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solv-int9707012.txt |@word consider:1 results:2 invent:1 extensively:1 gd:4 inverse:1 dickey:5 th:1 te:1 case:3 conjecture:1 very:1 vastly:2 school:1 hamiltonian:5 leave:1 lˆ:14 consistent:1 second:9 44d:1 residue:1 established:1 plays:1 stands:1 brackets:4 above:2 new:1 respectively:2 realizations:2 here:4 understanding:1 china:2 free:2 along:1 equations:2 remark:1 studied:1 poisson:10 changes:1 via:1 projection:1 replace:1 use:1 would:1 prove:2 next:1 nucl:1 taken:1 type:2 more:2 sort:1 operators:1 odinger:1 known:2 cases:2 science:1 equation:4 modified:4 following:10 example:2 proof:7 beijing:2 wˆi:1 give:1 calculation:1 sokolov:2 states:1 b405:1 provide:1 get:1 write:1 maps:2 map:6 mas:1 algebra:3 may:2 δvi:2 wˆ1:1 revealed:1 short:2 natural:2 third:2 lemmas:1 attracts:1 rather:3 so:3 hierarchy:10 indeed:2 satisfied:1 course:1 paper:3 its:6 thank:1 interesting:1 coordinates:2 better:1 absence:1 systems:4 into:1 combination:1 now:3 dirac:1 university:1 side:1 arxiv:1 energy:1 related:2 our:4 special:1 shown:2 matrix:3 gradient:1 res:38 since:2 denotes:1 geom:1 induced:2 math:12 foundation:1 theory:3 w1x:1 ısica:1 departamento:1 standard:1 ramos:1 complicated:5 publ:1 turn:1 int:2 universidad:1 lax:6 first:2 initial:1 miura:11 given:2 ian:1 system:1 construct:1 structures:1 cite:1 gives:1 para:1 completed:1 serve:1 kupershmidt:6 completes:1 were:2 dtq:2 need:1 constrained:5 any:2 lie:2 wilson:4 liu:5 generalized:3 kac:1 shall:1 nothing:1 soliton:2 considered:3 physica:2 kp:4 usual:1 physics:1 notion:2 oevel:4 show:1 supported:1 relation:1 substituting:1 find:1 lemma:9 only:2 inherited:1 integrable:2 boris:1 v1x:1 cheng:1 viewpoint:2 means:1 dependent:1 familiar:1 de:2 v1t:1 aim:2 dz:1 dx:20 fields:1 differential:1 factorization:2 espa:1 national:1 see:4 w2:2 w1:2 w0:2 tensor:5 importance:1 various:1 between:4 recently:1 rims:1 initially:1 wn:3 attention:2 however:1 wi:1 bilal:1 huang:1 solv:1 tensors:1 essentially:1 last:2 many:1 taking:1 according:1 etc:1 context:1 expression:2 relevant:2 v2t:1 simple:3 v2x:2 mkdv:1 due:1 been:1 ai:5 reduction:4 much:1 interest:1 pi:1 define:4 direction:1 corresponding:2 convert:1 xiong:3 spain:2 p2:4 p1:3 easier:1 will:2 while:1 orica:1 bonora:2 played:1 thus:3 vn:3 reads:1 mod:1 verified:1 shaw:1 things:1 make:1 same:1 modification:2 hierarchies:1 several:1 development:1 used:1 hand:1 v0:2 v1:5 v2:6 identity:1 schr:1 well:1 concrete:1 δwi:11 soviet:1 left:1 gelfand:3 just:1 yen:1 obtain:2 rest:1 feher:1 formulated:1 drinfeld:2 world:1 resa:1 previous:1 point:1 transformed:2 lett:6 easy:1 theorem:11 moody:1 transformation:4 know:1 using:3 apart:1 modifications:1 like:1 δl:75 steps:1 δh:22 δf:46 δg:31 mathematical:1 madrid:1 kdv:2 integration:1 comments:1 provides:1 scientific:1 kyoto:1 bi:1 fordy:1 simpler:2 commun:8 konopelchenko:1 introduced:1 marshall:3 down:1 2v2:5 2v1:1 en:1 references:2 operator:10 algebras:3 there:2 u0:1 mkp:3 complete:1 form:2 hq:1 jul:1 made:1 us:4 harnad:1 un:1 problem:1 similar:2 called:2 associated:4 defined:3 abstract:1 ciated:1 general:2 pˆ:3 bracket:9 na:1 graduate:1 field:2 interested:2 role:2 conclude:1 complutense:1 models:1 problems:1 a0:2 important:1 a8:1 structure:4 acknowledgment:1 implies:1 assume:1 pseudo:1 remarked:1
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solv-int9707013.txt |@word forger:2 consider:2 chain:1 depends:1 caused:1 global:1 results:7 gg:3 montr:3 consists:1 follow:1 vega:3 gl:3 contributions:3 sch:3 whose:4 supposedly:1 inverse:1 number:1 calculate:1 paris:1 technique:1 tr:2 nonlocal:2 shall:3 charge:5 does:5 those:4 th:2 under:3 worth:1 chirally:1 conjecture:1 far:1 dokl:2 witten:1 surprise:1 difference:2 matrices:1 deformations:2 condition:1 leads:2 level:2 did:1 issue:1 solution:3 integro:1 announced:1 guiding:1 recall:3 referred:1 unexpected:1 neighborhood:1 b281:1 mussardo:1 b137:1 integrability:2 b135:1 qmn:4 further:2 dynamics:1 theory:4 established:1 what:1 nonlinear:1 invertible:1 brackets:11 section:8 maillet:3 current:14 infinitesimal:1 above:3 new:5 method:3 satisfy:4 edited:1 full:1 simultaneously:1 behavior:1 ibid:1 ggr:1 divergence:1 neveu:1 here:3 understanding:2 reported:1 b269:1 them:1 ansatz:6 standard:2 appears:1 change:2 contraction:1 instituto:1 spite:1 involved:2 study:4 studied:3 exemplifies:1 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solv-int9707014.txt |@word consider:3 results:1 invent:1 gd:11 edu:1 factorizing:1 inverse:3 tw:1 show:3 finally:1 δhk:2 th:2 under:7 applied:1 very:1 corollary:1 hamiltonian:10 turns:1 proposition:5 nthu:1 francesco:1 elegant:1 second:15 what:1 brackets:3 sum:2 expressed:1 above:1 acknowledgments:1 satisfy:1 explore:1 china:3 address:1 equations:4 change:1 obtained:2 studied:2 resulting:1 poisson:15 chang:2 tasks:1 would:2 commun:5 comparing:1 ψi:1 therefore:2 becomes:4 particular:1 cases:1 science:1 work:1 modified:6 following:3 example:3 proof:5 want:1 give:1 δv1:1 council:1 provide:1 verify:1 maps:1 pure:3 map:1 mas:1 blocks:1 algebra:2 after:2 mapping:2 δvn:2 lax:11 tsing:1 third:5 order:1 typical:1 hierarchy:14 satisfies:1 still:2 its:2 symmetry:1 ln:26 interesting:2 li:15 systems:3 main:1 auto:1 acklund:2 now:4 yu:1 discuss:2 february:1 university:2 l2:1 l1:7 pacheva:1 arxiv:1 ed:1 related:1 our:1 out:1 respects:1 shown:3 space:1 res:35 conjectured:1 lecture:1 math:10 linear:4 free:1 standard:1 admits:1 ramos:1 besides:1 int:2 δij:6 chiao:1 hence:4 first:2 manuscript:2 miura:7 variables:3 clear:1 simplified:3 aratyn:1 another:1 given:1 statement:2 realization:2 scheme:2 unpublished:1 gives:1 hua:1 kupershmidt:2 kind:1 future:1 ming:1 need:1 constrained:5 hsien:1 wilson:2 petviashvili:1 note:3 liu:5 generalized:4 added:1 simplify:2 but:1 letter:3 nothing:1 soliton:1 especially:1 professor:1 kn:19 kp:6 kw:2 ckp:1 physics:1 fact:1 oevel:2 dickey:6 reductions:1 supported:1 substituting:1 inspiring:1 based:1 knowledge:1 yen:1 only:2 explicitly:1 integrable:2 hope:1 cheng:1 di:1 de:1 dr:1 schoutens:1 kadomtsev:1 differential:7 factorization:9 summary:1 mapped:2 tu2:1 see:1 w2:1 w1:3 discussions:1 terms:8 nonstandard:1 best:1 functionals:1 hsinchu:2 reading:1 email:1 recently:1 wn:6 however:2 wi:10 wj:3 concentrate:1 huang:2 solv:2 δai:15 thank:1 last:1 many:1 etc:2 expression:2 relevant:1 simple:3 polynomial:1 respect:2 bouwknegt:1 transformations:2 been:6 defined:2 reduction:1 much:2 treat:1 basic:1 algebras:4 inv:1 corresponding:2 itzykson:1 xiong:2 present:1 case:2 transformation:6 will:5 property:3 conformal:1 bonora:2 played:1 vi:2 thus:3 vn:5 tu:2 containing:2 shaw:2 grant:1 modification:1 φi:1 hierarchies:2 several:1 singapore:2 v1:4 v2:2 purpose:1 tung:1 knk:2 well:1 δwi:13 gelfand:2 just:1 less:1 obtain:1 via:1 thanks:1 taiwan:2 nissimov:1 preprint:3 transformed:1 lett:4 theorem:3 usage:1 republic:3 remaining:1 lacking:2 world:2 like:2 follows:2 δl:16 korteweg:1 δk:1 δf:52 δg:37 zuber:1 classical:2 δbj:15 b1:7 kdv:3 provides:1 yields:1 prob:1 demonstrated:1 scientific:2 bm:7 each:1 bi:3 bj:14 substituted:1 although:1 properties:1 simpler:2 about:1 compatible:1 into:5 nsc:1 appropriate:1 because:1 references:1 δun:2 operator:19 amazingly:1 there:1 u1:5 u2:3 mkp:1 was:2 δln:23 form:4 δkn:9 δu1:1 jul:1 hk:1 encoded:1 line:1 true:1 adler:1 us:1 un:3 ui:2 submitting:1 problem:1 piece:1 similar:1 called:4 associated:5 ai:12 abstract:1 aj:2 general:3 constructed:2 national:3 no:1 field:1 bracket:6 role:1 department:2 mathematics:1 a1:7 important:1 structure:26 conclusive:1 building:1 implies:2 factorized:2 vries:1 pseudo:1
