφ2:3 qp:1 kadomtsev:1 arxiv:1 factorization:1 acknowledgments:1 investigate:3 mapped:2 set:1 fibered:1 national:4 morosi:5 differs:1 depends:1 sec:4 result:1 discussions:1 terms:2 between:9 approach:1 recently:1 however:1 δaa:1 solv:1 equal:1 connection:1 comes:1 lm:35 point:2 simple:2 superfield:2 concluding:2 mathieu:4 transformations:7 addition:2 due:1 been:2 int:2 reduction:3 inv:1 define:1 corresponding:1 θm:6 cotangent:2 mail:2 general:1 case:3 while:1 revisited:1 property:9 loop:2 thus:1 iv:2 ii:2 tu:2 2ux:1 itself:2 mod:1 different:1 shaw:2 grant:1 φx:4 formulations:4 cross:1 same:1 paa:2 φd:6 φi:1 hierarchies:15 independent:1 hand:2 tung:1 popowicz:1 center:1 well:1 coordinate:1 proposed:1 dφ1:4 obtain:2 reviewed:1 drinfeld:2 taiwan:4 liu:1 seems:2 transformed:1 lett:2 bnm:4 theorem:6 formal:2 transformation:40 eigenfunction:2 know:1 press:1 using:1 apart:1 appearing:1 like:1 follows:7 δu:5 δn:2 δm:4 korteweg:1 multiplicative:2 δa:6 parity:2 pφφ:2 kdv:4 transport:1 generates:1 provided:1 grading:1 footing:1 superfields:4 does:1 provides:2 superextension:1 bi:12 super:6 about:1 rederived:1 discussed:5 o:1 compatible:1 a2:3 introduced:1 cambridge:1 φxx:1 superderivative:2 into:2 nsc:1 phase:2 references:1 sov:1 operator:7 tabulated:1 bosonic:1 unambiguous:1 support:1 there:3 transform:1 u2:2 inner:2 was:2 naturally:1 triggered:1 but:2 adler:1 applying:1 ux:2 wish:1 up:1 us:1 hsinchu:2 backlund:2 ud:2 called:1 pij:1 constant:1 defined:3 pseudo:1 abstract:1 denote:1 supersymmetric:1 constructed:2 tedious:1 grassmann:1 no:1 whereas:1 other:3 role:1 department:2 mathematics:1 briefly:3 intepretation:1 radul:4 a1:4 meaning:1 important:1 variable:2 structure:6 building:1 factorized:2 dφ:5 vries:1 dτ:2 hnm:1 together:1 4n:1 4a:2
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solv-int9711006.txt |@word exotic:1 chain:6 sentence:1 timedependent:1 results:6 years:1 paper:5 birmingham:2 stepanenko:2 existence:1 expressions:2 preprint:6 matrices:3 technique:1 absence:1 strange:1 th:2 mail:2 must:1 hope:1 kingdom:1 dependent:4 mention:1 pfaffians:1 aforementioned:1 using:1 nov:1 exact:2 easily:1 school:1 determinants:2 like:1 hamiltonian:1 reduces:1 arxiv:1 list:1 solved:2 mapped:1 small:1 2m:2 university:1 kalinin:2 reference:1 approximation:1 imply:1 our:6 special:1 page:1 even:1 shown:1 since:1 rev:1 dipole:2 comments:1 sites:1 state:1 ref:3 ass:1 earlier:1 terms:1 linear:2 agreement:1 answers:1 however:1 reported:1 found:1 solv:5 checked:1 appears:1 obtained:4 last:4 equal:3 reduced:1 reobtain:1 comment:2 xx0:1 point:1 bham:2 numerically:1 dimensional:1 xy:6 references:3 statistics:1 described:1 temperature:4 would:1 only:1 been:1 next:1 calculation:3 anisotropic:2 e54:1 ph:2 molecular:3 was:4 correction:1 more:3 questionable:1 form:1 exactly:1 aware:1 coherent:1 authors:2 known:1 partially:1 case:2 cyclic:4 correlators:8 symbolically:1 paragraph:1 limit:1 uk:2 were:2 problem:5 kitanine:2 claim:1 ac:2 give:2 int:5 abstract:1 general:5 cond:1 numbers:1 any:2 functions:1 united:1 thermodynamical:1 same:1 note:1 b15:1 anisotropy:1 papers:2 finite:1 izergin:2 conclusion:1 heisenberg:2 used:1 mat:1 aggregates:3 correlation:1 2tt:1 representations:1 astronomy:1 response:2 edgbaston:1 recent:1 kni:1 onedimensional:1 clear:1 later:1 explicit:1 without:2 time:7 comparisons:1 model:1 physics:1 dimension:1 fact:1
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solv-int9711007.txt |@word partial:1 consider:2 chain:5 rev:4 magnetic:4 global:2 results:1 leads:1 scalar:1 commute:1 ga:3 intricate:1 gm:4 disk:1 c1:1 gi:3 gr:3 whose:1 inverse:3 calculate:1 eigenbasis:1 tw:1 charge:1 grabowski:1 under:1 analogous:1 digit:1 far:2 every:1 difference:3 matrices:1 condition:4 dim:3 trl:2 hamiltonian:11 cosine:1 xyz:1 solution:7 large:3 solved:2 λnm:3 gauge:1 smaller:1 nonautonomous:1 l2l:1 past:1 integrability:2 further:1 dynamics:1 expressions:1 theory:1 bilinear:1 index:1 what:1 giving:3 sum:1 uniform:1 3k:2 3n:3 new:4 method:2 satisfy:1 kicked:10 q0:2 respectively:3 even:1 here:1 hki:1 ansatz:3 represented:1 quite:2 equations:4 logarithmic:3 digits:1 great:1 involved:1 study:1 larger:1 periodic:1 resulting:1 su2:1 action:1 fourier:2 makes:1 via:1 spatially:1 jadranska:1 names:1 liml:1 propagators:2 unit:1 positive:1 negative:1 properties:1 few:1 prelovˇsek:3 call:1 therefore:2 thru:1 bethe:1 more:3 operators:1 vm:8 particular:1 known:2 potential:3 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solv-int9711008.txt |@word nwu:1 consider:1 similarity:1 magnetic:1 dynamic:1 trigonometric:1 leads:2 commute:1 edu:1 whose:1 depend:1 funct:2 tr:4 elliptic:9 dressing:2 enjoying:1 case:4 fax:1 r12:11 r13:4 straightforward:1 very:2 results:2 matrices:1 condition:1 dij:1 hamiltonian:5 turns:1 nondynamical:3 t2:2 t1:2 gauge:1 anal:2 second:1 further:3 canonical:1 section:1 2q1:11 expressed:1 version:3 above:1 new:10 3a:2 contrast:1 satisfy:1 neveu:3 l21:2 l22:2 china:3 address:1 obtained:5 antisymmetric:1 institute:1 studied:1 allows:1 poisson:9 classification:1 namely:2 talon:1 would:2 motivate:1 call:1 type:3 th:3 billey:1 operators:1 particular:1 known:2 equation:13 theories:1 following:1 example:1 beijing:1 calculation:1 r23:4 r21:2 g2:4 g1:4 provide:1 feature:1 far:1 hou:1 parameter:1 algebra:4 may:1 lax:30 geometrical:1 constants:1 natural:1 dynamical:15 effective:2 schneider:2 element:1 fortunately:2 so:1 representation:10 interpretation:1 paper:6 through:2 satisfies:5 still:3 its:3 group:1 li:1 systems:1 mail:1 overcome:1 good:1 nov:1 yu:1 developments:1 structural:1 february:1 2q:18 always:1 university:1 presented:1 l2:7 l1:5 crossing:1 found:9 mean:1 baxter:8 sklyanin:8 quantum:8 our:2 eq:25 special:1 out:1 shown:1 matrix:32 rep:1 particles:2 investigation:1 rational:1 lecture:1 math:4 theory:1 standard:1 difficulty:2 completely:2 yuri:1 ruijsenaars:3 could:3 motion:4 first:2 variables:6 number:1 restrict:1 another:2 open:1 given:10 hyperbolic:1 introduction:1 system:7 construct:8 speaking:1 kind:1 integrability:1 urumqi:1 yang:8 w2:1 ann:1 modern:1 generalization:3 manner:1 seen:1 lie:3 depending:1 calogero:7 potential:4 generalized:4 olshanetsky:1 algebraic:1 connected:1 why:1 bracket:7 exp:1 mailing:1 fact:1 show:1 purely:1 relation:4 analogue:1 find:6 q1:3 q2:3 avan:3 only:2 integrable:3 moser:7 dependent:1 ones:1 suris:1 dt:2 evolution:1 babelon:1 approach:1 arxiv:1 summary:1 qi:5 shi:1 qj:3 set:1 exists:1 depends:2 us:4 recently:1 braden:1 subject:1 interacting:1 review:1 written:3 difficulties:1 closed:3 between:3 enjoys:1 transfered:1 terms:3 august:1 p2i:1 however:1 comm:2 wr:1 solv:1 c21:1 equal:1 quantization:2 cn:1 cm:20 q12:7 except:1 dimensional:2 moreover:1 described:2 due:2 int:1 reduction:1 pj:1 pi:3 meeting:1 define:1 box:1 func:1 ours:1 spin:2 present:1 p2:5 p1:5 look:1 will:1 unitary:1 vol:4 xian:1 ii:1 quantize:1 reads:1 im:1 gervais:3 d12:2 generic:2 make:2 same:2 c12:1 antisymmetry:1 complex:1 northwest:1 hierarchies:1 development:1 independent:1 used:2 numerical:9 upon:3 felder:3 identity:2 well:1 solve:1 model:27 usual:1 being:2 generally:1 aspect:1 adv:1 candidate:1 wen:1 lett:4 iπ:1 transformation:4 possible:3 world:1 particle:2 follows:3 specific:1 integrals:2 δi:1 old:2 classical:10 some:3 q21:6 proper:1 ccast:1 ourselves:1 l11:2 l12:2 does:3 chains:1 2q2:7 annal:1 bo:1 properties:1 most:3 o:3 eight:1 perelomov:1 references:1 operator:19 hep:3 there:2 appl:3 way:3 was:7 lnσ:1 function:2 complete:1 form:4 whether:1 cij:1 up:2 cim:2 krichever:9 limit:1 problem:2 qij:6 defined:5 abstract:1 denote:1 exist:2 laboratory:1 functions:1 no:3 when:1 field:1 setting:1 mathematics:1 vertex:1 commutator:1 variable:2 structure:4 longer:3 d21:2 physics:1 governed:1 international:1 nuovo:2
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solv-int9711009.txt |@word represent:4 darboux:1 consider:4 results:7 leads:1 scalar:16 proposition:1 generalize:1 antichiral:4 expressions:1 gl:6 lptens:1 row:2 devoted:1 whose:1 calculate:1 superspace:4 spin:6 dickey:2 tr:11 tp:11 quasi:1 those:1 th:7 under:2 analogous:1 lkp:2 case:33 conjecture:4 straightforward:2 very:2 conjectured:3 choice:1 djs:2 entries:3 fab:2 fac:1 faa:7 matrices:18 condition:2 school:1 hamiltonian:20 t2:17 solution:2 t0:3 t1:1 large:1 discrete:9 differential:4 math:6 dealt:1 indices:1 gauge:5 superalgebras:2 programme:1 consistent:4 direct:1 sign:3 second:20 j22:2 j21:2 rigorous:1 substitute:1 even:1 index:1 what:2 nonlinear:1 stands:1 brackets:6 section:8 expressed:1 consistently:1 subspaces:1 krivonos:8 new:15 method:2 exercise:2 coefficient:2 compact:1 simultaneously:1 respectively:11 component:1 here:6 nonsingular:1 represented:3 november:1 equations:18 appears:1 z2:3 obtained:4 remark:1 kanno:1 leaves:1 studied:4 excursion:1 simply:2 lred:2 poisson:4 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solv-int9711010.txt |@word concept:1 partial:1 consider:3 remarkable:1 similarity:2 skip:1 results:3 invent:1 eds:1 scalar:1 grateful:1 consists:1 expressions:1 whose:1 inverse:3 chain:1 paris:1 tr:1 recurrence:1 uniqueness:2 petersburg:4 elliptic:8 under:1 applied:1 kρ:2 straightforward:1 very:1 rise:1 trigonometric:1 entries:1 