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solv-int9707015.txt |@word consider:1 schwartz:1 less:1 indeed:2 over:1 supported:1 vanishes:1 elimination:1 relation:3 solutions:2 correspondences:2 july:1 chasles:2 note:1 weierstrass:2 const:1 chosen:1 cux:1 jan:1 simple:1 only:3 valid:1 coefficients:1 easy:1 theorem:3 derivative:1 analogous:1 solvable:1 transformation:3 euler:3 discriminants:1 correspondence:2 g3:4 g2:5 depends:1 was:1 acklund:3 connects:1 dokl:1 sssr:1 cannot:1 integrable:2 they:1 lattices:1 unique:1 groups:1 loss:1 evolution:1 kadomtsev:1 cvx:1 irreducible:1 differential:2 solution:1 remind:1 exhausted:1 nauk:2 yields:1 each:2 permutability:1 noted:2 function:1 arxiv:1 exists:1 related:1 see:2 mat:2 acad:1 uspekhi:1 kdv:3 out:1 birational:1 g22:1 nondegenerate:2 distinctive:1 µv:1 its:2 symmetric:1 written:1 does:1 connecting:1 above:2 between:1 formula:3 contrast:1 linear:1 degree:1 equivalent:1 arbitrary:3 veselov:1 standard:1 bt:9 dx:1 substitution:2 solv:1 equations:6 change:2 wx:2 obtained:2 admits:1 about:1 fibering:1 trinomial:1 constraint:3 novikov:3 study:1 called:1 compatible:1 fiz:1 connection:1 nothing:1 evident:1 hence:1 imrn:1 fractional:1 first:1 shabat:1 uvw:2 appeared:1 explained:1 transformations:1 reducible:1 xx:1 grants:1 references:1 representations:1 polynomial:4 respect:1 should:2 derivatives:1 given:1 takes:1 addition:1 teor:1 question:1 uw:1 relations:1 substitutions:3 their:1 accordingly:2 quadratic:1 type:2 possible:2 gives:1 zeroes:2 holomorphic:1 commutativity:1 arises:1 corresponding:1 elliptic:1 form:5 both:1 under:1 but:2 gap:1 correspondingly:1 virtue:1 particular:1 known:1 cases:3 2vx:1 than:1 vxxx:1 case:2 ux:3 adler:2 ut:1 equation:8 uv:3 up:1 us:1 krichever:3 h2u:1 while:1 values:1 assume:1 intas:1 shift:1 demonstrate:1 property:2 example:1 multivalued:1 u2xx:1 impedes:1 constant:1 generality:1 int:1 coincides:1 vw:2 sokolov:1 curves:2 2ux:1 itself:3 vt:1 vu:1 turns:1 vx:3 formally:1 dynamics:1 uxxx:1 k0:4 defines:2 rfbr:1 different:1 petviashvili:1 no:1 rather:1 feature:1 same:1 k3:2 k2:2 k1:4 other:5 take:1 k5:2 k4:2 finite:1 parameter:1 composition:3 buchstaber:1 superposition:3 4u3:1 derived:1 polynomials:1 hand:1 diagram:1 algebraic:2 nonlinear:4 work:1 variable:2 k6:2 contain:1 meaningful:1 class:1 yamilov:1 independently:1 toda:1 nevertheless:1 clear:1 h2v:1 curve:1 reducibility:1 without:1 µu:2 ext:1 construction:1 principle:3 time:1
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solv-int9707016.txt |@word 51b:3 partial:3 consider:6 results:3 fluids:1 leads:2 roy:1 mild:1 go:1 sci:1 involved:1 inverse:2 technique:1 nonlocal:7 finally:3 does:1 excluded:1 anharmonic:5 alternating:4 applied:1 conjecture:1 straightforward:2 very:6 springer:1 wave:10 every:1 exact:4 condition:1 look:1 riemann:1 presented:1 turns:2 t4:3 t5:1 t2:2 solution:8 integro:3 vector:1 small:5 akns:2 prevent:1 zn:2 ten:1 sin2:2 sign:2 approximation:8 integrability:1 dynamics:3 odd:1 theory:2 even:1 what:2 nonlinear:16 appear:3 sum:1 3j:5 3i:1 version:1 goes:1 new:1 method:1 coefficient:1 here:4 atoms:1 water:1 free:1 eikx:3 equations:11 appears:1 obtained:5 institute:1 shift:2 study:1 studied:2 periodic:1 resulting:1 fourier:1 changes:1 u3x:1 9i:1 elaborated:1 summations:1 substitution:1 modifying:1 put:1 santini:1 sgn:2 summation:1 derivatives:2 use:1 takes:1 prove:1 remains:1 neighbours:2 next:1 few:1 call:1 m2:2 mckean:1 type:8 theoretical:1 more:3 introducing:1 becomes:5 operators:1 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solv-int9707017.txt |@word proposition:12 casimirs:1 customary:1 consider:5 remarkable:1 funct:4 rev:2 datum:1 results:8 gx:1 bakas:1 scalar:1 gd:3 gb:1 ga:4 francesco:1 vl0:1 gk:3 row:1 compact:1 whose:6 inverse:1 depend:1 calculate:1 bivector:1 γs:10 disposal:1 γq:23 equivalence:4 canonical:4 ts:2 tq:3 leibniz:1 finally:5 critical:1 those:5 th:1 ti:3 libermann:1 updated:1 vlj:5 embodies:1 vxx:1 orthogonal:1 rise:1 dell:1 geometrical:7 rl:4 isomorphism:6 every:3 kashiwara:1 summarized:2 matrices:1 deformations:1 condition:6 obvious:1 hamiltonian:14 induction:1 notes:1 t2:5 sorba:1 vnl:1 t1:5 differential:18 math:16 gauge:1 anal:4 superalgebras:1 homomorphism:1 broader:1 direct:1 translating:1 second:4 dordrecht:1 further:2 linear:4 bilinear:1 aim:1 intersection:1 nonlinear:2 plays:1 appear:1 brackets:27 ak2:1 section:18 sln:5 schoutens:1 en:8 above:1 fractional:3 saldini:1 devoted:1 notions:1 degree:2 respectively:2 farrill:1 component:1 here:1 xλ:1 objects:1 tangent:10 groups:1 lpλ:6 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solv-int9708001.txt |@word represent:1 consider:1 secondly:1 both:1 sca:3 torii:2 computation:1 causes:1 aug:1 finally:2 present:4 under:1 applied:1 cellular:2 lecture:1 difference:2 school:1 presented:2 notes:1 solution:16 discrete:16 convenience:1 small:1 noted:1 maximization:1 direct:1 bilinear:3 appear:2 section:4 expressed:1 uniform:1 version:5 above:2 new:6 method:2 operating:1 concluding:2 equations:5 obtained:1 ultra:16 study:1 δqi:1 p2:8 products:1 automaton:2 mobility:1 explained:1 replace:2 univ:1 would:1 sake:1 suppl:1 next:1 call:1 opposed:1 type:2 more:1 introducing:2 operators:1 particular:1 known:1 hold:1 logarithm:1 mf:1 tokyo:4 science:3 equation:18 work:1 mj:39 values:2 ρt:7 following:2 example:1 figure:4 o:2 sense:1 holds:2 those:2 simplicity:2 suppose:1 applications:2 types:1 short:1 natural:1 brussel:1 st:7 algorithms:1 pleasure:1 order:1 ito:1 over:1 soc:3 thomson:1 paper:2 through:2 japan:3 satisfies:2 its:5 derive:1 thank:1 acknowledge:1 chosen:4 interesting:1 fruitful:1 lt:39 systems:1 mail:1 τt:12 freely:1 introduce:1 now:2 discuss:1 university:3 iwanami:1 2d:11 inequality:2 each:3 found:1 arbitrariness:2 series:1 reduce:1 idea:1 operator:1 toda:14 owing:1 eq:24 since:1 rev:1 research:1 max:9 formula:1 adaptive:1 math:1 mτ:1 theory:1 quite:1 admits:1 york:1 cornerstone:1 enormous:1 ministry:1 int:1 flanders:1 first:1 variables:2 clear:1 relations:2 another:1 given:4 rewritten:2 introduction:1 construct:3 eqi:1 assumption:1 gives:1 japanese:1 pni:2 authors:1 eq1:1 limiting:1 kf:1 eai:1 generality:1 randomly:3 sat:1 acceleration:1 lim:3 latter:1 note:1 k2:2 k1:8 take:3 tokihiro:3 so:1 calculus:1 most:1 remarks:2 acknowledgements:1 soliton:29 especially:1 considered:3 neighboring:1 professor:1 universiteit:1 points:1 exp:4 tanabe:1 physics:1 show:1 supported:1 ki:2 postdoctoral:1 solutions:9 keywords:1 analogue:7 find:1 q1:22 q2:8 parameters:2 should:2 he:1 dependent:5 combinations:1 meguro:1 takahashi:5 determinants:1 fields:1 arxiv:1 qi:13 london:1 qn:1 observed:1 culture:1 see:2 computer:2 result:1 discussions:1 review:1 µn:1 µi:3 between:1 αi:2 recently:1 importance:1 jp:1 however:1 solv:1 received:1 σb:4 taking:3 figures:2 comes:1 simple:1 period:1 dimensional:4 respect:1 been:3 defined:1 expected:2 pi:12 pn:1 komaba:1 pl:1 define:1 direction:1 σj:16 θa:4 fund:1 waseda:1 general:1 θt:16 case:2 ǫb:8 p1:20 pacs:1 ǫj:11 value:1 aim:1 ǫp:1 replaced:1 many:2 aid:1 property:1 procedure:2 discretize:1 jpn:2 vn:1 vt:6 grant:2 same:1 ep1:1 resulting:1 finite:1 interpolation:2 development:1 independent:2 numerical:2 brussels:1 identity:1 recent:1 well:2 without:1 epi:1 entry:1 possesses:1 proposed:2 newton:1 obtain:5 press:1 intervals:1 ucker:1 sciences:1 δpi:1 lattice:17 other:1 lett:4 transformation:1 vrije:1 possible:1 belgium:2 using:2 loss:1 sorting:1 like:1 δt:13 δa:11 mathematical:1 nagai:2 affects:1 integration:1 prog:1 scientific:1 kyoto:1 equivalent:2 discussed:3 pleinlaan:1 recognized:1 stand:1 discretization:8 cambridge:1 ηc:3 ηi:1 references:1 ea1:1 log:4 support:1 there:1 dispersion:2 start:1 milne:1 was:1 function:2 form:1 differences:1 convergence:2 partially:1 moriwaki:1 us:3 limit:5 autonomous:2 chelsea:1 called:1 ac:1 qin:2 constant:3 ai:1 abstract:1 fellow:1 engineering:2 education:1 constructed:1 satsuma:4 nk:1 nc:3 when:3 graduate:1 rewriting:1 field:1 setting:1 electrical:1 papers:1 department:1 mathematics:1 dienst:1 denote:1 ku:1 a1:1 important:1 bounded:1 variable:6 sides:1 algorithm:1 interval:2 theor:1 equivalently:1 hirota:5
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solv-int9708002.txt |@word gd:2 represent:1 consider:8 chain:1 funct:1 induces:1 equalities:2 global:2 splitting:17 invent:2 projected:2 leads:3 eds:1 scalar:3 commute:2 francesco:1 expressions:2 gl:1 devoted:1 whose:7 aug:1 show:3 tr:11 contained:1 nonlocal:2 containing:2 finally:3 tm:5 burlington:1 those:6 th:4 under:10 semenov:1 exposition:1 include:1 tb:5 δhb:1 ta:1 applied:2 belonging:1 straightforward:2 orthogonal:1 far:3 quadruplet:7 connects:1 dokl:1 choice:4 wishes:1 every:1 inequivalent:1 difference:1 matrices:2 condition:14 partitions:1 dim:5 specify:1 presented:5 turns:1 sklyanin:1 solution:3 leave:1 solved:1 vector:18 dealt:1 anal:1 inspection:2 originally:2 freidel:1 application:1 mn:2 consistent:4 coefficient:1 direct:6 sign:1 zero:7 lines:2 settled:1 involution:4 further:4 dynamics:1 implemented:1 linear:16 bilinear:3 established:2 intersection:1 nonlinear:5 invertible:4 brackets:20 sum:6 expressed:2 maillet:1 reminiscent:1 nondegeneracy:3 version:3 suspect:1 goes:2 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solv-int9708004.txt |@word ibid:1 iǫ2:1 iǫ0:1 sci:3 consider:7 chain:5 skip:1 particular:7 results:10 integration:1 four:6 generalize:1 grateful:1 go:1 integrity:2 increase:4 inverse:3 terms:4 calculate:1 aug:1 collisions:1 33a:1 29d:1 29e:1 tr:3 29c:2 send:1 29a:1 supported:2 lower:1 quasi:26 critical:8 gbit:1 th:2 stable:5 stabilizing:1 iνk:1 must:4 alternating:11 pay:1 fax:1 adiabatic:3 amplitudes:42 worse:1 ηm:1 very:15 quadruples:1 springer:3 wave:1 electron:1 figs:1 refractive:1 experimentally:3 difference:3 exact:2 iut:1 condition:5 switches:6 solves:1 level:1 transmission:1 ref:1 notes:2 list:3 solution:21 large:5 involution:1 adjust:1 authorized:1 angelis:1 dealt:1 indices:1 eigenvalues:15 refer:1 optics:4 ρk:1 configurations:8 prevent:1 smaller:1 tel:1 lecture:1 direct:1 pulse:3 cosh:14 approximation:3 consists:1 rate:1 value:21 growing:1 further:2 air:4 theory:6 even:2 what:2 nonlinear:9 appear:1 d2:9 section:2 analogously:2 expressed:1 d3:9 current:1 version:1 above:10 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solv-int9708006.txt |@word gt:1 partial:1 consider:1 rev:1 results:3 gx:2 eds:4 go:1 lakshmanan:1 contributions:1 cases:3 whose:2 inverse:1 const:1 aug:1 finally:2 those:1 dressing:1 p2:7 advantage:1 very:4 wave:1 davey:1 difference:1 condition:3 solves:2 turns:1 list:3 solution:9 try:1 solved:2 relation:9 direct:2 sign:1 zero:2 pass:1 further:4 odd:3 substitute:1 bilinear:17 aim:1 what:2 nonlinear:13 appear:5 section:2 expressed:1 wxxx:1 above:5 new:13 method:11 3d:2 satisfy:3 condensed:1 degree:5 nimmo:1 here:3 xλ:1 ansatz:1 others:1 alone:1 depend:1 sine:3 equations:33 obtained:2 search:4 balance:1 involved:1 study:1 scatter:1 suggests:1 ekx:2 usually:2 involves:1 genuinely:1 useful:2 classification:2 1ss:7 f3:2 univ:1 derivatives:5 use:4 working:1 prove:1 contains:3 guideline:1 call:1 therefore:2 taken:1 type:6 until:1 more:4 introducing:1 µi:2 furthermore:1 initial:2 under:1 odinger:2 particular:4 known:2 eη:4 hold:1 producing:1 must:3 ramani:4 springer:1 equation:15 work:1 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solv-int9708007.txt |@word since:1 managed:1 consider:5 chain:5 funct:1 alg:1 magnetic:1 results:4 leads:2 eε:33 scalar:1 12c:1 travaux:1 grateful:1 types:1 follow:2 expressions:2 inverse:2 depend:1 calculate:2 aug:1 everything:1 paris:2 technique:2 recurrence:4 finally:4 petersburg:2 th:2 semenov:1 characterised:1 norm:3 case:16 conjecture:1 presently:1 advantage:1 very:3 translations:1 noncommuting:1 choice:2 non:1 corollary:1 putting:1 rationality:1 summarized:1 continued:1 condition:1 four:1 hamiltonian:1 notes:1 sklyanin:3 list:1 solution:2 leave:1 vector:3 indices:1 eigenvalues:1 anal:1 force:2 zj:8 zk:1 lecture:1 direct:2 zero:1 masson:1 correlator:4 etats:1 estimated:1 fonction:1 linear:2 even:1 index:1 what:2 section:9 expressed:2 lengthy:1 intersect:2 new:4 method:3 contrast:1 satisfy:3 respectively:6 equals:1 here:2 understanding:1 behaviour:1 following:3 les:1 ansatz:4 groups:1 concluding:1 equations:5 change:1 suggest:1 obtained:5 shansky:1 institute:2 involved:1 study:3 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solv-int9708008.txt |@word concept:1 consider:4 remarkable:1 results:1 invent:1 leads:1 gd:21 generalize:1 francesco:2 go:2 follow:3 expressions:1 factorizing:3 inverse:1 depend:1 calculate:1 aug:1 dickey:4 nonlocal:14 v12:1 finally:2 helps:1 th:5 under:8 case:6 supported:1 straightforward:1 orthogonal:1 rise:1 choice:3 ai:7 hamiltonian:14 t2:43 correct:1 diz:3 science:1 gauge:3 anal:1 sukhatme:1 consistent:1 past:1 second:22 htp:2 further:1 panda:1 what:3 nonlinear:2 stands:1 brackets:8 diag:1 sum:4 hp:3 expressed:6 above:2 new:9 acknowledgments:1 coefficient:4 respectively:3 realizations:2 neveu:1 equals:2 here:3 abandon:1 explore:2 china:3 ht2:1 ht1:1 represented:1 equations:3 change:4 obtained:3 remark:1 antisymmetric:1 study:4 δqi:2 p2:3 poisson:9 chang:1 suitable:1 control:1 tu:1 useful:1 family:1 requiring:1 natural:1 virasoro:14 would:3 commun:7 covariant:8 positive:1 contains:2 negative:1 ψj:5 few:1 nucl:3 ψi:14 therefore:4 δv1:4 operators:6 2w2:1 appendix:3 particular:2 iii:3 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solv-int9708010.txt |@word ibid:1 partial:4 consider:5 pointing:1 results:4 illustrated:1 roy:1 commute:1 computation:2 parameterization:4 3a2:4 gk:2 gj:1 gi:3 3a4:2 whose:3 c0:1 disposal:1 restriction:1 those:1 elliptic:5 under:4 include:1 applied:1 g4:4 g3:19 g2:18 g1:16 orthogonal:1 far:1 wave:1 difference:1 deformations:1 condition:8 four:5 dij:1 hamiltonian:7 turns:3 solution:7 solved:1 vector:1 math:6 further:3 still:1 l2j:1 direct:4 integrability:21 writing:1 dynamics:1 linear:3 subscripts:1 what:1 3x:2 stands:1 brackets:1 trivial:2 section:6 find:5 3i:1 fifth:1 above:6 new:5 3a:7 acknowledgments:1 satisfy:2 degree:1 3a5:1 q3:6 here:4 l21:1 reported:1 l23:1 l22:1 possibility:1 groups:1 others:2 directions:1 along:1 strong:1 equations:2 obtained:2 search:2 my:1 study:2 studied:3 allows:1 reports:1 chaundy:1 suggests:1 poisson:2 permutation:1 action:1 changes:1 ˇi:1 classification:3 extra:2 weaker:1 d31:1 univ:1 derivatives:5 use:4 proceed:1 would:2 covariant:1 bx:2 next:1 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solv-int9709001.txt |@word partial:7 consider:7 j12:4 results:2 illustrated:2 scalar:3 commute:1 gs:1 expressions:1 gl:1 inverse:2 bx1:1 tr:9 under:1 case:6 g2:4 g1:4 choice:2 electron:1 resonant:1 matrices:5 condition:5 leads:2 solves:1 presented:2 permits:2 solution:11 integro:2 fourier:1 der:1 takhtajan:1 direct:3 second:12 j22:4 zz:1 further:1 dynamics:1 4e2:1 canonical:2 spectral:1 index:1 g22:1 section:2 selected:1 expressed:1 above:1 order:13 method:11 satisfy:5 respectively:4 equals:1 here:15 hkl:3 equations:8 appears:1 interpret:1 obtained:4 items:1 study:2 studied:2 allows:1 permit:1 action:3 suitable:1 named:1 via:3 family:1 fba:23 apply:3 φks:2 derivatives:2 conventional:6 takes:3 yangian:1 theme:1 next:1 linear:7 ψi:4 call:1 therefore:1 taken:3 type:2 bethe:2 more:2 separated:8 nauka:1 formally:1 initiated:1 brings:1 operators:39 particular:3 known:3 cases:1 must:1 πni:1 account:1 effectively:1 equation:11 det:5 following:7 example:5 proof:2 f1:6 f2:6 sokolov:1 indicates:1 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solv-int9709002.txt |@word limited:1 similarity:6 magnetic:14 consists:2 localized:4 whose:1 const:2 γt:1 under:18 chirally:1 rise:9 every:1 solution:26 convenience:1 vector:30 degeneracy:6 uncovers:2 consistent:6 direct:2 pulse:46 approximation:5 second:9 even:12 established:1 lights:1 above:4 new:19 increasing:1 pioneering:1 residual:1 here:5 atoms:5 reported:1 asymmetry:1 obtained:8 suitably:1 study:2 suitable:1 changes:8 appropriately:1 projection:1 miramontes:1 explained:7 replace:2 b347:1 total:2 linearly:1 plot:2 negative:1 whereas:1 call:1 therefore:11 care:1 type:16 until:2 esi:1 hahn:9 populations:1 solitons:20 odinger:4 curvature:4 circumstances:1 ma:7 mc:1 mb:9 setup:1 work:11 theories:3 mt:2 deficiencies:1 mq:2 transparency:9 guise:1 