difference:2 matrices:1 deformations:1 condition:1 treating:1 notations:1 symplectic:1 swapping:1 hamiltonian:8 did:1 induction:1 notes:1 sklyanin:5 list:3 solution:2 leave:2 discrete:6 vector:6 indices:1 eigenvalues:3 work:1 zi:1 periodicity:1 zk:3 mi:9 direct:3 second:1 qλn:1 manner:1 dynamics:5 fonction:1 canonical:15 spectral:4 established:2 what:1 nonlinear:3 bλ1:7 bλ2:2 brackets:1 section:9 expressed:2 version:1 poles:1 above:4 boundary:1 new:12 construction:1 method:1 pioneering:1 notions:1 qλ2:1 qλ1:3 abstractly:1 here:5 papageorgiou:1 exceptions:1 leeds:3 separation:12 concluding:1 november:1 quite:1 equations:12 obtained:3 remark:1 institute:2 shift:2 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solv-int9711011.txt |@word sector:3 partial:1 consider:5 exponentiation:2 results:1 fapesp:1 olive:1 ferreira:13 displaying:1 compact:1 γr:2 tr:1 tn:10 those:2 th:6 dressing:2 te:1 ingredient:1 p2:1 straightforward:3 dokl:1 choice:1 novel:1 putting:1 annihilated:1 eds:1 z12:1 solution:3 t1:1 vector:3 eigenvalues:3 akns:2 zm:1 zn:2 zj:2 zero:2 zz:2 odd:1 zr:2 theory:1 abb:1 xω:1 stands:1 chicago:2 section:7 en:2 above:4 new:1 method:2 satisfy:3 1997b:3 1997a:1 respectively:3 component:2 equals:1 bj:1 consideration:1 equations:1 z1:48 z2:38 obtained:3 instituto:1 suitably:1 involved:1 vectors:2 products:2 action:1 hospitality:1 specialize:1 via:1 useful:1 f1:1 ipi:2 ipm:1 anomalies:1 should:2 unit:1 use:1 would:1 commun:3 positive:3 contains:1 pedagogical:1 next:1 ψh:1 therefore:3 ip:1 type:1 more:3 untwisted:1 flat:1 γm:3 solitons:9 operators:22 validity:1 appendix:1 known:2 cases:1 eα:8 must:1 equation:7 work:3 oscillator:1 mk:3 labeled:1 following:7 root:10 example:1 tau:5 f2:1 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solv-int9711012.txt |@word consider:1 lack:1 four:4 commute:4 comments:1 ga:1 antichiral:16 expressions:2 gl:30 fmrx:1 row:2 compact:1 calculate:1 j13:20 superspace:3 jαβ:10 tr:2 tp:1 jh1:2 list:10 finally:4 jh2:1 present:3 th:1 under:1 arranged:1 include:3 applied:3 comm:3 straightforward:2 very:3 rise:8 induce:1 choice:2 putting:1 entries:2 fab:5 fac:1 faa:3 matrices:5 condition:2 arrange:3 illustrated:1 school:1 hamiltonian:28 t2:2 t1:3 large:3 admissible:20 convenience:1 indices:5 relation:1 superalgebras:13 programme:1 grateful:1 ten:1 second:29 j24:11 j23:12 value:1 j21:18 further:2 ba:3 even:1 aim:4 what:4 nonlinear:6 appear:2 invertible:1 brackets:18 giving:1 section:6 ffff:1 current:1 above:2 krivonos:10 international:1 satisfy:3 nonlinearly:1 respectively:6 here:8 understanding:1 others:1 consideration:1 november:1 equations:13 z1:13 z2:12 obtained:4 remark:5 suitably:1 technical:1 involved:1 reason:1 resulting:2 poisson:9 action:1 hospitality:1 suitable:1 studies:1 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solv-int9711013.txt |@word consider:3 results:2 leads:1 scalar:1 commute:6 francesco:1 expressions:5 whose:5 depend:1 γp:2 finally:2 under:1 norm:1 witten:1 affect:1 dij:3 hamiltonian:7 irreducible:1 solution:2 try:1 convenience:1 vector:1 demonstrated:2 eigenvalues:1 periodicity:1 integrability:2 further:1 odd:3 linear:1 even:4 brackets:3 giving:1 sum:2 pijk:3 expressed:2 current:2 above:1 consisting:2 coefficient:1 respectively:4 neveu:1 them:1 address:1 represented:1 equations:5 institute:1 study:1 vectors:8 products:7 poisson:4 fourier:1 examining:1 formulated:1 requiring:2 namely:2 explained:1 wit:1 summation:1 total:1 virasoro:7 derivatives:2 charge:15 would:1 positive:1 contains:1 single:2 quasi:4 cho:1 few:2 nucl:8 associated:1 theoretical:1 more:1 duality:1 operators:3 factor:1 ghandour:1 mansfield:1 vasiliev:1 known:1 iv:1 iii:1 fermionic:1 quartic:1 feigin:2 science:2 equation:7 theories:12 fock:2 values:5 following:4 nonsingular:1 example:1 proof:1 bordner:2 wang:1 give:2 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solv-int9711014.txt |@word consider:3 corps:1 nonrational:1 global:1 results:2 four:1 eds:1 entropy:8 houches:1 follow:1 lkj:4 ty:1 paris:3 deterministic:1 tn:3 quasi:1 under:1 worth:1 conjecture:1 emerged:1 very:2 rationality:1 continued:1 condition:2 presented:1 turns:1 large:1 discrete:10 anal:1 equation:1 proof:1 zn:2 findings:1 prediction:1 located:1 likely:2 evaluated:1 pass:4 dynamics:2 canonical:2 even:1 nonlinear:1 3n:1 above:5 values:1 led:1 degree:18 component:1 here:3 papageorgiou:1 behaviour:1 refinement:1 les:2 depend:1 strong:2 equations:6 appears:1 obtained:3 institute:1 study:3 allows:1 commonly:1 periodic:1 bol:1 pick:1 suitable:1 changes:1 cancellation:1 useful:1 f1:2 f2:1 establish:1 use:1 asymptotic:1 would:3 nijhoff:1 contains:1 tightly:1 next:2 therefore:3 more:4 initial:3 berlin:2 particular:1 projective:2 ramani:5 springer:2 infinities:1 work:1 cancellations:3 cat:1 nine:3 following:1 arrive:2 example:2 refine:1 f0:4 claim:1 compare:1 impose:1 wang:1 figure:4 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solv-int9711015.txt |@word partial:1 consider:2 rev:2 leads:1 proposition:15 tuba:1 go:1 follow:1 expressions:2 research:1 inverse:3 turkish:1 tn:1 program:1 ti:2 wjk:4 straightforward:1 wji:7 very:3 choice:1 ankara:2 corollary:9 σti:1 condition:2 generalised:1 four:1 presented:1 t2:1 solution:8 t0:1 t1:1 solved:1 vector:3 math:1 indices:3 anal:1 integrability:4 bilkent:1 nonlinear:1 sub:3 giving:1 sum:1 3u:1 lengthy:1 fuchssteiner:3 above:9 new:4 satisfy:6 full:1 degree:6 respectively:2 here:3 them:1 expansion:1 2kl:2 equations:33 change:1 2kk:2 obtained:2 technical:2 study:2 studied:2 step:1 ignoring:1 sjk:1 published:1 symmetrical:2 divide:1 family:1 bri:1 total:1 rki:1 unit:2 use:1 would:1 commun:1 distinct:2 cilk:1 next:1 few:1 m1:4 m2:3 themselves:1 type:2 more:2 brings:1 operators:11 under:1 particular:2 known:1 cases:5 iii:1 must:2 recall:1 equation:14 work:9 det:7 klk:2 values:1 following:19 example:8 decoupled:1 proof:1 references:1 council:1 give:8 loosing:1 degenerate:6 vanish:1 boussinesq:1 far:1 sik:5 sij:11 sil:10 classifying:1 fr:1 mat:1 bkl:4 mapping:1 bkj:3 lax:3 faculty:2 fj:3 fk:2 constants:20 sx:2 dynamical:2 correspond:1 st:1 sj:5 so:2 fundamental:1 sl:3 order:3 uvx:1 exclusive:1 hierarchy:1 indeed:1 over:1 satisfied:2 2sx:1 2v:1 existence:4 satisfies:2 urses:3 before:3 sciences:3 clk:2 fiz:1 systems:9 olver:2 ly:1 yi:2 non:9 yj:5 scaling:1 they:1 identically:1 nov:1 now:2 discuss:2 δ2i:1 2u:2 term:6 university:2 2a:1 each:4 found:1 constraints:11 directly:1 reduce:2 used:1 our:2 eq:2 χij:13 out:1 rt:1 matrix:4 rs:1 since:1 rx:1 denotes:1 may:2 investigation:1 rj:1 classification:14 linear:2 quite:1 admits:3 complicated:1 ask:1 definition:3 int:1 hence:7 first:3 xj:11 xk:6 major:1 xi:13 symmetry:3 variables:4 rank:1 philadelphia:1 done:1 another:3 given:33 perturbation:1 similarly:1 introduction:1 eqs:1 system:47 relations:1 their:2 echet:1 listed:4 convention:1 siam:1 gives:1 academy:1 exactly:1 part:16 jordan:1 vxxx:2 determines:1 sections:1 kjk:1 imply:1 determined:1 were:1 powers:1 symmetries:9 generality:2 any:2 solitons:1 satsuma:1 χik:15 depending:3 instance:2 take:2 subject:2 towards:1 shall:4 simplify:1 said:1 qxxx:2 pair:2 class:8 kk:3 kj:31 ki:12 kn:3 km:1 kl:14 segur:1 principle:14 physics:1 ito:3 supported:1 multicomponent:1 hereditary:1 find:2 highest:3 based:1 parameters:8 should:1 only:5 explicitly:3 coefficients:2 integrable:14 do:1 σ1i:1 get:1 de:1 symmetrically:1 silk:4 liu:10 evolution:3 arxiv:1 cikm:3 cij:16 including:1 cri:1 crl:1 set:2 exists:2 δji:4 namely:1 recently:3 qti:2 satisfying:1 its:8 symmetric:10 enough:1 between:1 αi:1 previous:2 conditions:3 terms:2 uux:1 extend:1 jr:1 cijk:13 solv:1 both:1 last:3 many:2 taking:2 kji:1 kjm:1 admit:1 context:1 rosenau:2 among:3 point:2 simple:1 simply:2 respect:6 turkey:3 arts:1 addition:3 observing:1 three:1 been:2 defined:2 aijk:14 abstract:1 define:1 corresponding:3 quantities:2 xxx:11 determination:1 derivative:3 xiong:1 case:15 guarantees:1 pacs:1 will:5 ail:4 aik:3 aij:9 gave:4 procedure:2 wki:4 bonora:1 coupled:10 yk:8 iv:1 ii:2 middle:1 2ux:2 itself:1 vt:3 vx:3 uxxx:4 different:1 containing:2 cjl:1 akj:3 recursion:33 belong:3 same:1 member:1 parts:2 modification:2 proved:1 higher:2 independent:1 extended:2 vvx:1 upon:1 functions:2 flows:1 hand:1 purpose:1 ablowitz:1 localities:1 lower:1 severe:1 without:3 components:1 σ0i:1 proposed:1 cj:2 obtain:3 detail:1 karasu:3 summed:1 scattering:1 σni:2 adding:1 skp:1 infinitely:2 tubitak:1 seems:1 add:1 interested:1 corollaries:1 lett:3 skm:2 east:1 transformation:3 skj:6 bim:2 bij:25 bik:9 depends:1 easily:1 possible:1 admitting:3 loss:1 appearing:2 like:1 qxk:5 reduces:2 korteweg:1 arbitrary:7 conclusion:1 because:2 classical:1 some:2 back:1 examples:2 choosing:1 kdv:26 kmk:2 subclass:4 prog:1 scientific:1 equivalent:2 bi:16 illustration:1 bv:1 although:1 properties:1 simpler:1 works:1 extension:6 constraint:3 91a:1 krj:1 cik:2 extensions:2 introduced:2 follows:2 into:1 functional:1 χkj:9 bihamiltonian:1 χkl:9 determine:1 einstein:1 operator:29 assumed:2 there:2 question:1 transform:1 appl:1 crucially:1 was:1 transformable:1 complete:2 form:7 repeated:1 properly:2 2vx:1 rjk:1 rji:5 partially:1 ux:4 whether:3 ut:5 uv:3 6uux:1 up:1 us:2 cil:2 assume:3 problem:1 subclasses:3 called:4 constant:3 ai:4 ak:3 aj:9 general:3 conserved:1 physica:1 ckj:6 ni:6 nj:15 nk:1 nl:7 nm:1 locality:2 na:1 when:4 δ1i:1 application:3 other:2 fokas:10 department:2 mathematics:1 theor:2 nice:1 sijk:24 symbol:2 hirota:1 problems:1 4d:1 structure:1 implies:4 ranks:1 vries:1 time:3 n1:4 n2:3 starting:1 original:2