example:16 transition:6 give:2 relativistic:1 preserving:1 cartan:1 degenerate:29 absolute:2 recovery:4 provide:1 verify:1 feature:1 how:2 nontrivial:3 b458:1 description:4 modulation:14 earlier:8 law:10 meaningful:1 types:2 attempt:1 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solv-int9709003.txt |@word represent:1 ui:1 grobe:7 sch:3 rev:15 broaden:1 particular:7 primed:2 gg:3 scalar:2 commute:1 generalize:2 gb:16 broader:3 bergmann:1 partial:2 expressions:1 denotes:1 fusing:2 consider:7 whose:5 inverse:1 violate:2 description:1 technique:2 tp:1 steadily:1 supported:1 finally:2 program:1 elliptic:1 under:2 arranged:1 ωs1:2 belonging:1 breathing:3 amplitudes:7 advantage:2 g0:18 far:1 frequencies:9 rise:1 distort:1 choice:4 electron:2 resonant:1 affect:1 exact:4 condition:5 solves:2 presented:1 did:1 positions:1 solution:33 ri:1 large:1 solved:1 convenience:1 vector:3 phase:5 h11:1 small:1 zhu:1 optics:1 originally:1 configurations:1 upper:1 slower:5 ga:16 consistent:1 zc:2 sin2:2 direct:1 pulse:39 sign:12 past:1 second:1 iσ2:1 hopefully:1 linear:6 even:2 what:1 nonlinear:12 rate:2 section:1 zhang:1 expressed:1 agrees:2 secant:4 above:2 new:14 row:1 method:2 satisfy:2 degree:2 exchange:1 respectively:3 bsri:1 component:3 here:3 atoms:2 tangent:1 free:5 sinh:4 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solv-int9709005.txt |@word iterative:1 consolidated:1 consists:7 localized:1 whose:9 const:3 calculate:4 γk:66 neighbours:1 under:57 every:1 formula:30 bringing:1 vast:1 school:1 solution:20 vector:2 indices:6 enjoy:1 direct:26 approximation:3 elegant:1 second:21 expressive:1 even:7 established:1 supplied:1 symes:1 above:13 new:8 consisting:5 simultaneously:2 notions:2 mem:1 here:18 sogo:1 referring:1 obtained:8 suitably:1 study:1 approaches:2 stressed:1 complicated:1 suitable:3 changes:23 elaborated:1 plenum:1 highly:4 brought:1 brl:5 unit:3 nonlinearization:1 would:3 negative:1 substitutions:2 definiteness:1 call:9 therefore:7 volterra:48 type:13 fractions:14 th:1 successful:1 brings:1 odinger:3 curvature:3 correspondingly:4 hold:7 must:1 springer:4 rights:1 work:5 mi:2 cancellations:1 theories:1 mv:16 mp:2 exceptions:1 example:15 give:5 relativistic:18 calvo:1 want:1 times:1 attract:1 end:24 provide:1 verify:5 feature:11 how:5 preferable:1 description:1 transforming:1 earlier:1 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solv-int9709006.txt |@word consider:3 primed:2 l13:4 ihep:1 inverse:6 equivalence:1 uniqueness:1 fermionic:2 putting:1 entries:2 matrices:1 condition:2 solves:2 irreducible:2 solution:5 discrete:3 vector:2 gauge:3 ten:1 sign:1 sergeev:3 zero:2 irreducibility:1 theories:1 r123:18 trivial:1 maillet:2 nine:2 acknowledgments:1 3d:1 here:2 l23:4 quite:1 equations:8 appears:1 interpret:1 z3:5 institute:1 allows:2 contradiction:2 mx:1 usually:1 via:1 protvino:1 b224:1 would:1 prove:1 suppl:1 tightly:1 nucl:1 call:1 associated:2 type:1 formally:1 operators:1 curvature:1 known:2 cases:1 must:1 te:3 onsager:1 unessential:1 recall:1 equation:17 work:1 modified:1 ferro:3 foils:1 ms:1 concepts:1 following:2 example:1 something:1 f1:1 f2:1 f3:1 korepanov:3 give:3 numbers:1 sense:1 enslapp:1 rather:2 s2:1 discussion:1 six:4 maps:4 nontrivial:2 parameter:2 sin:2 map:6 may:3 realized:1 sx:1 dynamical:1 su:1 element:1 so:8 fundamental:1 representation:1 order:1 holds:1 pointed:1 soon:1 interpreted:2 paper:2 statistical:1 signs:1 existence:1 its:3 group:1 thank:1 chosen:1 ll:1 solving:1 fruitful:1 forms:2 choose:1 mail:1 them:1 somebody:1 descendants:1 introduce:1 scaling:1 they:2 multidimensional:1 now:2 yu:1 term:1 classified:1 each:1 found:1 x12:4 x13:4 side:2 baxter:6 holonomy:1 weight:1 inhomogeneous:1 used:1 our:2 eq:3 special:1 out:1 matrix:2 space:4 pentagon:2 research:1 acting:2 ra:6 math:2 foundation:1 linear:1 associate:1 given:2 free:1 standard:1 admits:1 surely:1 r1:4 r2:4 r3:2 impose:1 first:3 xk:6 xi:1 xb:9 xc:9 variables:4 xa:9 number:1 another:1 differ:1 rewritten:1 introduction:1 system:1 relations:4 their:1 r145:2 gives:6 part:1 x2:44 x3:62 x1:64 x6:4 x4:1 x5:1 18b:1 kind:1 second:1 submitted:1 supposed:1 ybe:1 argument:1 generalization:1 say:1 depending:1 note:2 electric:4 object:1 most:1 connected:4 automorphism:1 pair:1 class:1 ka:1 considered:2 ko:1 yang:6 subsequent:1 physics:2 ambiguities:1 supported:1 relation:3 solutions:5 substituting:1 kx2:4 d2:3 d3:4 d1:3 parameters:3 should:1 only:4 factor:1 integrable:3 partially:1 local:7 do:1 triangle:1 dk:1 words:1 stroganov:1 arxiv:1 common:2 set:1 sep:1 j1:2 j2:2 j3:2 result:1 greece:1 discussions:1 ways:1 nuclear:1 state:1 simplest:1 x23:4 terms:2 however:1 key:1 solv:2 both:2 cos:2 many:1 russia:1 etc:1 connection:1 expression:1 ck:1 conclude:1 appeared:1 quadrilateral:1 dimensional:6 simply:1 respect:3 considering:2 described:1 lattice:1 three:5 z1:6 z2:6 interest:1 abstract:1 systems:2 describe:1 reasonings:1 formed:1 else:1 c3:1 c2:1 c1:1 case:15 tetrahedron:10 trick:1 while:1 suppose:2 ix:2 thus:6 itself:1 different:3 grant:1 realizing:1 same:1 arguments:2 proved:1 several:1 independent:5 investigated:1 hand:2 necessity:1 correspondent:1 mangazeev:1 well:3 solve:1 position:1 model:1 left:2 just:1 being:3 obtain:2 rest:1 preprint:1 simple:1 lett:2 transformation:3 euler:1 possible:1 unique:2 formal:1 like:1 excluding:1 follows:1 either:1 twelve:1 right:2 classical:1 kashaev:5 some:4 understood:1 b2:1 b3:1 proper:1 ferroelectric:1 l12:4 manipulations:2 pron:1 decomposition:1 proc:1 bc:1 equivalent:6 bk:1 step:3 permitted:1 algebraic:1 freedom:1 nijhoff:1 letters:1 into:1 rotations:1 functional:15 references:1 operator:1 bosonic:1 numerate:1 there:7 lot:1 was:3 function:1 form:5 regard:1 but:3 construction:1 russian:1 wholly:1 he:3 commun:1 up:2 us:1 problem:2 called:1 constant:3 ad:1 int:2 ak:1 sxk:1 general:4 single:2 tedious:1 again:2 functions:4 integrability:2 no:2 extract:1 boos:1 when:2 field:1 branch:1 elements:1 star:1 models:4 a1:5 a3:3 a2:3 sides:1 structure:2 network:1 equivalently:1 weights:5 time:1
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solv-int9709007.txt |@word consider:3 results:2 scalar:2 proposition:3 ga:1 expressions:2 row:8 whose:2 preserves:1 paris:1 finally:3 tj:7 tk:36 th:11 ti:3 analogous:1 te:1 applied:1 ginn:1 wji:1 erale:1 geometrical:7 difference:2 matrices:1 condition:1 school:1 solves:1 did:1 solution:1 leave:1 discrete:17 vector:2 deleting:2 zn:2 des:1 mi:9 zero:1 canonical:1 bilinear:3 nonlinear:1 appear:5 section:1 expressed:3 version:1 sur:1 above:1 new:6 net:1 viii:1 respectively:1 here:3 understanding:1 desired:1 objects:1 china:1 directions:2 layout:1 equations:8 differential:1 obtained:10 technical:1 involved:1 studied:1 akj:1 leibnitz:1 suitable:1 f1:1 wik:1 wij:3 replace:1 santini:6 apply:1 use:2 prove:1 sake:1 next:3 linear:1 m1:9 m2:3 means:1 more:2 ecole:1 company:2 dressing:1 appendix:4 bogdanov:1 known:1 hold:1 must:1 ma:5 xℓ:2 equation:4 mn:7 det:2 mk:11 mj:10 obvious:1 mp:1 following:9 example:2 proof:5 beijing:2 give:2 process:1 dress:1 simple:1 end:1 darboux:4 holds:2 write:4 how:2 cons:1 circular:3 simplicity:2 levy:15 algebra:1 replacing:6 ζi:13 after:1 representations:2 fj:1 fk:3 data:1 compatibility:2 fn:1 element:1 spain:1 order:3 interpretation:1 ξi1:1 satisfied:1 paper:1 through:1 japan:1 nets:3 its:1 before:1 ima:1 le:1 la:1 doliwa:6 absence:1 systems:3 main:4 freeman:2 them:3 combination:1 acklund:1 introduce:2 ξij:1 mention:3 xiℓ:3 ξim:1 multidimensional:8 now:2 easily:1 each:3 2m:6 pb95:1 constraints:1 en:2 ei:2 lam:2 elementary:2 used:1 ckℓ:2 our:9 shown:2 matrix:11 since:1 parallelogram:1 rd:2 aji:1 contained:1 ajk:1 reader:1 formula:3 evaluation:1 math:3 ζk:3 theory:2 ısica:1 departamento:1 standard:2 completely:1 york:2 l173:1 geometry:1 introduction:1 universidad:1 first:7 xk:4 qki:6 xi:3 features:2 qkl:2 conjugacy:1 number:2 xd:2 ℓk:5 relations:1 ξji:1 ξjm:4 given:8 cartesian:5 xid:2 rewritten:1 manakov:2 xii:1 adjoint:5 system:4 least:1 