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solv-int9712001.txt |@word represent:1 partial:1 consider:4 leads:2 scalar:1 grateful:1 consists:1 expressions:1 relationships:5 sukhov:1 inverse:1 calculate:4 equivalence:8 under:10 worth:1 advises:1 rise:1 geometrical:4 corollary:1 trough:2 associated:5 difference:1 matrices:3 condition:4 dij:3 list:1 moldova:2 vector:8 indices:1 anal:2 des:1 direct:4 tex:1 second:8 arnold:1 further:1 substitute:4 residue:1 what:1 nonlinear:2 expressed:2 sur:3 above:1 ufa:4 new:1 equivalent:2 simultaneously:1 degree:1 here:5 canonically:1 les:3 others:1 z4:1 method:1 equations:27 change:8 z3:1 obtained:1 institute:1 studied:1 sbornik:1 resulting:1 changes:1 uniquely:2 mail:2 classification:2 austria:1 apply:1 univ:1 unit:2 derivatives:1 use:2 would:1 prove:2 sake:1 france:1 call:1 therefore:1 themselves:1 type:1 metric:1 more:2 nauka:3 pavlov:1 subcases:1 ecole:2 operators:2 line:1 odinger:1 particular:1 known:1 projective:3 cases:1 hold:1 iii:1 account:2 equation:16 work:1 det:5 erwin:1 kamran:8 obvious:1 following:14 dec:1 root:1 proof:1 give:1 calculation:2 sokolov:2 cartan:5 degenerate:1 lamb:1 huge:2 rather:1 verify:1 holds:1 s4:1 write:2 instead:1 ordinary:7 parameter:2 fp:1 finslerian:1 information:1 may:1 after:1 derived:2 dx2:1 residues:1 plane:3 shadwick:1 choice:1 natural:1 dynamical:2 third:1 sr:1 explicit:4 su:2 fundamental:1 order:11 norden:1 help:1 ordre:1 professors:1 course:1 paper:5 london:1 y1:6 existence:1 y2:1 its:3 derive:1 la:2 jacoby:1 affine:3 coordinates:17 writing:1 choose:1 derivative:3 main:1 wellknown:1 them:7 ya:1 sssr:1 they:4 multidimensional:1 now:6 yu:1 easily:1 2r:1 2s:1 invariants:1 university:3 l3:1 higher:2 side:4 mikhailov:5 arxiv:1 financial:1 arbitrariness:1 journ:1 reduce:1 our:1 special:11 matrix:5 space:1 res:1 since:7 vectorial:1 increase:1 transforming:2 rational:1 formula:5 math:11 pinchuk:1 theory:5 state:2 admits:1 base:1 surely:1 definition:1 geometry:6 transition:1 times:2 hence:1 inst:2 first:6 manuscript:1 researches:1 variables:6 xz:1 done:1 another:3 array:1 electronic:1 given:4 publication:3 introduction:1 system:1 construct:2 their:4 too:1 calculations:3 siam:1 scheme:2 structures:2 gives:3 way:1 relationship:3 academy:1 moscow:3 exactly:2 authors:1 x2:1 x0:10 x1:9 than:1 coefficients:8 double:1 painleve:1 project:5 determined:1 str:2 were:2 enables:1 treated:1 russia:2 conforme:1 symmetries:1 rewrite:1 electrodynamics:1 ann:2 argument:1 any:2 lie:3 jour:1 note:1 sciences:1 s21:4 take:4 finding:1 formulas:4 straightening:1 shall:6 denominator:5 algebraic:1 regular:1 connected:2 phase:1 class:5 surprising:1 considered:1 clear:1 coincides:1 typeset:1 physics:1 bulletin:1 quantity:3 supported:1 chapters:1 spaces:3 gauge:4 substituting:3 d2:1 find:4 q1:1 theorie:1 based:1 parameters:3 written:2 should:1 factor:2 local:3 get:9 de:6 mahomed:1 ones:1 dx:1 invariant:3 during:1 du:1 differentiating:1 qs:2 fields:4 differential:20 expansions:5 acknowledgments:1 twice:1 see:5 result:3 y0:7 sem:1 curvilinear:2 liouville:1 symmetric:1 enough:1 closed:3 tresse:1 mul:1 αj:1 conditions:1 preserve:2 multiplied:2 olver:5 tensorial:1 however:1 js:2 vanishing:1 solv:2 both:2 many:1 taking:1 equal:1 chosen:1 connection:3 expression:1 among:1 relativity:1 point:29 simple:1 lagrangians:3 address:2 pole:2 polynomial:6 respect:5 connexion:2 pseudoscalar:5 pr:2 pp:1 described:1 transformations:20 z0:4 skew:1 due:2 been:1 int:2 reduction:1 z2:1 abhandlungen:1 algebras:2 systems:1 fund:2 determination:1 hamburg:1 denote:5 present:1 case:1 p1:1 kazan:2 means:6 value:1 replaced:1 intas:1 conformal:1 von:1 ir:2 thus:1 according:1 vanish:1 different:2 grant:1 geometrization:1 same:4 archive:1 rules:11 arguments:1 bol:1 wilkens:1 defines:2 european:1 extended:1 hand:4 purpose:1 potentials:1 pures:1 normale:1 analysis:1 s22:4 without:1 components:9 arising:1 obtain:1 differentiation:1 preprint:2 had:1 transformed:5 easy:3 theorem:8 transformation:13 aspects:1 sharipov:8 sums:1 varietes:2 using:2 ams:1 advanced:1 apart:1 follows:3 arbitrary:5 mathematical:1 right:4 classical:1 some:3 espaces:1 diff:1 nonzero:1 describing:1 zwei:1 subclass:1 proc:1 esi:1 s12:4 s11:4 expansion:1 broken:1 hsu:1 raum:1 properties:1 chapter:1 central:1 certainty:1 theorems:1 numerator:2 dependence:1 o:5 covariant:1 wien:1 invarianten:1 soc:3 transcendents:1 into:10 bound:1 appropriate:1 references:2 weight:7 support:1 long:1 appl:1 fraction:6 function:6 head:2 complete:1 form:21 but:1 russian:1 dy:1 adler:1 applying:2 nonlinearity:1 differentielle:1 us:2 below:1 submanifolds:1 problem:4 called:1 uber:1 proved:1 defined:5 certain:2 abstract:1 doesn:1 general:1 coordinator:1 formulation:1 check:2 constructed:1 functions:2 no:2 when:1 field:23 other:1 republic:1 details:1 theor:1 conclusion:1 neufeld:1 problems:3 polynomials:1 variable:1 lanl:1 4s:1 rule:2 4q:1 time:1 international:1 having:1
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solv-int9712002.txt |@word represent:1 superfields:17 leads:1 scalar:10 commute:1 antichiral:3 expressions:1 superspace:3 xiong:1 tr:12 tp:2 tn:2 conjecture:2 comm:1 rise:1 entries:2 faa:4 matrices:3 condition:2 four:1 hamiltonian:7 irreducible:2 t2:24 t3:6 involution:5 manifestly:1 direct:1 second:9 further:1 residue:3 established:1 what:1 bb:3 brackets:3 sum:1 selected:1 expressed:1 above:2 krivonos:8 new:12 acknowledgments:1 3d:3 coefficient:2 full:1 led:1 respectively:6 component:1 here:4 represented:1 november:1 strong:1 equations:8 appears:1 obtained:3 remark:1 studied:1 lred:4 hospitality:1 family:6 private:1 total:1 unit:1 derivatives:5 projector:1 would:1 covariant:1 contains:3 negative:1 nucl:1 call:1 therefore:2 type:2 theoretical:1 more:2 started:1 operators:11 4j1:2 known:1 fermionic:10 ii:1 valued:3 recall:2 equation:1 work:1 reproduce:1 values:1 following:4 nonsingular:1 dec:1 example:1 gallot:2 solved:1 preserving:2 standard:3 rescaling:1 enslapp:1 boussinesq:8 rather:1 pure:1 warner:1 parameter:1 gnls:5 inputs:1 product:1 description:3 algebra:1 after:1 derived:4 lps:4 fa:1 lax:37 representations:1 stress:1 correspond:1 su:2 complexity:1 ones:2 representation:5 order:1 restriction:1 hierarchy:21 indeed:1 over:3 satisfied:3 paper:1 looks:1 mentioned:1 existence:2 still:1 its:5 refs:1 djs:2 derive:1 thsun1:2 interesting:1 better:1 ls:11 communication:1 mail:1 puzzle:1 them:1 propose:1 daj:1 scaling:1 dap:1 they:1 identically:2 bogoliubov:1 now:1 discuss:1 dj1:7 easily:2 2d:4 2f:6 l2:1 l3:1 l0:1 l1:2 characterized:1 mean:1 differential:5 dωj:1 simplicity:1 operator:29 laboratory:1 operation:1 ep:1 out:2 matrix:29 space:3 since:1 research:1 acting:1 ref:1 integrated:1 math:3 foundation:1 quite:1 surely:1 counterparts:2 besides:1 dubna:3 generate:1 e2:2 definition:2 chiral:4 ordering:1 length:1 first:2 number:5 bellucci:1 supersymmetrization:1 given:3 rewritten:2 introduction:1 eqs:4 system:1 their:9 dfg:1 gives:1 moscow:1 part:1 because:1 representing:1 coefficients:1 ivanov:1 kind:2 zero:1 preparation:1 russia:1 symmetries:1 delduc:2 unchanged:1 generalization:3 any:3 liu:1 coincide:3 trace:1 price:1 difference:2 letter:2 pair:6 class:1 considered:2 flow:7 ext:1 kp:7 physics:1 section:1 fact:3 reductions:5 supported:1 relation:1 trivial:1 sorin:7 based:1 should:2 analytic:1 only:3 integrable:1 hamiltonians:3 local:2 do:1 dl:2 his:1 dj:4 goes:1 means:4 df:12 familiar:1 dd:2 db:2 straightforwardly:2 da:6 cannot:1 dz:2 words:1 lbos:2 exhibiting:1 densities:1 fields:3 transposition:1 arxiv:1 contain:4 j1:55 j2:24 j3:9 observed:2 see:3 w4:1 terms:5 dls:2 closed:1 simplest:2 subscript:1 multiplied:1 recently:2 ld:1 js:2 reproduces:1 ws:4 jj:8 analyzed:2 thank:1 last:5 limits:1 region:1 admit:1 labelle:1 expression:1 δab:2 conclude:2 corresponds:2 solv:5 anti:1 respect:1 mathieu:1 transformations:1 basis:2 chirality:2 three:4 been:10 int:5 reduction:2 interest:1 basic:1 algebras:4 systems:1 families:4 commutes:1 coincides:1 understand:1 derivative:3 spin:1 former:3 present:5 case:22 appearance:1 value:1 rectangular:1 aim:1 while:3 replaced:2 intas:1 property:4 bonora:4 vj:2 thus:2 non:3 obeying:1 vs:2 vanish:1 rfbr:1 different:2 grant:3 generic:4 pay:1 same:2 unity:1 hierarchies:25 finite:3 yung:2 extended:4 parametrizes:1 flows:4 infinite:5 popowicz:1 nevertheless:1 no:3 well:2 peculiarities:1 without:2 components:3 coordinate:3 possesses:2 usual:1 proposed:2 being:2 obtain:1 alternative:1 previous:1 seems:1 belongs:1 lett:5 remaining:3 2j3:2 2j2:8 2j1:7 read:1 decomposed:1 superfield:6 using:1 like:2 sissa:2 admitted:1 byproduct:1 arbitrary:1 spins:3 δa:1 therein:1 right:1 discrete:1 some:2 understood:1 examples:3 kdv:20 dimensions:1 toppan:1 integration:2 comments:1 does:2 decomposition:1 provides:1 reasonable:1 power:1 imaginary:1 super:10 properties:2 simpler:1 extension:2 commutator:1 discussed:1 extensions:1 act:1 introduced:2 consequently:1 h2:4 h3:1 into:1 h1:3 integral:1 square:2 references:2 elementary:1 bosonic:21 there:1 u1:2 long:1 way:1 jinr:5 was:2 opposed:2 complete:1 form:4 hp:5 but:1 construction:1 russian:1 j12:9 j13:2 partially:1 inside:1 up:2 us:6 ωj:2 limit:4 uj:2 demonstrate:1 problem:1 aa:1 ab:1 defined:2 recognize:1 abstract:1 aj:2 ap:4 single:1 exist:1 our:1 supersymmetric:22 constructed:3 grassmann:1 functions:2 variety:1 detail:1 other:3 details:1 conclusion:1 elements:1 generates:1 symbol:1 includes:2 a0:2 parities:1 structure:5 corresponding:5 pseudo:4 time:1 original:1
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solv-int9712003.txt |@word φ1j:1 φ1k:1 concept:1 consider:18 chain:1 secondly:1 induces:3 global:3 unique:1 results:1 leads:7 scalar:4 proposition:2 parameterization:5 oldest:1 gj:13 whose:5 preserves:4 inverse:9 depend:1 calculate:1 zone:1 description:1 tu:2 father:1 editors:2 γk:5 γj:15 finally:1 restriction:4 petersburg:2 elliptic:7 dressing:3 semenov:1 dsj:1 td:2 te:1 γg:6 ingredient:1 case:16 r12:5 wjk:1 g1:1 orthogonal:8 a18:1 rise:3 springer:4 dwj:6 geometrical:7 reinterpret:1 every:1 entries:2 matrices:19 groups:1 bxx:4 dubrovin:2 obvious:1 riemann:11 hamiltonian:22 evaluation:1 sklyanin:1 t2:1 solution:14 hereafter:1 try:1 admissible:2 vector:8 math:18 splitted:1 indices:1 div:1 shansky:1 der:1 possibility:1 upper:1 encloses:1 neighborhood:1 zj:7 zk:4 miller:2 fibres:1 kowalewski:1 faddeev:2 brill:3 zero:2 benenti:1 korteweg:2 reine:1 invariant:1 dynamics:5 theories:2 odd:2 canonical:13 even:4 what:1 nonlinear:7 brackets:7 giving:2 2g1:1 sum:2 sj1:4 abels:1 while:1 expressed:2 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solv-int9712005.txt |@word inverse:1 lieb:1 suny:1 consider:2 chain:2 indeed:1 magnetic:1 particular:1 nikita:1 discovered:1 paper:2 relation:2 sunysb:1 edu:1 mentioned:1 substituting:1 expressions:1 steklov:1 scattering:8 find:5 itp:1 principal:1 now:1 depend:1 calculate:2 kernel:3 density:1 ln:1 brook:1 corrections:1 should:2 supported:1 charge:3 valid:3 derivative:3 main:2 solvable:1 momentum:2 emphasize:1 identical:1 do:1 his:1 df:4 between:1 comparing:1 introduce:1 integrable:1 dx:1 vacuum:1 press:1 immediately:1 bogoliubov:1 unique:1 dq:11 finite:1 necessary:1 2r:8 particle:6 hamiltonian:2 did:1 fields:1 edges:1 arxiv:1 solution:1 izergin:1 specific:1 solved:1 vector:1 alternatively:1 xviii:1 university:1 characterized:1 mathematical:1 coefficient:1 exists:1 implies:1 det:3 energy:1 2c:2 reduce:1 elementary:1 value:3 existence:1 quantum:3 relates:1 dµ:4 rapidity:1 canonical:1 nonzero:1 ru:1 phases:3 cψ:1 matrix:2 space:1 section:1 rev:1 expressed:1 research:1 particles:4 everything:1 state:1 cambridge:1 use:2 fractional:3 new:2 ground:1 acknowledgments:1 math:1 body:1 foundation:2 give:1 terms:1 obey:1 respectively:1 attention:1 given:1 here:6 standard:1 completely:1 concentrate:1 ansatz:1 solv:1 bose:5 method:1 models1:1 appears:1 chapter:6 interaction:1 would:1 language:1 most:1 institute:1 many:1 transition:1 allows:1 equal:3 etc:1 hψ:1 important:1 act:1 zittartz:1 conformal:1 proof:2 other:1 stony:1 functions:2 xj:2 xk:1 formulated:1 follows:2 simple:1 relate:1 vii:1 integral:3 nsf:1 three:1 dimensional:2 represented:1 references:1 another:2 operator:3 respect:4 precisely:2 insti:1 size:1 derivatives:3 slavnov:1 usa:1 prove:2 introduction:1 equations:3 there:2 system:1 relations:1 properties:1 defined:3 difference:1 quadratic:2 way:1 basic:2 resolvent:3 was:2 bethe:1 define:1 function:5 field:1 only:2 complete:1 relationship:1 xxz:2 moscow:1 exactly:1 gas:5 odinger:1 but:1 hn:2 delta:1 russian:1 c2:1 spin:3 production:1 reflection:1 case:1 wide:1 multi:1 2πif:1 vladimir:1 science:1 equation:8 work:1 mi:1 us:3 fock:1 fermi:7 formulæ:1 nonlinear:1 shift:1 already:1 dec:1 similar:1 russia:1 dλ:1 mechanics:1 dedicated:1 constant:2 rewrite:1 int:1 abstract:1 describe:1 thus:2 surface:5 ii:1 sphere:1 dν:4 ras:1 our:1 ic:2 property:2 result:1 iˆ:4 containing:1 national:1 no:3 convenient:1 60th:1 vanishes:1 chemical:1 ny:1 antisymmetry:2 potential:1 take:1 pauli:1 liniger:1 proved:1 degenerated:1 parameter:5 sufficient:1 heisenberg:2 spectral:5 used:3 description:1 models:1 permit:1 what:1 hand:1 hence:1 phy:1 birthday:1 waves:1 phase:4 class:1 identity:10 commutation:1 schr:1 coupling:2 using:3 clear:1 grant:2 explicit:1 korepin:3 like:1 yang:2 fact:1 exp:1 correlation:1 occasion:1 model:6 physics:1 order:3 turns:1
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solv-int9712006.txt |@word belong:1 unities:1 they:2 just:3 show:1 over:1 lack:1 find:1 choose:2 invent:1 four:2 paper:1 relation:5 solutions:2 statistical:1 wholly:1 ural:2 multiplier:1 factorizing:3 reader:1 intersection:1 based:1 parameters:3 explained:1 exact:1 point:3 seems:1 state:1 poles:1 spirit:1 only:1 other:4 corresponds:1 systems:3 integrable:3 constant:3 freely:1 solvable:1 remaining:1 columns:1 correspondence:2 division:1 non:1 move:3 dj:7 provides:1 straightforward:1 means:3 propose:1 chapter:1 introduce:1 geometrical:1 cannot:1 five:6 closely:1 half:3 associated:1 now:2 matrices:7 geometric:1 evolution:1 several:1 obvious:1 later:1 turns:1 university:1 arxiv:1 solution:2 appear:1 solved:1 intervals:1 each:11 gauge:2 a123:3 lines:3 mean:1 function:1 lenin:1 because:2 transforming:1 constructing:1 classical:3 kashaev:2 variables:4 some:5 up:2 sergeev:2 inhomogeneous:1 namely:1 examples:1 specified:1 yangbaxter:1 our:1 intact:1 special:2 out:3 subscripts:1 a13:1 nonlinear:1 dimensions:2 discrete:3 sum:1 while:3 expressed:1 research:1 re:2 written:1 version:1 decomposition:2 intersect:2 example:1 international:1 get:2 subtracted:1 conditions:1 shows:1 meromorphic:2 outgoing:3 turning:1 degree:4 whose:1 ufa:1 arbitrary:2 points:6 however:1 diagonal:2 its:1 address:1 solv:4 outer:3 baxter:1 equations:2 permitted:1 change:2 z3:2 obtained:1 restrictions:1 search:1 fixed:1 incoming:3 reverse:1 impose:1 institute:1 many:1 vectors:4 put:2 according:2 through:2 quantization:1 suggests:1 plane:6 nothing:1 passing:1 genus:1 block:1 arbitrarily:1 does:1 initial:1 twelve:1 into:2 others:1 compare:1 three:6 dimensional:7 represented:1 employing:1 references:1 planes:4 z5:2 elementary:1 moreover:1 open:3 between:1 remain:1 given:1 described:1 chelyabinsk:1 needed:1 amazingly:1 there:3 system:5 least:1 z1:2 ψk:5 permanent:1 call:1 inner:4 way:3 taken:2 attach:4 scheme:1 consistent:1 more:2 zeroes:2 a32:1 a31:1 corresponding:4 relaxing:1 relax:1 becomes:1 relaxed:3 exactly:1 reasoning:1 but:3 αj:2 particular:1 known:2 number:3 cases:1 z4:2 divisors:3 those:5 must:3 case:1 b145:1 functional:2 local:2 inside:1 tetrahedron:9 attached:3 integrability:2 us:6 ferro:1 will:8 below:1 determined:2 limit:1 freedom:2 following:3 problem:5 dec:1 similar:2 russia:2 say:1 abcd:3 a21:1 a22:1 a23:1 korepanov:3 orientation:1 figure:1 chosen:1 int:4 december:1 abstract:1 sense:1 them:4 correspond:1 already:1 reads:1 itself:1 exist:1 numbers:7 av:1 follows:1 well:1 yang:1 a33:1 ones:1 depict:1 form:2 equation:3 latter:1 six:4 generally:1 same:2 write:1 nontrivial:1 complex:2 take:2 divisor:3 instead:2 φk:5 divides:1 belongs:2 simplicity:1 product:6 elements:2 a11:1 electric:1 see:1 a12:1 models:4 algebro:1 time:1 vertex:2 functions:1 z2:2 algebraic:4 edges:12 connected:2 multiply:1 changing:1 interested:1 parallel:1 matrix:4 dynamical:5 assume:1 physics:1 space:8 curve:2 vertices:1 having:1 edge:6 so:3 south:1 components:2 consistency:1 position:1 arising:1 order:1 fact:1
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solv-int9712007.txt |@word represent:1 consider:5 chain:1 results:1 four:2 proposition:1 gn:2 gj:3 nakayashiki:1 inverse:1 depend:2 graph:1 tr:2 th:1 supported:1 orthogonal:1 regional:1 conditions:20 wave:5 vertex:1 corollary:2 every:1 fǫ:1 condition:1 school:1 hamiltonian:3 foda:1 sklyanin:3 t2:20 miwa:3 t1:24 vector:1 zn:12 zi:4 zj:10 zk:3 ued:1 integrability:2 follow:1 canonical:1 spectral:5 index:3 nonlinear:1 section:8 b441:1 above:4 increasing:1 method:1 satisfy:2 respectively:3 here:15 ansatz:10 invented:1 equations:3 z1:12 box:2 dec:1 institute:1 study:3 studied:2 periodic:2 usually:1 fourier:2 iλσ:2 summations:1 sgn:5 summation:1 use:2 takes:1 prove:1 eτ:3 next:1 few:1 nucl:1 ψn:84 therefore:8 takeo:1 type:1 theoretical:2 minor:8 more:1 operators:6 odinger:2 valued:1 science:1 equation:6 work:1 det:17 fock:2 values:3 following:14 arrive:6 proof:1 give:1 december:1 permutations:1 states:1 sphere:1 degenerate:4 occur:1 kedem:1 ηm:1 holds:4 orthogonality:2 chemical:2 mccoy:2 parameter:2 sin:29 de:1 thermodynamic:6 derived:1 cbms:1 magnetizations:1 representations:10 fj:2 fn:1 λ2j:3 remember:1 third:1 whenever:1 korepin:4 element:1 so:3 sn:13 correlation:31 representation:3 integrand:2 words:1 order:1 acts:1 help:4 ith:1 developed:1 paper:5 statistical:1 y1:1 japan:2 satisfies:3 y2:1 write:2 derive:7 chosen:1 fined:1 systems:1 main:1 h0:12 ηk:1 framework:1 they:2 bogoliubov:1 now:4 nos:1 eigenvalue:1 finite:7 kǫ:3 university:2 fσ:2 fτ:3 2l:16 2n:3 2i:1 en:9 formulate:2 series:1 operator:4 fs:1 quantum:5 our:8 