indicate:1 gives:3 ξj2:3 ξj1:4 para:1 alonso:1 qlk:2 qli:1 translation:1 x1:1 than:1 coefficients:2 treatise:1 iteration:1 see:2 xi1:1 boston:1 ann:1 modern:1 curves:1 say:1 conjugate:3 need:4 any:2 depending:1 convenient:1 mechanism:1 liu:2 liv:1 potential:1 so:1 fj1:1 shall:1 hammond:1 letter:3 formulae:5 pair:1 iterate:2 soliton:1 fji:3 partition:3 points:5 ohta:1 reprinted:1 show:2 reductions:1 supported:2 multicomponent:1 notations:1 miwa:2 relation:3 solutions:8 based:1 should:2 lemma:6 only:2 going:2 integrable:4 δxi:1 get:5 dg:1 de:2 lattices:9 xℓi:7 gen:1 determinants:6 continuum:2 arxiv:1 remove:1 set:1 sep:1 espa:1 namely:2 result:6 w1:6 recently:2 analog:1 techniques:2 surfaces:2 written:1 closed:4 nimmo:2 conditions:1 schreier:1 notice:2 terms:6 wn:4 wk:5 wj:7 wi:4 however:3 jn:2 ji:4 solv:1 last:8 chelsea:2 according:1 laplace:4 vℓ:1 proyecto:1 expression:1 ck:4 among:1 relevant:2 co:1 point:1 appeared:1 quadrilateral:18 dimensional:2 represented:1 iterations:1 sequences:2 moreover:1 transformations:8 second:1 basis:1 been:4 mart:1 int:1 reduction:1 much:1 basic:1 applying:2 pi:3 abstract:1 lett:6 direction:1 corresponding:2 ınez:1 quantities:1 theorem:6 observe:1 denote:1 present:1 case:4 multi:7 nski:7 rectangular:2 aim:4 while:1 sli:1 aik:2 aij:6 orica:1 wki:1 planar:1 vectors:2 vd:1 century:1 thus:1 mql:2 iv:1 characterize:2 reads:2 ij:1 wkp:1 orthogonal:1 shift:2 different:1 same:1 proceeds:1 wℓ:1 fkp:1 extended:1 again:1 nj:2 hand:1 v1:2 tsujimoto:1 coordinate:1 fk1:1 construct:1 just:1 tangent:1 being:2 obtain:3 ζi1:1 facts:1 eorie:1 villars:1 preprint:1 zakharov:1 character:1 parametrization:2 lattice:29 cicyt:1 transformed:5 δkℓ:2 easy:1 bℓk:3 transformation:11 bidimensional:1 real:1 bik:5 ζij:1 possible:1 background:2 using:3 necessary:1 δx:1 follows:2 remind:1 arbitrary:2 δb:1 because:1 madrid:1 some:3 choosing:1 per:1 exposition:1 eisenhart:1 sperner:1 expansion:3 unsw:1 found:3 xkℓ:6 gauthier:1 planarity:1 about:1 meaning:1 o:1 compatible:1 konopelchenko:2 introduced:1 block:8 considerations:1 soc:1 publishing:2 previously:1 qjk:2 square:1 references:1 operator:4 there:3 appl:1 way:1 analyze:1 was:2 function:1 kronecker:1 hj:1 hk:10 hi:26 partially:1 made:1 compute:3 cie:1 casorati:6 us:2 ωi:1 limit:1 iterated:3 ωn:1 manuel:1 similar:3 called:1 detailed:1 qil:1 ab:1 constant:1 qik:7 qij:10 defined:6 ak:5 determinant:5 general:4 chap:1 imai:1 formalism:1 check:1 ni:2 functions:8 nk:1 nn:4 no:2 na:1 when:2 graduate:1 nas:5 kp:3 briefly:1 complutense:1 ξp:1 symbol:1 time:1 medina:1 ξi:18 ξj:9 ξk:17 variable:1 qijk:1 assume:1 rule:1 equivalently:2 combescure:1 hirota:2 n1:4
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solv-int9709008.txt |@word limited:1 folklore:1 represent:3 magnetic:24 four:4 consists:4 sci:2 localized:16 whose:9 u3:4 violate:1 attracted:1 paris:1 similarity:1 unanswered:1 edward:1 θt:1 under:17 discretization:1 attractors:9 rise:7 every:1 figs:3 uncertain:1 fractal:3 vast:1 prize:1 beam:1 sensor:2 solution:31 admissible:2 vector:6 shows:3 ups:1 favoured:1 force:2 somewhere:1 direct:7 pulse:4 approximation:7 elegant:1 second:9 10v:1 even:23 established:2 dr1:1 specification:1 steiner:2 above:24 new:37 net:1 increasing:1 ever:2 coefficient:4 evolving:1 sio2:1 simultaneously:1 notions:2 men:1 drew:1 atoms:1 reported:1 κz:1 q12:2 represented:1 path:4 marchenko:1 du2:1 logarithmic:1 obtained:18 balance:1 rigorously:2 study:13 changed:2 approaches:1 reports:7 γs:1 drn:1 fourier:1 changes:4 golden:4 secure:4 classification:3 infinte:1 highly:6 santini:4 roles:2 total:1 kosevich:2 existed:2 linearly:2 uξ:2 derivatives:3 quasi:1 func:3 would:10 inductive:2 century:9 bundles:1 ki3:1 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solv-int9709009.txt |@word represent:1 sci:1 consider:5 chain:2 secondly:1 rev:2 magnetic:1 lack:1 leads:2 scalar:2 intricate:1 lakshmanan:8 fronts:4 inverse:1 equivalence:3 nonlocal:2 γj:1 γi:2 th:1 include:2 indicating:2 straightforward:2 orthogonal:6 rise:2 induce:1 geometrical:6 wishes:1 deformations:1 condition:2 alma:5 presented:1 turns:1 notes:1 solution:1 vector:5 rk:1 originally:1 strachan:7 solutions:4 zl:6 10b:1 10a:1 past:1 second:1 pass:2 further:3 dynamics:6 linear:10 even:2 nonlinear:18 appear:1 bdu:1 consistently:1 renaissance:1 above:6 lifshitz:1 new:3 edited:2 kaup:1 respectively:6 here:4 l21:1 tangent:3 κy:3 κt:1 equations:48 19b:2 box:1 institute:1 vectors:1 triad:5 york:3 uniquely:1 via:2 family:2 extra:1 9a:1 inducing:1 9c:1 9b:1 santini:1 unit:4 derivatives:1 prove:1 finally:1 few:1 nucl:1 eyy:1 type:1 metric:1 introducing:2 brings:1 odinger:4 curvature:2 thompson:1 berlin:2 uxx:2 particular:1 known:2 iii:4 springer:3 pursue:1 science:1 equation:26 work:1 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solv-int9709010.txt |@word consider:3 remarkable:1 global:2 results:6 leads:2 roy:1 proposition:14 higher:1 computation:1 go:2 follow:2 expressions:1 θp:2 relationships:1 content:1 certainly:1 replacements:1 schiff:4 paris:1 description:1 passage:1 presents:1 finally:3 critical:4 th:1 under:3 λs1:2 analogous:1 crest:1 necessary:4 case:7 conjecture:1 straightforward:8 very:2 rise:5 wave:3 p1:3 every:1 bihamiltonian:1 li:2 exact:1 condition:2 identity:1 illustrated:3 riemann:1 solves:4 presented:3 turns:1 presumably:1 solution:64 t0:41 t1:29 leave:1 commute:2 pbb:1 equation:54 zm:2 zn:11 consistent:1 direct:2 sign:9 matrices:4 haak:1 zero:10 constantin:3 evaluated:1 substituting:2 theo:1 further:1 dynamics:2 quite:2 approached:1 aim:2 what:1 nonlinear:5 ct1:1 giving:1 section:13 brief:1 hereditary:1 current:2 birkhoff:7 version:1 umbilic:1 fuchssteiner:3 above:7 sup:1 new:8 method:1 exercise:2 satisfy:3 compact:1 full:1 simultaneously:1 degree:2 respectively:2 here:13 understanding:1 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solv-int9709011.txt |@word consider:5 yasuhiro:1 similarity:4 alg:1 results:2 nato:1 eds:1 scalar:1 proposition:13 grateful:1 parameterization:3 expressions:2 whose:2 calculate:1 ty:1 equivalence:1 11x2:3 young:6 uniqueness:1 tm:8 4nn:4 p2:2 stud:1 corollary:1 putting:3 entries:1 matrices:1 condition:3 obvious:1 wronskians:2 list:1 solution:7 t0:1 t1:1 τˆn:2 pil:3 wronskian:2 grantin:1 ekvac:1 direct:1 xhn:1 painlev:10 4x2:3 linear:1 bilinear:11 3z:2 nonlinear:2 appear:2 section:1 expressed:14 version:1 3n:20 above:3 3b:1 3a:1 ˆn:2 satisfy:2 degree:4 exchange:1 respectively:4 here:1 bi:1 xλ:2 concluding:1 ratio:2 equations:19 z1:1 obtained:5 remark:4 dividing:1 remarks:2 shift:7 study:1 studied:2 hiroshima:2 suggests:1 6n2:2 schur:14 technique:1 useful:1 9n:4 hermite:8 apply:1 univ:1 derivatives:2 use:1 prove:3 finally:4 next:3 comparing:1 associated:2 type:1 diagrams:2 fokas:1 ρxx:9 appendix:2 labelled:1 particular:3 known:5 cases:3 derivation:1 ramani:1 nauk:1 characterize:1 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solv-int9709012.txt |@word represent:3 nfn:1 partial:2 consider:10 maximum:1 electron:3 keep:1 global:20 amplifier:1 results:4 nato:1 leads:6 eds:2 ginzburg:1 proposition:6 computation:2 doted:1 consists:1 gn:2 amplified:1 denotes:1 causes:1 layers:1 whose:1 inverse:4 calculate:2 reformulate:2 i2:1 graph:2 funct:2 including:2 quasi:15 monotonically:1 tanaka:1 those:5 elliptic:2 stable:2 tf:2 suita:1 indicating:1 division:2 supported:1 provides:3 abelian:5 far:1 frequencies:1 subject:1 wave:9 corollary:8 dispersions:1 fall:1 resonant:1 specific:1 parameter:2 exact:1 conserved:4 four:2 riemann:60 cable:2 level:9 transmission:5 shock:21 solution:54 t0:48 vector:1 progress:1 guiding:1 small:10 eigenvalues:5 anal:2 accumulation:1 hasegawa:2 zm:4 zn:10 work:1 compensated:1 oscillation:3 sin2:7 direct:1 pulse:60 ρl:1 approximation:5 limǫ:1 zero:21 bg:1 design:1 evaluated:1 further:4 dynamics:3 leakage:1 quite:3 theory:11 spectral:14 3z:1 what:1 nonlinear:16 appear:1 giving:1 section:11 ast:4 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solv-int9709013.txt |@word partial:4 consider:9 remarkable:1 results:1 four:3 eds:1 commute:2 lakshmanan:1 expressions:1 manipulations:1 ihep:2 u3:18 pron:1 equivalence:6 finally:1 analogous:1 fermionic:1 belonging:1 wished:1 advantage:2 choice:1 putting:1 matrices:9 condition:11 irreducible:1 notes:1 solution:5 try:1 discrete:2 math:6 indices:2 relation:2 equation:18 possibility:2 ten:1 lpthe:1 sergeev:9 surrounding:2 integrability:5 theories:1 theory:7 spectral:2 what:2 nonlinear:1 stands:1 invertible:1 giving:1 sum:1 expressed:2 maillet:3 current:2 suspect:1 above:2 new:1 acknowledgments:1 3d:5 degree:1 here:3 l23:5 poverty:1 l24:4 consideration:2 equations:8 appears:3 interpret:1 obtained:2 institute:1 shift:1 vectors:1 mx:1 permutation:1 usually:2 surely:1 makes:1 via:1 projection:1 vij:1 protvino:1 b224:1 additive:1 would:1 nijhoff:3 suppl:1 next:1 comparing:1 nucl:1 call:1 type:9 more:4 sort:7 successful:1 iu:1 operators:6 curvature:3 surface:1 known:4 cases:3 must:2 graphic:1 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solv-int9710002.txt |@word represent:2 minors:1 consider:10 chain:7 nauchn:1 trigonometric:1 four:1 iim:1 scalar:9 proposition:1 go:1 gn:7 expressions:2 research:1 gj:1 row:1 isometric:1 inverse:3 depend:3 calculate:9 zone:2 bogoliubov:6 simple:1 quasi:3 petersburg:1 th:1 iij:1 norm:1 p2:1 2γn:1 1the:1 g2:4 g1:1 r11:1 dokl:1 results:4 putting:2 lynch:1 nieto:2 difference:1 matrices:7 partitions:2 subsets:2 presented:3 anisotropy:1 t2:3 solution:6 t1:3 large:2 solved:3 vector:1 math:10 small:1 gauge:2 tognetti:2 optics:2 qism:1 solutions:4 zm:6 zn:2 ze:1 sin2:2 zero:7 correlator:1 further:1 odd:1 quite:1 canonical:1 bilinear:2 established:1 nonlinear:3 plays:1 darkness:6 section:8 analogously:2 expressed:6 suq:1 ground:1 method:4 filled:1 hˆopital:1 satisfy:3 λii:12 fiz:2 d1:9 respectively:3 even:1 equals:1 here:8 reported:1 ansatz:4 sinh:12 represented:11 luis:1 strong:1 equations:18 appears:3 obtained:8 antisymmetric:1 institute:1 shift:1 vectors:5 suggests:1 periodic:1 products:7 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solv-int9710003.txt |@word consider:2 chain:4 magnetic:5 leads:1 consists:1 follow:1 expressions:1 certainly:1 inverse:1 γt:1 does:2 γn:1 stable:4 tf:2 supported:1 string:1 very:1 connects:1 wave:3 wishes:1 condition:7 level:2 ref:1 anisotropy:1 shock:24 solution:1 large:2 discrete:1 small:2 ρj:1 pulse:2 cosh:1 approximation:4 zero:3 value:1 further:1 dynamics:3 choices:1 analogue:2 theory:1 aim:1 what:2 nonlinear:3 uniform:2 above:4 new:3 ever:1 nakamura:1 shocks:2 coefficient:1 condensed:1 exchange:3 respectively:1 component:2 preserves:1 here:4 atoms:1 reported:4 magnetism:1 cos3:1 cos2:2 represented:1 path:3 strong:1 equations:4 change:1 obtained:2 remark:1 parameters:2 institute:1 study:1 vectors:1 amount:1 poisson:2 domains:3 suitable:4 followed:1 projection:2 highly:1 total:3 readily:2 use:4 predictions:1 comparing:1 program:1 ψn:3 therefore:2 associated:1 type:1 lowering:1 solitons:5 operators:2 ti:2 odinger:1 berlin:1 normalized:1 poggi:1 known:1 balakrishnan:1 springer:2 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solv-int9710004.txt |@word ibid:1 chain:2 magnetic:1 trigonometric:9 leads:1 eds:2 expressions:1 gl:1 preserves:1 calculate:1 zeroing:1 rel:6 finally:2 elliptic:6 under:2 worth:4 degeneration:1 interacting:1 kρ:1 g3:30 g2:53 implicitly:1 ηij:4 results:1 discretizations:2 difference:16 exact:1 deformations:2 condition:1 riemann:1 presented:1 turns:1 solution:2 leave:1 convenience:1 differential:6 eigenvalues:4 findings:1 sin2:2 second:5 odd:1 substitute:3 even:4 what:2 12a2:17 sheeted:1 3n:2 above:2 new:4 3a:1 3g:1 exercise:1 body:4 simultaneously:1 degree:3 respectively:2 here:2 canonically:1 explore:1 separation:1 represented:1 standard:1 equations:9 obtained:2 instituto:1 institute:1 4p:1 study:7 studied:1 mx:1 periodic:8 proof:1 changes:1 lrel:1 montreal:1 extra:2 natural:2 coinciding:1 seligman:1 use:1 proceed:2 would:1 sake:1 positive:4 contains:1 quasi:3 next:1 nucl:1 noting:1 call:2 ibragimov:1 taken:1 themselves:1 isospectrality:1 type:8 theoretical:2 more:1 separated:1 th:4 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solv-int9710005.txt |@word limited:1 dewitt:1 consider:1 secondly:1 vectorial:1 results:2 leads:1 proposition:18 edu:2 expressions:3 row:5 compact:1 preserves:1 inverse:2 depend:1 analytic:1 superspace:1 tw:2 concerned:1 tu:2 pˆn:6 tn:32 reductions:1 finally:2 tm:8 th:2 ti:1 case:6 straightforward:2 far:1 removing:1 wave:44 corollary:1 2γx:1 manin:4 condition:4 χd:2 superdifferential:1 bn:3 induction:2 t5:2 t3:4 t1:1 leave:1 convenience:1 vector:1 science:1 relation:1 ωij:5 permutability:1 equation:14 wronskian:6 coordinate:1 nthu:1 consistent:1 d3:2 direct:1 past:1 second:1 odd:13 spectral:1 nonlinear:3 stands:1 iterating:5 trivial:1 section:1 expressed:6 find:1 version:2 above:1 new:3 method:2 contrast:1 satisfy:1 edited:1 respectively:5 residual:1 here:5 replacements:1 china:3 address:2 represented:2 sine:1 equations:6 z2:1 obtained:7 remark:2 larger:2 chang:1 suitable:1 involves:1 useful:2 ls:1 rφ:1 schief:1 vˆ0:28 use:1 would:3 prove:1 positive:1 negative:1 next:2 few:1 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solv-int9710006.txt |@word partial:1 consider:5 alg:2 results:1 leads:1 gf:1 commute:1 generalize:1 montr:2 edu:1 consists:1 homomorphism:3 expressions:9 involved:1 eη:4 compact:1 whose:2 inverse:4 referring:1 graph:16 finally:1 those:2 elliptic:14 ti:3 tr1:1 td:2 tb:4 applied:1 belonging:1 r12:15 string:2 orthogonal:2 far:2 implicitly:1 springer:1 wave:1 endpoint:2 antipode:5 summarized:1 associated:1 difference:5 matrices:13 look:2 four:2 jurˇco:3 beginning:2 immediately:1 hamiltonian:18 did:1 proc:1 nucl:3 t2:31 solution:3 t1:35 solved:1 vector:6 dealt:1 indices:9 frolov:1 reyman:1 hasegawa:2 upper:2 says:1 dealing:2 consistent:1 direct:3 fold:1 second:2 follow:2 further:1 rrt:1 yang:9 spectral:4 index:3 what:1 appear:3 giving:1 sum:6 contracted:3 analogously:2 symes:2 version:2 above:1 capital:1 new:4 order:1 method:1 pictorially:2 exchange:1 respectively:1 component:5 discrete:1 here:9 diagonal:1 tachyons:1 objects:1 groups:17 path:12 along:1 equations:12 appears:2 differential:2 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solv-int9710008.txt |@word represent:2 consider:6 remarkable:1 rx:1 results:3 θzz:2 eds:2 ga:2 zinn:1 sung:1 forget:1 compact:1 b268:1 inverse:1 const:7 equivalence:1 quasi:1 present:2 elliptic:4 stable:1 hill:1 case:16 conjecture:1 g3:2 string:7 very:1 zachos:3 choice:1 sze:1 exact:1 fomenko:1 dubrovin:1 presented:2 solution:8 discrete:1 differential:1 guitter:1 noted:1 configurations:12 revolution:1 arctan:1 ten:1 dealing:1 sin2:1 sin1:2 second:3 zz:4 theory:8 spectral:1 established:1 letts:3 while:2 expressed:1 above:4 new:3 method:2 coefficient:1 polyakov:8 respectively:1 here:5 understanding:1 cylindrical:1 them:1 represented:1 path:1 along:1 equations:12 change:2 obtained:2 great:2 studied:1 allows:1 completely:2 example:4 periodic:3 prym:1 action:7 via:1 useful:1 classification:1 namely:3 plenum:1 total:1 ϕ2x:1 unit:1 virasoro:1 use:3 takes:2 would:1 antikink:1 chooses:1 nucl:3 m2:4 eϕ:1 means:1 more:2 nauka:1 immersion:1 becomes:2 odinger:2 curvature:7 particular:7 known:4 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solv-int9710009.txt |@word partial:2 consider:6 chain:5 invent:1 scalar:3 commute:1 tricomi:1 cancels:2 computation:1 expressions:1 research:1 gk:20 compact:1 inverse:2 calculate:3 company:1 finally:2 th:7 under:2 analogous:1 lkr:12 hill:1 applied:2 g3:1 g2:1 g1:1 very:1 corollary:1 every:1 faa:1 matrices:2 arrange:1 did:1 tanh:1 solution:2 leave:1 item:1 vector:1 ndimensional:1 small:3 lk1:1 abbreviated:1 work:1 zi:1 zk:5 oscillator:2 coefficient:3 sign:2 approximation:2 second:2 value:1 pass:1 further:3 theory:3 even:2 aim:1 trivial:1 sum:13 3u:1 henceforth:1 bl:3 3n:1 above:2 new:5 solitonic:2 method:9 filled:1 satisfy:1 degree:6 