special:4 jimbo:4 matrix:4 space:3 rev:1 research:1 dλ1:1 formula:1 iλx:1 math:3 attentions:1 foundation:1 theory:1 free:1 standard:1 earliest:1 definition:1 dirichlet:6 dλn:1 starts:1 impose:1 konno:1 davis:1 promotion:1 first:2 variables:2 number:1 iht:5 open:10 size:2 given:16 temperature:11 πd:1 introduction:1 relations:6 zσ:2 assumption:1 fermions:3 calculations:1 exploring:1 x2:71 translation:1 x1:72 dynamical:16 determined:1 were:1 rewrite:1 lim:3 sciences:1 potential:2 gσ:1 take:3 coincide:2 formulas:3 algebraic:2 formulae:8 acknowledgements:1 especially:1 calculated:3 coincides:1 kn:1 km:1 exp:5 sum:1 fact:2 show:1 vǫ:9 ki:2 iǫ:10 relation:2 solutions:1 ground:10 ature:1 parameters:6 state:14 lemma:10 only:2 explicitly:1 factor:2 integrable:3 local:2 equilibrium:1 notation:1 means:1 dependent:2 µj:6 expectation:4 obtain:6 dz:1 dx:1 ds:5 determinants:2 fields:11 arxiv:1 µ2j:3 cǫ:15 kernel:5 set:5 j1:8 depends:3 result:1 dµ:7 λki:1 αw:1 eigenstates:1 symmetric:1 written:1 µn:14 µk:6 between:1 fermi:4 boundary:19 approach:3 side:1 recently:1 attention:1 however:1 jn:11 concentrate:1 solv:1 bose:12 distribution:1 cos:3 limits:1 wu:2 temper:1 hψ:1 among:1 simple:2 dimensional:2 sequences:2 respect:2 conference:1 kernels:1 slavnov:3 basis:1 δλj:1 been:6 int:1 much:1 interest:1 kronecker:1 obtained:5 determinant:21 partly:1 xxz:3 gas:7 deter:1 jǫ:8 spin:1 case:11 ǫg:2 ǫf:1 ǫe:5 value:2 ǫp:2 a21:1 cons:4 vol:2 ij:2 id:1 pay:1 began:1 iξ:1 same:1 arguments:1 constructed:1 independent:1 used:8 sym:4 parametrized:1 purpose:4 invariance:1 identity:1 eigenvectors:1 schr:2 analysis:2 without:1 coordinate:1 organization:1 model:5 left:1 trigonometric:1 eitλ:3 intervals:1 transforms:2 λk:1 λj:16 scattering:1 λn:39 density:4 gj1:1 thermodynamics:2 other:2 treatment:1 theorem:3 diagonalization:1 solvable:1 finitetemperature:1 represents:2 possible:2 know:1 vacuum:4 using:6 ams:1 fj1:2 insert:1 particle:2 mesure:1 integrals:1 arbitrary:1 works:1 dµv:1 mathematical:1 neumann:6 some:1 nonzero:2 cψ:1 dz1:2 does:1 decomposition:2 lattice:1 chains:1 kyoto:3 equivalent:1 about:1 impenetrable:8 commun:3 dependence:1 o:1 dzn:2 compatible:1 ensure:1 fredholm:18 ξm:1 iµj:1 into:1 integral:18 references:1 ηr:2 elementary:1 weight:3 prepare:1 there:1 way:2 ixs:1 toeplitz:1 function:10 kojima:5 form:9 simplifications:1 sequel:3 delta:1 line:2 he:1 coset:2 society:1 antiferromagnetic:1 us:4 bethe:10 limit:5 problem:4 ix1:1 called:6 eigenvector:1 mechanics:2 interval:1 constant:3 defined:12 abstract:1 dξ:5 dν:1 dλ:3 formulation:1 ing:1 physical:1 functions:33 completeness:2 when:1 vanishes:1 field:5 interested:3 eiht:3 mathematics:1 izergin:1 stat:1 models:2 wǫ:7 ξr:2 problems:1 ξj:1 ising:3 coupling:1 assume:1 factors:8 time:8
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solv-int9712008.txt |@word consider:1 chain:3 magnetic:2 desirable:1 results:3 commute:3 generalize:1 houches:2 expressions:1 row:1 whose:1 inverse:3 tl:2 th:3 tr0:1 include:1 straightforward:1 p0i:1 trigonometric:2 matrices:1 obvious:1 hamiltonian:4 large:1 vector:1 indices:2 eigenvalues:8 degeneracy:2 takhtajan:1 coefficient:1 sign:1 jump:1 integrability:4 theory:1 spectral:1 what:1 foregoing:1 sur:1 above:5 expresses:1 method:3 satisfy:3 full:1 here:2 condmat:2 les:2 ansatz:11 address:1 equations:5 appears:1 obtained:5 dividing:2 shift:3 study:1 studied:1 periodic:1 products:1 characterizing:1 permutation:2 action:1 involves:1 highly:2 unit:3 use:1 charge:1 takes:1 would:1 distinct:2 positive:1 finally:2 therefore:1 taken:1 bethe:10 reflects:1 lowering:1 operators:7 particular:2 known:2 cases:1 hold:1 logarithm:1 states:5 unessential:1 equation:5 work:1 vega:1 values:3 following:1 dec:1 root:1 proof:2 nearest:1 give:1 calculation:1 december:1 generically:1 involve:1 numbers:1 degenerate:2 counting:1 yang:4 g1k:1 verify:3 six:2 feature:1 fermion:1 how:1 fourth:1 parameter:5 sin:25 product:4 mat:2 algebra:6 may:1 thermodynamic:1 after:1 derived:2 residues:1 reflect:1 lax:2 representations:5 light:1 explicit:1 correspond:1 su:16 greek:1 inhomogeneity:1 superscript:1 restriction:1 acts:1 help:1 over:3 satisfied:4 paper:1 through:1 γµi:1 statistical:1 satisfies:2 recovers:1 its:1 roots:3 group:2 la:1 ln:3 exact:1 conjugation:1 spoiling:1 defining:3 deformation:3 non:2 affected:1 adjacent:1 combination:1 introduce:1 framework:2 they:5 identically:2 now:1 ebec:1 term:2 hepth:1 each:3 found:4 universit:1 baxter:4 square:1 ei:11 ej:3 reduce:1 operator:10 obtains:3 quantum:5 out:1 canada:2 shown:3 jimbo:1 matrix:19 space:4 since:2 rev:3 rational:6 reader:1 cα1:1 math:3 shows:2 linear:1 state:1 free:4 completely:1 card:2 definition:1 interaction:1 introduction:1 βa:2 dλp:1 consequence:2 features:1 symmetry:5 number:1 xx:6 multiplying:1 least:1 given:7 unitarity:1 relations:6 their:1 zeros:1 expand:1 fermions:4 exactly:1 part:2 peculiar:1 coefficients:2 ste:1 double:1 imply:2 determined:1 were:4 gives:1 ybe:6 fcar:1 symmetries:2 correction:2 argument:1 generalization:2 intertwining:1 seen:2 any:1 generic:1 built:1 latter:1 physique:1 note:2 generalized:1 lectures:1 multiple:1 fundamental:1 trace:3 algebraic:6 cyclicity:1 shastry:3 remarks:1 class:1 unequal:1 calculated:1 reflecting:1 fact:2 supported:1 spaces:3 gauge:1 solutions:2 parameters:4 written:3 only:1 generators:2 l0i:1 integrable:4 hamiltonians:4 local:1 get:2 de:2 aβ:3 new:2 dp:1 qu:1 approach:1 arxiv:1 l01:2 email:1 qc:1 cycles:1 traceless:1 remains:1 reveals:1 set:8 clarified:1 relative:1 see:1 result:1 recently:2 αp:3 still:1 tensor:2 sites:3 enough:1 µi:12 between:2 complications:1 boundary:1 conditions:1 checks:1 latin:1 terms:3 however:2 vanishing:2 add:1 comm:2 solv:2 holds:1 both:1 cos:2 taking:4 equal:8 nserc:1 context:1 contribution:1 0i:1 expression:1 otherwise:1 detailed:1 cn:6 conclude:3 simple:2 ca:1 corresponds:1 dimensional:7 simply:1 considering:1 ei3:1 ei2:1 puts:1 basis:1 union:1 copies:3 momentarily:1 dropping:1 t1α:1 generating:1 corresponding:1 commutes:1 xxz:7 spectrum:8 epartement:1 spin:1 those:2 divisor:1 case:1 multi:2 will:2 while:1 replaced:1 monodromy:4 applies:1 property:1 conformal:1 procedure:1 vectors:1 site:2 disjoint:3 regularity:1 cond:2 conserve:1 hubbard:4 pav:1 perform:2 belong:2 same:4 unity:1 complex:2 diagonalize:1 avoids:1 couple:1 higher:5 extended:1 trivially:2 inhomogeneities:1 phy:6 infinite:1 identity:2 recent:1 eigenvectors:3 well:1 without:1 sets:2 model:12 usual:2 λr:1 λp:4 just:3 denser:1 obtain:1 underlying:2 λk:2 λj:9 λi:1 scattering:3 yet:1 letting:2 δpm:2 seems:1 cc:1 lets:1 setting:1 lett:2 easy:2 diagonalization:5 transformation:1 real:1 depends:1 eigenvalue:4 advances:1 iγ:1 possible:4 fusion:1 vacuum:1 r0i:1 using:4 mod:2 systematically:1 alternatively:1 specific:1 yields:1 follows:1 works:1 therein:1 shed:1 because:2 some:2 eiγ:2 eiλ:1 foy:1 manipulations:1 does:1 chains:1 forgets:1 refer:1 faddeev:3 ba:1 power:2 retains:1 arbitrary:3 mathieu:1 rus:1 cα:2 properties:2 integers:2 central:1 carried:1 influences:1 column:1 mutually:1 neighbor:1 act:2 introduced:2 projectors:1 thacker:1 subset:1 mechanics:1 h2:3 bazhanov:1 h1:1 functional:1 three:1 nothing:2 hermitian:2 references:2 laval:6 elementary:1 proportional:1 bosonic:1 additional:1 transfer:5 start:1 quadratic:3 lowest:1 complete:2 form:6 multistate:1 hp:2 differences:1 but:3 construction:2 hm:1 raising:1 coupling:1 whether:1 ikπ:1 limit:7 distribution:1 similar:2 eigenvector:2 aa:6 pii:5 ab:1 int:3 certain:1 abstract:1 am:1 twist:1 conserved:4 dλ:2 check:2 tedious:1 amounts:1 when:1 vanishes:2 field:3 other:2 details:1 quantities:4 stat:1 elements:2 models:27 allowing:1 decorated:1 sides:1 structure:4 implies:1 auxiliary:3 factors:1 pseudo:1 implied:1 weights:1 n1:12 n2:26 avoid:1 8th:1
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solv-int9712009.txt |@word ψ1x:2 dewitt:1 partial:1 consider:3 φ1x:1 gb:3 ga:5 edu:2 follow:1 gi:1 equivalences:3 devoted:1 preserves:1 inverse:3 superspace:1 tw:2 tu:3 nonlocal:1 tn:7 δhn:12 quasi:4 alvarez:1 th:4 under:5 worth:1 applied:1 string:5 straightforward:2 very:1 wave:1 summarized:1 manin:3 hamiltonian:14 turns:3 t2:13 t1:2 leave:1 becker:1 solutions:1 ten:1 nthu:1 takhtajan:1 consistent:1 direct:1 sign:1 past:1 second:2 further:1 odd:7 dψ1:1 canonical:13 even:4 established:1 section:2 expressed:1 above:3 krivonos:2 new:1 method:3 satisfy:1 respectively:3 here:1 understanding:1 water:1 address:2 concluding:2 equations:18 z2:1 obtained:1 remark:1 study:3 studied:1 poisson:1 dickey:1 chang:1 sci:1 via:4 followed:1 2φb:2 2φa:2 establish:1 virasoro:1 use:2 would:4 commun:5 finally:1 next:1 few:1 nucl:1 lφ1:1 therefore:3 a29:1 ψb:31 associated:2 ψa:23 theoretical:2 solitons:1 operators:3 ti:1 berlin:1 particular:1 cases:1 iii:2 springer:2 science:2 equation:3 work:3 theories:1 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solv-int9712010.txt |@word restriction:2 fieldtheoretical:1 manifold:2 dx:1 ϕj:1 obtain:1 roy:1 london:1 solutions:5 grateful:1 follow:1 itp:1 o:1 slow:2 depend:4 parameters:4 functional:1 aνµ:4 coordinates:1 quasi:1 systems:1 theorem:2 mail:1 analogous:3 local:1 possessing:1 dm:1 iν:1 means:1 ya:3 frequencies:1 sums:1 evolution:2 dokl:1 landau:1 sssr:1 ϕn:29 ϕi:1 ϕk:1 ϕjk:1 integer:1 dt:1 averaged:1 wiley:1 runs:1 dubrovin:5 necessary:2 hamiltonian:7 fields:1 arxiv:1 solution:1 δn:2 discrete:3 vector:1 hydrodynamic:1 integrals:2 contain:1 found:1 view:3 set:2 financial:1 ser:1 see:1 uspekhi:2 mat:3 was:1 ru:1 vol:4 nonlinear:2 sub:2 brackets:3 giving:1 sum:2 shall:3 transforms:1 research:1 written:1 nauk:3 formula:1 conditions:2 method:5 satisfy:1 foundation:1 attention:1 terms:3 linear:1 each:1 proc:1 here:2 expansion:1 references:1 solv:2 based:1 maltsev:4 properties:1 mokhov:1 institute:1 novikov:5 theorems:2 mǫ:2 ϕin:2 periodic:2 poisson:3 york:1 soc:1 there:1 convolution:1 family:3 variables:1 number:5 dimensional:1 modulated:2 done:1 relations:2 respect:2 use:1 described:1 commutative:1 support:1 contains:1 system:5 construct:1 defined:6 conservation:2 ph:3 type:2 theoretical:2 qνµ:2 function:3 corresponding:1 grant:2 form:4 under:1 new:1 whitham:6 russian:2 structures:3 akad:1 work:3 smooth:1 transformation:1 will:1 intas:2 aid:3 dec:1 procedure:3 proof:2 ac:1 int:2 averaging:5 dirac:1 regularity:1 ij:3 numbers:3 any:1 functions:4 author:1 qν:4 same:1 field:1 other:1 arguments:4 luke:1 φi:2 coincide:1 finite:7 used:1 description:1 ϕ1n:1 after:1 variant:3 different:1 flows:1 surv:1 generated:1 waves:1 phase:3 appear:1 no:1 into:1 space:1 analysis:1 bracket:6 fundamental:1 sets:2 appl:1 physics:1 laws:1
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solv-int9712011.txt |@word represent:1 consider:4 chain:10 results:2 four:4 mni:1 mnk:1 houches:1 expressions:4 gk:1 gi:1 inverse:2 const:1 tain:1 those:2 elliptic:3 under:2 tr0:2 case:24 r12:11 r13:2 straightforward:1 very:1 mn1:3 mn2:1 mn3:1 springer:1 focus:1 every:1 ui:1 matrices:14 condition:7 trk:5 hamiltonian:11 notes:1 sklyanin:5 guo:1 solution:8 t1:2 solved:1 math:2 indices:1 qism:4 mn:12 integrability:5 linear:1 spectral:4 nonlinear:1 contributions:1 section:7 kun:1 version:1 above:6 new:4 method:2 satisfy:1 exchange:2 respectively:6 component:2 here:9 understanding:1 les:1 china:4 ansatz:1 depend:1 sine:1 equations:51 change:1 obtained:2 remark:1 institute:2 study:1 studied:4 subcase:14 recently:1 periodic:4 permutation:1 useful:2 classification:1 nearest:1 analyzing:1 use:1 commun:1 chi:1 next:1 comparing:1 nucl:3 ψn:6 therefore:2 m2:2 theoretical:1 subcases:4 billey:1 operators:4 odinger:1 particular:1 cases:2 hold:4 must:1 account:1 ksn:14 integrating:2 equation:47 work:2 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solv-int9712012.txt |@word represent:2 consider:2 crucial:2 results:2 leads:1 eds:1 scalar:1 proposition:4 expressions:3 issues:1 whose:2 inverse:3 const:1 dickey:1 tr:10 ts:2 tl:4 tk:2 th:1 dressing:3 random:1 zhang:1 very:1 rise:2 negev:1 wave:1 corollary:3 matrices:3 gurion:1 wronskians:1 turns:1 t2:1 t1:4 discrete:1 commute:2 math:5 upper:1 wronskian:1 consistent:2 imply:1 further:2 remarkably:1 dψ1:1 zs:5 subscripts:2 employ:1 what:4 nonlinear:2 appear:3 chicago:2 giving:1 expressed:3 above:3 new:6 satisfy:3 exchange:1 respectively:4 component:1 here:1 address:1 sheva:1 equations:10 box:1 remark:3 institute:1 vectors:1 allows:1 action:5 suitable:1 schur:1 via:1 schief:1 derivatives:1 use:3 proceed:1 would:1 commun:3 recalling:2 finally:1 ψj:17 ψk:8 nucl:1 ψi:1 ψn:3 therefore:1 ψm:3 themselves:1 ψa:5 type:6 israel:1 duality:4 initial:3 operators:8 under:2 curvature:1 eξ:1 particular:2 iii:1 account:3 recall:1 equation:1 work:1 det:1 suggestive:1 ms:16 mr:2 following:10 dec:2 tau:4 give:1 allowed:1 orbits:1 verlag:1 information:1 b405:1 requirements:1 darboux:1 write:1 pure:1 ordinary:1 sato:1 product:2 mapping:2 lax:15 multiplication:1 choice:1 realized:1 short:2 whenever:1 ueno:1 explicit:4 st:1 provide:1 so:2 allow:1 representation:3 order:1 hierarchy:15 indeed:1 rubtsov:1 through:1 y1:2 y3:2 y2:2 its:4 takebe:2 derive:1 ln:32 interesting:1 ll:2 lk:1 lr:4 condition:1 jacobi:1 derivative:2 main:1 defining:1 non:2 skipped:1 acklund:2 processes:1 introduce:2 qr:3 they:1 now:7 yu:1 hierarchies:4 several:1 always:3 university:2 hamiltonian:1 2d:3 each:1 found:1 entirely:1 tˆ1:3 aratyn:1 subsystem:2 differential:16 series:2 energy:2 ef:6 related:2 isospectral:2 toda:3 our:2 eq:8 special:2 out:1 shown:1 matrix:2 space:1 res:1 squared:1 research:1 vector:1 mα:4 stud:1 mβ:1 ref:1 announced:1 tsarigradsko:1 diagonal:1 standard:5 definition:1 pairs:1 takasaki:1 times:2 counterpart:1 turn:3 consequence:1 qn:2 adjoint:5 first:7 already:1 symmetry:12 2dtl:5 instances:1 relations:1 directly:1 given:1 indicate:2 eqs:4 system:8 construct:1 their:2 1b:1 brevity:1 gives:1 commutativity:2 acquire:1 stress:1 part:5 coefficients:1 ben:1 double:8 iteration:1 integrability:1 collecting:1 symmetries:6 rewrite:2 generalization:2 exchanging:1 any:10 elsewhere:1 subsystems:1 rearranged:1 zero:1 sj:1 efs:18 able:1 note:1 potential:1 generalized:2 indexed:1 canonical:1 calculus:1 spectral:3 shall:1 object:1 systems:1 took:1 connected:1 letter:1 successive:1 pair:1 stands:1 soliton:1 orlov:2 later:1 flow:2 physica:1 traditional:1 proceedings:1 kp:29 exp:2 physics:3 notion:1 ambiguities:1 oevel:2 akhiezer:1 show:1 supported:2 notations:4 purely:2 relation:3 find:1 just:1 parameters:1 lemma:1 generators:1 integrable:4 do:2 dj:2 cheng:1 notation:1 de:1 db:16 dw:1 evolution:3 kadomtsev:1 determinants:1 densities:1 reintroducing:1 arxiv:1 fixed:2 discussing:1 bulgaria:1 set:9 exists:3 namely:2 w3:2 w2:6 dµ:1 satisfying:1 eigenfunctions:2 nuclear:2 between:3 approach:2 adv:1 wl:3 terms:9 shabat:1 attention:1 wk:33 wj:7 however:1 solv:4 both:2 last:3 taking:4 according:2 contract:1 connection:1 embedding:2 expression:1 simple:2 represented:1 ps:1 transformations:5 second:3 addition:1 int:5 beer:1 workshop:1 basic:1 pk:1 ph:2 ak:4 pl:1 define:3 generating:2 aj:1 corresponding:1 pacheva:1 denote:4 xiong:1 present:3 case:1 multi:3 appearance:1 will:9 bonora:1 site:6 obeying:1 reads:1 il:2 dual:2 different:1 φs:11 grant:1 generic:7 belong:1 φa:5 φj:8 φk:8 φl:5 independent:1 used:1 see:3 upon:1 flows:8 hand:2 parametrized:1 infinite:9 lower:1 petviashvili:1 well:2 sets:1 coordinate:1 possesses:1 usual:1 proposed:1 being:1 sofia:1 dφ1:1 obtain:2 rest:1 transforms:1 world:1 facts:1 nissimov:1 zakharov:1 parametrization:1 lattice:3 transformed:1 easy:1 mod:1 adj:15 transformation:1 eigenfunction:3 read:1 ψba:6 background:1 using:5 unique:2 enriquez:1 like:1 follows:5 yields:2 arbitrary:1 right:1 some:3 springer:1 deduce:1 b1:1 proofs:1 lead:1 prop:1 does:1 exposition:1 bg:1 ba:2 problems:1 bk:5 step:1 qnm:3 qnn:1 about:1 column:1 bgu:1 act:1 introduced:1 rev:1 presence:1 into:6 within:1 obtaining:2 nsf:1 suppl:1 down:1 appropriate:1 references:1 δk1:2 operator:19 additional:2 comparing:1 there:3 transform:1 accordingly:2 way:1 was:1 function:8 complete:1 form:12 sequel:1 triangular:2 construction:3 fg02:1 absent:1 made:1 applying:1 embedded:1 inhomogeneous:2 us:5 below:2 ui:1 similar:1 called:2 detailed:1 taylor:1 af:1 defined:4 certain:1 abstract:1 pseudodifferential:1 bulgarian:1 general:2 scientific:1 dλ:3 supersymmetric:2 formalism:1 commuting:1 constructed:1 reexpress:1 again:1 functions:4 nm:4 nn:1 variety:1 index:2 whereas:2 when:1 illinois:1 field:1 other:1 potsdam:1 fokas:1 department:3 models:1 symbol:3 describe:1 polynomials:1 important:1 a7:1 variable:1 sides:1 structure:2 kiev:1 ghost:25 implies:2 dψ:1 dφ:2 baker:1 pseudo:10 orbit:8 together:1 equivalently:2 original:5
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solv-int9712013.txt |@word secondly:1 partial:1 consider:5 global:12 results:2 four:4 eds:1 scalar:1 proposition:1 broader:1 go:1 follow:1 expressions:3 disk:2 turrittin:1 row:12 relationships:1 ℜw:1 inverse:24 calculate:1 eα:2 equivalence:6 uniqueness:8 does:1 those:3 determinations:3 under:19 analogous:1 drazin:1 norm:1 placed:1 p2:3 conjecture:4 outside:1 very:1 saskatchewan:1 wave:27 chooses:1 putting:1 should:1 mout:28 matrices:1 condition:2 leads:4 riemann:31 level:1 did:1 tex:1 integrating:1 t2:2 solution:11 t1:2 large:1 solved:3 vector:14 h11:10 small:3 gauge:2 hospitality:1 optics:1 h12:15 solutions:15 upper:2 wronskian:1 neighborhood:2 computation:2 zj:68 consistent:1 direct:1 cosh:5 approximation:1 zero:7 evaluated:1 further:2 zw:4 primes:1 substitute:1 linear:2 even:1 established:1 nonlinear:4 appear:2 invertible:1 section:4 expressed:3 consequent:1 uj:1 poles:14 above:8 deift:3 3b:1 3a:4 apply:1 method:6 satisfy:13 compact:2 pm0:1 evaluating:1 degree:1 respectively:6 l1:1 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solv-int9712014.txt |@word magnetic:1 desirable:1 four:7 rˆ:13 consists:4 whose:10 replacements:1 under:5 conjecture:1 rational:1 rise:2 summarized:2 affect:1 bringing:2 school:1 ref:11 solution:37 vector:26 math:17 indices:4 unifying:2 commented:1 force:9 specially:2 direct:5 elegant:3 second:29 follow:2 implemented:3 even:2 above:21 new:6 ˆj:1 coefficient:2 here:18 possibility:1 represented:4 path:1 auxiliary:45 interpret:1 obtained:11 study:4 stressed:1 symmetrical:2 suitable:2 changes:2 cancellation:2 classification:1 explained:4 a22:2 total:2 derivatives:1 would:9 negative:1 call:2 therefore:7 