equals:1 here:9 b2n:6 b2k:3 sinh:1 consideration:1 equations:5 z1:1 obtained:2 algebra:2 institute:1 studied:1 products:1 su0:1 usually:1 texte:1 summations:1 summation:7 apply:1 should:1 derivatives:4 use:3 asymptotic:5 commun:1 covariant:1 positive:5 negative:7 next:1 nucl:1 call:2 therefore:3 m3:4 m2:22 compactly:1 type:2 more:7 flat:1 formally:4 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solv-int9710010.txt |@word consider:1 rev:1 global:3 leads:10 scalar:5 commute:2 go:1 expressions:1 issues:1 devoted:1 whose:1 finally:1 does:2 stable:2 string:1 straightforward:1 kumar:1 very:1 translations:1 choice:3 condition:1 four:2 hamiltonian:17 turns:4 solution:6 try:2 differential:1 realization:1 gauge:1 consistent:6 integrability:9 further:2 dynamics:1 odd:1 canonical:1 bilinear:1 established:2 nonlinear:10 appear:1 brackets:4 remain:1 expressed:3 d3:1 version:1 above:16 fractional:1 values:2 solitonic:10 method:1 contrast:1 satisfy:3 ibid:2 relates:2 respectively:1 realizations:1 here:4 understanding:2 address:2 concluding:1 constructive:1 equations:28 appears:1 change:2 obtained:3 ref:5 involved:3 study:3 studied:3 step:1 poisson:13 action:3 khare:2 u3x:8 useful:1 extra:1 highly:3 vis:2 total:9 establish:1 derivatives:5 use:1 takes:1 would:1 remains:1 next:3 linear:1 taken:1 type:30 entails:1 more:4 preserving:1 becomes:1 operators:1 under:4 curvature:2 gorshkov:1 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solv-int9710011.txt |@word gt:2 consider:2 funct:1 global:1 trigonometric:1 invent:1 four:1 commute:1 ga:3 devoted:2 griffin:1 inverse:13 depend:1 calculate:1 show:4 tr:1 unanswered:1 cλµν:1 those:1 elliptic:16 under:1 semenov:1 must:1 ingredient:2 case:4 conjecture:4 charles:1 rαβ:3 results:2 sons:1 rayner:1 δjk:2 entries:3 matrices:23 condition:1 generalised:1 presented:2 sklyanin:5 solution:7 math:5 manifestly:1 anal:1 petersburg:1 adjugate:1 employing:1 direct:1 second:4 further:2 spectral:7 index:1 what:1 invertible:3 brackets:1 section:5 brief:1 expressed:1 sur:1 new:8 satisfy:5 full:1 respectively:2 here:12 understanding:1 xλ:2 les:1 separation:3 xν:9 equations:7 appears:5 change:1 shansky:1 remark:3 antisymmetric:1 unproven:1 gln:4 study:1 tµ:3 krieger:1 poisson:4 action:1 involves:1 examining:1 shorthand:1 projection:1 characterises:2 rτ:2 talon:2 inverses:4 apply:2 weierstrass:3 use:2 takes:2 working:1 prove:3 remains:2 monographs:1 whittaker:1 suppl:1 distinct:1 comparing:1 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solv-int9710012.txt |@word represent:1 gt:5 remarkable:1 varying:1 splitting:2 leads:1 scalar:1 montr:3 computation:3 consists:1 gl:28 gj:3 gi:1 whose:2 inverse:2 depend:2 λin:4 segments:1 tr:9 acting:1 supported:1 γj:2 finally:1 petersburg:1 under:8 λir:1 labels:1 sherbrooke:1 h4b:1 preserved:1 very:2 account:1 results:3 valued:5 lecture:1 matrices:18 deformations:20 condition:1 riemann:6 hamiltonian:16 turns:1 notes:1 solution:3 vector:1 interchanging:1 eigenvalues:2 dαi:2 dαj:3 gb:6 ga:8 α2j:2 nonautonomous:5 direct:1 sign:1 second:3 plenum:2 pass:2 dynamics:1 odd:1 eλb:1 linear:3 subscripts:1 appear:1 invertible:2 chicago:1 giving:1 diag:3 sum:1 expressed:5 above:6 new:3 construction:2 consisting:3 full:2 ibid:1 respectively:2 even:1 here:1 provides:1 following:15 represented:1 along:5 equations:25 change:1 obtained:2 great:1 suitably:1 studied:1 allows:1 resulting:4 poisson:12 glr:4 fourier:4 changes:2 quotient:1 via:2 family:1 viewpoint:2 explained:2 isomonodromic:26 redefining:1 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solv-int9710013.txt |@word secondly:1 consider:2 remarkable:1 results:2 leads:2 roy:1 inverse:1 technique:1 finally:3 th:1 worth:1 applied:1 far:3 rise:1 springer:1 wave:22 nayfeh:1 resonant:1 common:1 four:1 notes:1 solution:29 correct:1 large:3 small:4 2k0:1 second:2 dynamics:6 theory:6 nonlinear:18 celebrated:1 uniform:1 version:1 3m:2 new:2 satifies:1 method:5 nonlinearly:1 never:1 here:1 understanding:1 behaviour:4 represented:1 sine:5 equations:8 appears:3 obtained:8 shift:1 study:6 allows:1 commonly:1 controversy:2 resulting:1 usually:3 fourier:1 inspires:1 via:1 montpellier:2 scales:2 manna:5 use:2 asymptotic:9 would:1 prove:3 contains:2 next:2 noting:1 therefore:1 reductive:2 expanding:2 taken:1 associated:1 type:2 solitons:2 operators:1 instantons:2 merle:3 berlin:1 particular:2 known:3 producing:2 account:1 defines:1 equation:9 work:2 modified:1 values:2 following:2 trans:1 stimulating:1 renormalization:1 give:1 relativistic:2 neglected:1 generically:1 lorentz:2 numbers:1 verlag:1 boussinesq:2 provide:1 discussion:1 peregrine:3 how:1 parameter:1 sin:1 profile:1 ubiquitous:1 description:2 4k02:1 wiley:2 φ2n:1 gardner:1 hence:5 plane:1 ω2n:6 coming:1 short:20 dynamical:1 sech:1 sw:17 su:1 rather:1 discretisation:1 allow:1 enter:1 representation:1 sg:9 order:4 indeed:6 displayed:1 interpreted:1 through:2 japan:2 still:1 its:2 before:1 solitary:1 group:2 thank:1 coordinates:1 actually:2 lw:7 lu:5 degrees:1 systems:6 non:2 they:5 hierarchies:1 occult:1 always:1 2m:2 bona:4 side:4 characterized:1 2k:1 series:9 related:1 constitute:1 frequency:5 sion:1 quantum:1 laboratory:1 eq:1 shown:2 space:1 u2n:3 m2n:2 sustain:1 lecture:1 occurs:2 math:4 shows:2 benjamin:5 linear:9 reformulated:1 b36:1 free:1 quite:1 kodama:1 york:2 longwave:1 times:1 motion:1 tor:1 gordon:8 corrections:1 first:5 indebted:1 already:2 variables:4 waves:15 number:6 2u2:1 long:6 another:1 precisely:1 xv:1 invariance:1 dispersive:6 perturbation:9 obtainable:1 introduction:3 amsterdam:1 system:3 ripples:1 sech2:4 their:1 scheme:2 λu2:2 gives:3 way:1 recursively:1 whitham:1 part:1 authors:1 eliminated:4 unicity:1 holland:1 cimento:1 kink:6 determined:1 amplitude:5 powers:1 perturbative:9 behaviors:1 argument:2 4k0:2 need:1 seek:1 orders:4 zero:2 convenient:1 physique:1 note:1 k2:4 k0:9 build:3 tool:2 cnrs:1 multiple:2 collaboration:1 object:1 propagate:4 phase:2 intrinsic:1 soliton:5 considered:1 later:1 face:1 exp:9 kt:1 velocity:3 kx:6 vries:4 2m2:2 relation:2 solutions:8 principal:1 slow:4 enough:1 topological:1 antikink:5 only:5 going:1 integrable:2 moser:1 oct:1 do:1 above:2 klein:3 get:1 secular:6 de:4 cannot:1 nicely:1 arxiv:1 yield:1 hydrodynamic:1 wish:1 london:2 requirement:1 set:1 relative:1 see:1 result:2 close:1 techniques:1 review:1 propagates:1 favor:1 written:1 between:2 invariant:1 approach:9 terms:7 kawahara:1 originated:1 however:1 hypothesis:3 answers:1 key:2 solv:1 both:1 lu2:1 many:2 according:1 etc:2 expression:4 λk0:1 very:3 point:1 asymptotically:1 leon:1 mkdv:2 2nx:1 simply:1 moreover:2 pp:1 publishing:1 three:2 been:2 goes:1 basic:1 expected:1 ǫ2n:2 choose:3 6m:1 present:1 case:8 look:1 tanh:4 expanded:1 value:1 will:9 while:4 suppose:1 behavior:1 ǫt:2 property:1 procedure:1 almost:1 characteristics:1 thus:1 them:2 uxx:1 expan:1 reads:1 vt:1 uxxt:1 different:2 propagation:2 perform:1 indistinguishable:1 same:2 any:1 proved:3 finite:1 higher:1 jeffrey:1 extended:1 numerical:1 interscience:2 hand:4 v2:2 purpose:2 infinite:2 2u0:3 well:3 analysis:2 finds:1 ωnl:2 components:3 firstly:1 model:10 φtt:2 being:2 obtain:3 summed:2 mahony:4 alternative:1 multiples:2 previous:1 preprint:1 infinitely:1 character:2 relevance:1 pitman:1 around:1 read:2 unveil:1 eorique:1 philos:1 using:1 unique:1 helpful:1 necessary:2 like:1 contradict:1 velocities:1 serves:1 δn:3 korteweg:4 pereira:4 reduced:2 right:4 old:2 neumann:1 classical:4 phenomena:1 understood:1 choosing:4 kdv:8 montero:2 scale:1 comments:1 does:2 tends:1 yields:2 propagating:1 substitutes:1 power:1 kruskal:1 expansion:5 weil:1 imaginary:1 2nη:1 2n:6 stokes:3 about:1 central:1 extension:2 um2:1 dependence:1 o:1 unidirectional:1 soc:3 φxx:2 previously:1 unbounded:1 into:1 within:2 because:1 rising:1 operator:2 proportional:1 france:1 methods:1 log:6 u4:4 initial:2 question:1 u0:20 fast:4 u2:12 dispersion:3 quadratic:1 namely:1 ed:1 was:2 naturally:1 function:2 north:1 m3:1 form:4 some:2 m2:12 sketched:1 but:2 repeated:1 amplify:1 ux:1 regularized:1 ut:1 up:6 us:3 perturbatively:1 limit:8 utt:1 problem:4 called:1 originating:1 taylor:1 constant:3 int:1 τ2n:2 linearity:1 our:2 physical:2 again:1 functions:1 ematique:1 whereas:1 water:1 arctan:2 field:5 interested:1 details:1 conclusion:1 models:10 important:1 bounded:1 variable:4 nonintegrable:1 rajaraman:1 kraenkel:4 assume:1 physics:1 4n:3 4m:4 4k:7 time:5 starting:1 nuovo:1