type:11 until:2 successful:1 brings:3 odinger:1 hole:7 must:1 springer:2 pursue:1 work:8 example:17 organized:1 reviewing:1 want:1 amplitudes:6 la1:3 la2:1 la3:1 end:6 provide:5 verify:5 enj:1 feature:6 far:4 lal:5 lai:12 laj:5 replacing:1 thermodynamic:1 after:18 demanding:2 lax:16 summarize:3 parallel:1 third:13 maintain:1 correlation:2 ohmann:3 stra:1 order:21 restriction:6 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solv-int9712015.txt |@word emile:1 consider:4 induces:1 leads:5 proposition:6 computation:2 expressions:2 gr:3 whose:1 ihes:1 depend:1 paris:1 show:3 tn:7 finally:1 edward:1 tj:2 tk:3 under:2 fay:2 string:1 dϕn:1 orthogonal:1 choice:1 every:3 fall:1 difference:5 matrices:4 deformations:3 annihilated:1 induction:1 t2:3 solution:10 t1:28 large:1 discrete:2 vector:6 louvain:2 upper:4 zn:1 wronskian:1 approximation:1 second:3 odd:1 khesin:3 theory:1 bilinear:8 stands:1 diag:3 ast:1 expressed:2 birkhoff:1 goes:3 view:2 new:1 equivalent:6 satisfy:3 full:4 simultaneously:1 component:2 strata:1 behaviour:1 groups:1 equations:8 aτ:1 obtained:1 shift:4 study:1 vectors:2 t21:5 fourier:2 schur:4 equivalence:1 useful:1 limq:1 wit:2 derivatives:1 asymptotic:1 usa:2 prove:2 contains:1 ψj:1 ψk:1 ψi:4 ψn:11 therefore:7 type:2 operators:17 ti:32 eν:1 flag:1 particular:5 known:1 foundations:1 hold:1 iii:5 circle:1 must:4 obeying:1 isomorphism:7 world:1 science:2 equation:7 work:1 det:2 reviews:1 modify:1 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solv-int9712018.txt |@word gt:1 partial:1 consider:1 gx:1 leads:1 proposition:10 edu:1 inverse:2 depend:1 turkish:1 graph:1 tt:5 tr:1 nonlocal:3 tn:1 uniqueness:1 under:2 p2:13 straightforward:2 very:1 ankara:1 matrices:1 condition:19 harmonicity:1 solves:1 t2:1 solution:1 t0:1 t1:1 indices:1 der:1 grundlehren:1 b22:1 b21:1 cosh:2 integrability:6 htt:1 bilkent:2 htx:1 spectral:2 established:1 nonlinear:1 expressed:1 above:5 new:3 satisfy:1 gµ:5 degree:2 respectively:1 here:4 sinh:2 xβ:1 xα:3 equations:6 nachr:1 obtained:2 remark:1 antisymmetric:1 technical:1 studied:2 suitable:1 total:1 derivatives:3 takes:1 would:2 covariant:1 finally:1 linear:2 m3:1 more:2 flat:2 becomes:2 dxµ:1 curvature:1 berlin:1 iia:1 particular:1 known:1 cases:2 nutku:1 springer:1 science:1 equation:25 work:2 det:4 dx2:3 ere:7 following:7 dec:1 example:1 give:5 monge:6 council:1 sense:1 verlag:1 provide:1 differentiability:1 write:1 maps:2 nontrivial:1 instead:2 parameter:3 may:8 mapping:1 levi:1 lax:9 faculty:1 law:1 heidelberg:1 imply:2 so:1 order:1 developed:1 satisfied:1 paper:1 2v:1 mentioned:2 satisfies:4 urses:3 before:1 sciences:1 ln:2 interesting:1 coordinates:1 forms:1 defining:1 non:1 mention:2 now:2 2t:4 2u:1 february:1 university:1 classified:1 2x:4 each:1 2m:1 2h:1 differential:3 hard:1 gaussian:1 related:1 investigated:1 eq:2 special:2 shown:1 matrix:6 space:4 since:1 research:1 math:3 theory:1 standard:1 base:1 members:1 pairs:1 language:1 r3:4 geometry:1 conformally:1 ds2:4 hence:4 first:2 xn:1 variables:1 prenticehall:1 xx:5 heinz:1 another:1 xt:2 given:13 minimality:17 obtainable:2 construct:1 their:1 1g:1 dt2:3 academy:1 part:1 x2:1 x0:1 x1:1 representing:1 covariantly:1 target:1 second:3 intersting:1 were:1 result:1 symmetries:1 curves:1 any:1 lie:1 mappings:1 k2:2 klasse:1 gα:5 shall:3 metrics:1 but:1 pair:7 class:1 xµ:1 soliton:1 considered:1 carmo:1 physics:2 laws:8 show:1 supported:1 relation:1 solutions:4 civita:1 trivial:1 find:4 q2:1 enough:2 analytic:1 only:1 explicitly:1 integrable:4 local:3 do:1 notation:1 ones:1 dz:1 dx:7 dv:1 dt:3 ds:2 approach:1 arxiv:1 hyperbolic:3 riemannian:2 mongeamp:1 w2:2 surfaces:10 satisfying:1 tensor:7 its:3 symmetric:1 written:3 between:4 boundary:1 conditions:4 email:1 importance:1 solv:1 both:1 cos:1 many:3 jersey:1 conclude:1 harmonic:6 dimensional:8 simply:1 respect:6 turkey:2 pq:3 transformations:3 addition:1 three:3 been:2 defined:2 kronecker:1 expected:1 define:2 6a:1 direction:1 arises:1 corresponding:1 hildebrandt:1 quantities:1 understand:1 manifolds:1 case:4 sampson:1 expanded:1 existance:1 choices:1 will:1 euclidean:2 du2:1 property:1 metric:10 dxν:1 surface:9 wissenschaften:1 same:3 hxx:1 higher:2 independent:1 zumino:1 used:3 trivially:1 upon:1 possible:2 eells:1 identity:1 recent:1 lower:1 well:1 solve:1 components:3 model:6 manifold:1 infeld:1 karasu:1 correspondance:5 using:4 letting:2 infinitely:2 tubitak:1 parametrization:1 interested:1 lett:1 transformation:7 identical:1 easily:1 term:1 background:1 amp:6 mod:1 like:2 follows:2 either:1 integrals:1 arbitrary:1 works:1 mathematical:1 acad:1 old:1 classical:1 some:5 born:1 examples:1 b2:2 provided:1 describing:1 dimensions:1 tuba:1 2xt:1 minimal:12 scientific:1 annal:1 equivalent:2 illustration:1 mokhov:1 eqns:1 o:2 nonvanishing:1 fen:1 a2:4 automatically:1 letters:1 hermitian:1 references:1 wess:1 there:2 conservation:8 way:4 function:13 transformable:1 hx:1 journ:1 form:1 ht:1 delta:1 partially:1 embedded:3 minkowski:1 us:1 backlund:8 similar:1 called:1 detailed:1 constant:2 int:2 certain:2 abstract:1 am:1 determinant:2 general:1 ottingen:1 defines:1 functions:8 differentiable:5 no:1 detail:1 field:3 other:1 b12:1 b11:1 department:1 mathematics:2 mathem:1 operators:1 a11:1 models:3 symbol:1 a1:1 important:1 implies:2 assume:2 sigma:9 unster:1 original:1
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solv-int9712019.txt |@word secondly:1 consider:14 rx:5 global:1 obstruction:1 scalar:1 gk:2 preserves:8 const:11 obstructions:1 quadruple:1 tl:7 does:1 manifolds:2 under:1 pˆy:7 pˆx:3 norm:1 izv:2 orthogonal:2 dokl:1 corollary:1 every:4 condition:1 hamiltonian:3 vector:14 neighborhood:2 sign:1 zero:2 tangential:1 even:1 will:1 compactum:1 giving:1 ˆy:5 axes:1 supplied:1 uniform:1 ˆb:2 ˆh:1 satisfy:1 respectively:1 canonically:2 tangent:3 along:9 z0:8 z1:2 remark:1 shift:3 vectors:5 allows:1 contradiction:3 yˆ:23 periodic:2 action:15 changes:2 projection:1 classification:1 replace:1 use:1 takes:3 would:1 prove:11 positive:8 bundles:1 vol:5 m1:2 therefore:12 m2:2 more:1 fractions:1 kozlov:1 everywhere:1 particular:1 known:3 cases:2 valued:1 vladimir:1 sphere:2 recall:2 det:1 mechanic:1 following:4 dec:1 def:10 proof:8 zametki:2 f1:2 triple:5 give:2 contradicts:1 numbers:3 degenerate:1 evidently:2 axis:5 notation:1 s1:14 acts:7 xˆ:5 how:1 nontrivial:1 pure:2 sin:5 product:1 description:3 fx:1 fy:1 singularities:1 mapping:3 plane:9 ff:1 fh:1 fk:2 parallel:3 constants:2 natural:2 lemmas:1 lines:1 element:4 diffeomorphism:5 fundamental:2 sl:10 representation:1 operations:1 indeed:1 paper:1 thesis:2 group:11 zˆ:5 tori:1 coordinates:13 actually:2 systems:1 derivative:1 non:8 auto:1 geodesic:32 yx:1 they:2 finite:1 tonian:1 university:2 iff:5 2b:3 each:1 babenko:1 directing:2 our:1 operation:1 mat:3 nonorientable:1 matrix:4 space:2 since:19 induces:2 may:2 rational:1 formula:19 fomenko:1 induced:1 independence:1 linear:9 free:2 standard:4 admits:3 completely:2 bolsinov:1 definition:6 taimanov:1 r2:31 could:1 ds2:1 hence:6 quadratically:20 first:5 physik:1 slipped:2 xb:1 variables:2 number:6 xy:1 impossible:1 given:15 introduction:1 top:1 system:7 construct:1 assumption:1 gives:1 isomorphic:1 moscow:2 akad:3 part:1 x2:1 dx2:13 specify:2 see:14 project:1 fˆ:6 were:3 bs1:1 need:1 any:7 oriented:5 k2:2 k1:2 circles:1 goryachev:1 shall:6 connected:2 pair:1 kb:1 considered:1 clear:3 flow:21 kl:2 points:1 reflections:1 subgroup:2 show:3 substituting:1 chaplygin:1 parameters:1 kovalevskaya:1 topological:3 lemma:8 only:2 generators:1 geodesics:1 factor:2 integrable:30 klein:14 df:1 de:1 words:1 dy:13 aλ:4 λyy:5 covering:9 arxiv:1 nauk:3 bab:1 homeomorphic:2 riemannian:1 body:1 set:8 ser:1 exists:13 differentials:1 depends:2 close:1 surfaces:3 nondegenerate:1 state:2 closed:2 between:1 preserve:2 triples:3 matveev:2 nu1:1 solv:1 p2y:1 p2x:6 cos:5 last:1 freely:1 equal:6 admit:2 uni:1 genus:1 co:3 point:3 simple:2 period:2 dimensional:1 polynomial:2 constant:13 pp:4 described:5 second:2 aˆ:2 px:17 py:18 describes:1 ph:2 abstract:1 describe:3 formed:1 angles:2 c1:2 c0:16 dh:2 present:1 case:2 aim:1 suppose:10 momentum:1 conformal:1 iy:3 va:1 orientation:2 almost:1 metric:56 thus:6 surface:4 dual:1 ib:1 different:1 suggest:1 same:2 shifts:9 complex:8 several:1 composition:2 independent:3 trajectories:2 flows:18 v1:3 v2:3 correspondent:4 reflection:7 sssr:3 without:1 bottle:14 coordinate:7 left:1 abab:2 obtain:3 bremen:1 torus:20 identify:1 integer:4 momenta:8 functionally:2 λxx:5 λxy:3 rigid:1 z02:1 easy:2 theorem:12 euler:1 real:1 using:5 mod:2 like:1 follows:1 velocities:1 either:2 integrals:1 arbitrary:1 iˆb:1 polynom:1 isometrically:1 slipping:4 critical:1 ba:1 equivalent:4 imaginary:1 integers:1 dˆ:2 theorems:1 generated:6 act:4 integral:21 functional:1 appropriate:13 references:1 matrixes:3 additional:1 there:15 u1:7 u2:7 quadratic:5 was:2 iˆ:1 function:18 hx:1 hy:1 complete:1 converse:4 but:1 volume:1 russian:3 coefficients:2 characteristic:1 smooth:9 us:7 liouville:12 coverings:2 ug:2 ua:1 called:7 ab:1 proved:10 b2:6 int:1 universal:2 specified:3 covers:1 denote:8 exist:1 ay:2 ax:2 az:1 functions:12 hpx:1 integrability:2 no:1 nc:1 cˆ:4 field:2 other:2 briefly:1 elements:4 reiφ:1 bounded:8 variable:2 structure:1 implies:1 assume:4 pseudo:4 n1:2 n2:3 n5:1 n6:1
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solv-int9712020.txt |@word lakshmanan:1 help:1 pointing:1 supported:1 obtain:2 rest:1 discovered:2 already:1 transforms:1 grateful:1 signs:1 mentioned:1 existence:2 scattering:1 find:1 row:1 q1:5 τo:2 q2:5 based:2 parameters:8 k2:17 ln:4 dr:1 4i:1 shifts:1 th:1 under:2 integrable:1 fundamental:1 transformation:4 division:1 cos2:2 belarus:3 notations:1 means:1 polarizations:1 analitically:1 possible:1 introduce:1 yang:1 electron:1 novel:1 invert:1 moreover:1 condition:1 easily:1 riemann:2 ref:4 arxiv:1 solution:4 sin:1 vector:6 mode:1 arbitrary:1 analytical:1 found:3 fixed:1 out:1 2i:1 solutions:2 arrival:1 takayuki:1 set:1 zh:1 significantly:1 const:1 there:2 easy:1 some:2 idea:1 cosh:1 intensity:1 elements:1 2ξn:1 arg:1 close:1 menyuk:1 eq:3 theory:1 sinα:1 instance:1 shown:2 nonlinear:3 describing:1 give:1 ieee:1 rev:2 below:3 research:1 collisions:1 state:3 envelopes:1 eksp:1 denoted:1 theta:6 before:2 approach:2 math:1 satisfy:1 foundation:1 fiber:1 recently:1 amplitude:1 retrieved:1 equivalent:3 each:1 component:2 use:2 here:1 quite:1 admits:1 completely:1 derive:1 expansion:1 references:1 solv:1 eiψ:1 along:1 jetp:1 equations:4 hilbert:2 verify:1 cos:2 valery:1 quant:1 column:1 many:1 studied:1 o:4 ql:1 fiz:1 minsk:1 plus:1 retarded:1 conveniently:1 referred:1 eqs:4 numerical:1 first:1 exhibit:1 twodimensional:1 author:1 classification:1 simple:1 ηj:1 due:2 put:1 hermitian:1 misprint:1 eiφl:1 another:1 sov:1 associated:1 hietarinta:1 logic:1 given:4 perturbation:1 asymptotic:1 leads:2 prove:1 manakov:14 teor:1 top:1 initial:2 iq1:1 system:10 iq2:1 defined:1 difference:1 therefore:1 way:1 2iη:1 was:5 define:1 complete:4 θl:3 transposed:1 relevant:1 solitons:12 eiφ2:1 exactly:1 odinger:2 but:1 contract:1 correspondingly:3 normalized:2 cosα:1 consult:1 technologies:1 denote:1 case:1 distance:1 polarized:1 type:1 work:1 radhakrishnan:1 us:3 alter:1 will:4 while:1 values:2 str:1 interaction:1 following:3 problem:2 dec:1 derived:1 minus:1 regimes:1 detailed:1 proved:1 coupled:2 int:1 characteristics:1 abstract:1 describe:2 general:3 states:1 collision:8 reads:2 governed:1 simulations:1 regime:3 information:1 angle:1 form:1 fibers:1 allow:1 when:2 arctan:2 polarization:13 sciences:1 k1:24 other:1 republic:1 academy:1 finite:1 φl:1 switching:8 formulas:2 used:1 description:1 iφ2:1 after:1 problems:1 phases:1 factored:1 prepared:2 eiφ1:1 ξj:1 importantly:1 additionally:1 representation:1 phase:4 representations:1 colliding:1 analytically:2 model:1 identity:1 matrix:1 soliton:18 schr:2 modes:1 acknowledgement:1 kj:1 parameter:1 no:1 well:1 analysis:2 optical:2 iψ:1 exp:7 time:2 velocity:1 iφ1:1 original:1 fact:4 tsuchida:1
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solv-int9801001.txt |@word 2m2:1 consider:4 funct:1 rev:2 particular:4 concern:1 results:14 subscripts:2 four:1 scalar:1 proposition:47 grateful:1 follow:2 expressions:6 lk:12 issues:1 soc:3 devoted:2 whose:2 λii:1 inverse:14 mutatis:1 tr:1 spec:1 γj:4 finally:2 does:1 tj:1 petersburg:1 under:2 mutandis:1 analogous:6 include:1 eichhorn:1 worth:1 norm:1 case:2 global:1 proved:3 rb:16 straightforward:1 very:4 edn:2 rise:1 cjk:3 dokl:1 wave:1 enn:7 corollary:10 p1:4 lnt:2 summarized:1 li:7 1s:6 matrices:14 deformations:2 condition:11 χd:10 generalised:1 entire:1 beginning:1 riemann:5 solves:10 level:1 evaluation:1 notes:2 differentiating:1 solution:47 fewer:1 ri:3 large:2 discrete:6 convenience:1 small:10 eigenvalues:6 anal:2 optics:2 noted:1 degeneracy:1 upper:7 abbreviated:1 expanded:1 tem:1 zd:17 takhtajan:1 consistent:1 sin2:4 direct:4 pulse:7 cosh:4 jump:13 rate:1 design:1 tangential:1 gn:94 chen:1 further:1 substitute:1 theory:7 even:4 intimately:1 nonlinear:29 discus:1 diag:2 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solv-int9801002.txt |@word represent:1 partial:1 consider:1 remarkable:1 results:1 invent:1 four:4 eds:1 pearce:1 generalize:4 follow:1 gl:1 gj:1 causes:1 inverse:2 sogo:1 elliptic:1 under:10 geom:2 multilinear:1 γf:2 string:1 g1:6 very:1 differently:1 wave:6 every:2 difference:10 matrices:1 condition:5 turns:4 solution:7 large:2 discrete:4 convenience:1 manifestly:2 gauge:11 58a:1 sign:1 sergeev:1 integrability:1 further:1 bilinear:8 what:1 nonlinear:11 plays:2 section:3 expressed:1 version:2 above:1 kyoto:1 new:8 ˆj:4 method:4 contrast:1 satisfy:6 ibid:2 exchange:5 respectively:2 here:1 behaviour:1 ansatz:1 others:1 represented:2 along:1 sine:1 equations:36 appears:2 obtained:2 convert:1 shift:3 study:1 vectors:2 permutation:1 changes:1 sci:1 via:2 claim:1 pinkall:1 highly:3 santini:2 korepanov:2 univ:1 derivatives:1 covariant:1 jpn:7 examined:1 next:1 call:5 therefore:2 iteratively:1 type:1 bethe:1 becomes:1 operators:2 particular:1 known:1 must:5 ramani:2 tokyo:2 equation:26 work:1 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solv-int9801003.txt |@word consider:2 four:1 ηi1:7 go:2 gn:2 devoted:1 inverse:1 tz:6 schiff:9 tx:3 iii:2 tt:2 technique:2 ts:2 program:1 kη:1 multilinear:2 worth:1 applied:1 song:2 very:1 ηin:1 connects:1 wave:4 trouble:1 exact:5 condition:6 duffy:2 leads:1 solution:33 differential:1 math:4 λi1:4 shows:3 enforce:1 wronskian:7 direct:9 integrability:2 further:1 odd:1 bilinear:12 plays:1 d2:1 expressed:3 fuchssteiner:1 above:3 new:9 method:12 nakamura:3 full:1 degree:4 respectively:2 eλ2:1 here:6 cylindrical:2 operating:1 ansatz:1 strong:4 equations:10 appears:1 z2:8 λin:4 obtained:5 sending:1 search:1 institute:1 shift:1 study:2 studied:1 allows:1 p2:22 resonance:4 adopting:1 mz:4 der:1 involves:1 captions:1 extra:1 substitution:3 plenum:1 summation:2 should:1 ψz:2 derivatives:3 conventional:3 proceed:2 would:1 prove:2 contains:1 single:1 suppl:1 ψt:2 next:1 depicted:1 noting:1 call:1 therefore:2 m2:1 taken:1 more:1 introducing:1 solitons:7 operators:2 curvature:1 particular:1 cases:2 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solv-int9801004.txt |@word represent:3 soliton:1 partial:1 consider:23 chain:8 magnetic:3 results:14 leads:1 scalar:2 disappears:2 generalize:1 go:2 expressions:16 nl:2 inverse:1 depend:11 calculate:8 zone:1 bogoliubov:1 iii:1 technique:2 tr:15 finally:5 petersburg:2 excluded:2 under:9 analogous:1 presentation:1 worth:1 degeneration:1 p2:1 belonging:1 g2:9 g1:29 orthogonal:1 dq:4 account:8 limiting:1 wave:8 formula:3 difference:3 matrices:40 qqn:2 eit:3 obvious:3 riemann:1 hamiltonian:10 die:1 solution:2 mpa:1 large:2 solved:2 vector:3 eigenvalues:5 tognetti:2 noted:2 degeneracy:1 zn:13 zj:2 d3:1 onecomponent:1 zb:1 sign:2 fold:1 second:6 tildes:1 masson:1 correlator:4 further:4 dynamics:1 zp:2 gm:6 zr:9 canonical:4 even:2 will:13 what:6 nonlinear:1 appear:1 sum:28 symmetric:3 poles:1 above:10 zrn:6 zrm:1 increasing:1 method:3 filled:2 satisfy:4 simultaneously:1 eikj:1 expand:1 d1:1 respectively:4 component:19 eika:3 quasimomenta:18 desired:1 ansatz:6 represented:7 strong:3 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solv-int9801005.txt |@word represent:1 sco:1 allowed:1 consider:5 chain:2 rod:2 results:1 invent:1 gx:1 skii:1 commute:1 entropy:1 computation:1 go:1 sci:1 iu2:1 regularize:1 whose:2 preserves:1 inverse:3 remarkable:1 zreg:2 quasi:1 critical:1 elliptic:3 under:4 dxdx:1 include:3 worth:2 applied:2 belonging:1 string:6 orthogonal:1 very:4 choice:2 me:4 wishes:1 affect:1 exact:2 condition:18 presented:1 ref:4 t5:1 t2:4 t3:4 t1:4 large:3 convenience:1 vector:8 ndimensional:1 gauge:2 noted:3 configurations:3 concluded:2 upper:3 force:4 occurrence:1 dealing:1 measurable:1 discriminated:1 painlev:1 value:7 pass:1 further:1 dynamics:3 estimated:1 linear:1 even:9 nonlinear:5 appear:7 t2n:9 section:1 expressed:5 find:2 current:1 version:1 above:1 boundary:3 new:5 method:5 codimension:2 satisfy:1 compact:1 respectively:1 here:9 tangent:1 expansion:2 represented:3 path:6 along:3 observing:1 appears:4 change:2 obtained:2 sending:2 remark:1 covers:1 study:1 stretching:14 isotopy:2 later:2 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solv-int9801006.txt |@word represent:1 sci:1 consider:5 remarkable:1 rev:4 rod:1 mnv:7 four:3 eds:1 generalize:1 grateful:1 parameterization:3 disk:1 compact:3 whose:2 inverse:3 languages:1 γi:3 critical:1 squeezing:4 under:1 tr2:7 applied:2 conjecture:3 confirmation:1 jensen:4 r10:1 very:1 dokl:1 geometrical:4 matrices:3 condition:2 notations:2 tokyo:2 did:2 turns:1 classical:2 solution:2 t0:11 large:1 convenience:1 vector:4 dealt:2 indices:4 gauge:1 noted:1 configurations:1 neighborhood:7 ga:2 ten:1 iγi:1 japanese:1 second:3 tangential:1 further:6 dynamics:2 linear:1 even:2 index:3 nonlinear:3 appear:1 trivial:9 section:6 expressed:10 current:1 paying:1 expresses:1 ground:2 method:1 thin:3 polyakov:3 component:1 here:5 canonically:1 objects:1 tangent:4 represented:2 path:1 along:4 equations:1 appears:2 interpret:2 obtained:9 sending:2 my:9 vectors:3 later:1 periodic:1 loop:1 real:2 koppe:1 studies:3 langer:1 uniquely:1 useful:1 divide:1 extra:2 hermite:2 ls:3 pf1:1 pf2:1 univ:1 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