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solv-int9710014.txt |@word sci:2 results:2 existing:1 scalar:3 proposition:1 expressions:1 preserves:4 analytic:1 mallet:1 paris:5 ıa:1 finally:2 tk:9 th:2 dressing:1 te:1 case:6 ginn:1 orthogonal:8 very:1 erale:1 geometrical:1 telling:1 matrices:1 school:1 ωti:1 solution:5 leave:1 solved:2 vector:2 anal:1 permutability:8 second:3 further:1 quite:1 theory:2 established:2 nonlinear:1 appear:1 invertible:1 expressed:1 version:1 sur:3 above:2 ˆi:1 ˆj:1 chelsea:2 contrast:1 satisfy:3 respectively:3 gabay:1 here:4 desired:1 les:2 china:1 sine:1 equations:18 appears:1 vectors:5 suitable:1 useful:1 combescure:1 santini:3 apply:3 schief:2 additive:1 would:1 prove:3 recalling:2 next:1 therefore:2 taken:1 associated:1 gauthier:1 type:3 more:1 company:2 ti:5 particular:3 known:2 orthogonaux:1 must:1 valued:1 ma:3 recall:1 equation:3 des:2 lincei:1 following:5 trans:1 example:2 proof:6 beijing:2 give:2 sitzungsber:1 dress:1 darboux:8 discussion:1 holds:1 how:1 those:1 polit:1 cicyt:1 levy:1 applications:2 data:13 compatibility:2 constants:1 transposed:1 introduced:1 clarkson:1 imply:1 whenever:1 lemmas:1 lines:2 spain:2 fundamental:23 order:1 multidimensions:1 indeed:2 satisfied:1 years:1 through:1 nets:6 its:4 le:3 thank:1 la:2 ln:2 solving:2 coordinates:4 absence:1 systems:9 wales:1 main:1 conversations:1 acklund:2 framework:1 they:3 rotation:1 now:4 βki:9 βkj:3 escuela:1 easily:1 several:1 equality:1 university:2 hamiltonian:1 2x:1 orthonormal:4 found:2 pb95:1 referred:1 en:2 ei:4 lam:16 ed:2 related:1 constitute:1 literature:1 our:2 out:1 matrix:4 space:3 vectorial:39 rd:1 reader:1 rm:1 rn:2 math:2 hydrodynamic:2 linear:2 ısica:1 departamento:2 standard:2 atica:1 york:2 definition:1 geometry:4 introduction:1 gordon:1 δij:1 universidad:2 hence:2 south:1 first:4 there:1 number:1 u0:4 done:1 given:11 cartesian:3 tangent:5 manakov:3 bologna:1 adjoint:1 system:3 appl:1 statement:1 cite:1 gives:3 para:1 continuous:1 coefficients:2 treatise:1 princeton:2 iteration:1 zero:3 historical:1 were:4 ber:1 rend:2 boston:1 matem:1 generalization:1 manner:1 conjugate:11 any:2 emes:1 liu1:1 latter:1 able:1 note:1 potential:2 take:1 so:1 coincide:1 canonical:1 shall:1 involving:1 letter:1 remarks:1 acknowledgements:1 soliton:2 observation:2 considered:1 later:1 coincides:2 points:2 deuxi:1 fact:1 show:3 supported:2 spaces:1 solutions:4 find:3 layout:1 lemma:9 only:2 ribaucour:25 integrable:2 oct:1 ges:1 do:2 get:2 syst:1 de:5 new:7 lattices:3 net:2 eme:1 determinants:1 differential:4 twice:1 ecnica:2 set:1 imposing:1 espa:1 aplicada:1 edition:2 see:4 result:6 recently:2 curvilinear:1 surfaces:5 estad:1 tsarev:2 liouville:1 grammian:1 state:1 between:1 geometria:1 limit:1 conditions:3 notice:2 terms:1 iterated:1 comp:2 transpose:1 however:1 analyzed:1 universitaria:1 amer:1 prescription:1 many:1 laplace:2 connection:1 proyecto:1 coefficents:1 expression:1 co:1 point:2 quadrilateral:3 dimensional:7 solv:2 sequences:2 moreover:1 basing:1 marchenko:1 transformations:18 basis:6 three:2 been:1 int:2 arxiv:1 inv:1 define:1 curves:1 func:1 present:3 applied:3 multi:1 means:2 value:2 will:1 euclidean:1 ıstica:1 suppose:1 orica:1 di:1 iterating:1 cons:3 thus:1 surface:2 iv:1 characterize:2 dual:1 different:2 gets:1 composition:4 independent:1 extended:1 parametrized:1 v1:4 v2:4 identity:1 prescribed:3 jonas:1 well:2 thought:1 coordinate:4 dimension:1 spherical:1 just:2 alternative:1 eorie:2 previous:1 villars:1 conjugates:1 preprint:2 kluwer:1 nas:2 zakharov:5 conclude:1 character:4 transformed:2 lett:1 theorem:9 transformation:46 zanichelli:1 background:4 press:1 using:3 like:1 follows:5 reduces:2 ees:2 yields:1 arbitrary:1 ξti:3 because:1 methods:1 classical:1 discrete:1 madrid:3 some:2 examples:1 choosing:1 describing:1 diverses:1 integration:1 assuming:1 eisenhart:3 prob:1 minimal:1 refer:1 equivalent:2 βij:11 βik:2 publishing:2 leurs:1 extension:5 important:2 continous:1 constraints:2 jacques:1 soc:1 ingenier:1 doliwa:4 integral:1 appropriate:2 acad:2 references:1 demoulin:1 initial:1 u1:1 transform:2 specifically:1 bianchi:2 editions:1 was:7 form:3 hj:2 hi:5 berl:1 partially:1 applying:1 up:1 us:1 ωi:5 konopelchenko:1 avaliable:1 un:1 ui:47 submanifolds:1 uk:2 uj:5 manuel:1 similar:1 called:1 constant:4 defined:1 abstract:1 describe:1 proven:2 denote:2 βji:4 again:1 functions:2 integrability:2 no:1 na:1 when:2 graduate:1 lezioni:1 mathematics:1 superposition:2 complutense:1 ξi:14 ξk:4 ago:1 independently:2 implies:4 pseudo:1 together:3 reprinted:3 requires:1
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solv-int9710015.txt |@word represent:5 partial:3 consider:8 chain:3 rev:1 varying:1 trigonometric:3 l11:2 four:1 scalar:9 subtle:1 computation:1 c2:5 consists:1 follow:3 remarkably:1 seemed:1 layers:1 certainly:1 compose:1 depend:4 clarification:1 advantage:1 b262:1 irrelevant:2 concerned:1 tr:1 good:1 tl:4 program:1 present:3 th:12 marks:1 tr1:2 worth:2 ingredient:1 r12:8 r13:5 straightforward:1 orthogonal:2 very:5 rise:5 translations:2 springer:1 results:3 literally:1 remarks:1 affect:1 difference:10 matrices:12 condition:18 leads:1 school:1 riemann:1 immediately:1 hamiltonian:5 did:1 turns:3 mb:5 itep:6 hereafter:1 magnet:4 involution:1 vector:6 antichiral:11 math:10 guiding:1 recall:4 a120:1 relation:1 refered:1 freidel:1 degeneracy:2 upper:2 grateful:1 direct:2 approximation:2 zero:16 summer:1 pass:2 further:1 canonical:2 bilinear:26 what:4 nonlinear:2 plays:2 stands:1 brackets:4 diag:1 section:8 selected:1 expressed:1 maillet:1 cell:3 version:5 intersect:1 lifshitz:1 t2:5 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solv-int9710016.txt |@word gt:2 gr:4 similarity:1 alg:3 equalities:1 particular:5 results:2 leads:1 scalar:4 proposition:6 montr:4 consists:1 clarified:1 consider:2 whose:2 inverse:1 depend:5 λin:1 tr:1 uniqueness:1 tm:1 tj:5 preserved:1 th:1 dressing:9 belonging:1 random:1 sherbrooke:1 h4b:1 rise:2 choice:1 valued:8 chooses:1 lecture:2 difference:1 matrices:22 deformations:11 condition:4 riemann:13 presented:1 notes:1 t2:6 solution:16 t1:8 large:1 involution:2 vector:3 interchanging:1 eigenvalues:3 ville:1 zn:2 wronskian:2 neighborhood:1 zi:15 zj:4 htw:2 second:2 plenum:2 further:4 reine:1 zs:2 spectral:11 3z:1 what:1 appear:3 invertible:2 rationally:5 giving:2 xσ:1 section:2 expressed:3 poles:6 above:3 3b:1 3a:1 consisting:6 satisfy:1 unbaum:1 full:1 simultaneously:2 degree:1 respectively:5 here:6 canonically:1 bakalov:2 resemblance:1 along:4 equations:19 z1:4 logarithmic:1 19b:1 obtained:10 suitably:4 vectors:1 resulting:7 loop:6 usually:2 suitable:3 relation:2 appropriately:1 via:2 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solv-int9710018.txt |@word represent:1 concept:1 lakshmanan:1 consider:5 chain:23 induces:1 magnetic:1 global:5 focus:2 leads:5 llm:1 go:2 remarkably:1 subjects:1 row:3 relationships:1 c0i:3 inverse:3 depend:1 tx:1 tt:2 tr:4 corrections:3 including:1 finally:5 preserved:1 elliptic:1 under:7 semenov:1 tc:5 sent:1 belonging:4 r12:13 r13:2 very:1 p0:1 dokl:2 trigonometric:12 witten:3 every:1 entries:2 exact:7 deformations:1 condition:5 generalised:4 school:1 immediately:1 presented:3 tra:4 proc:1 bonds:1 having:1 t2:2 solution:10 d2:1 t1:2 large:3 discrete:2 kondo:1 unrelated:1 interchanging:1 dealt:1 indices:1 c01:5 c02:5 unifying:12 trt:1 qism:5 zm:1 zn:1 el:1 hans:1 specially:1 disciplines:1 l2i:3 dealing:1 l2k:2 seventies:1 among:1 past:1 integrability:14 proved:1 further:1 cft:13 theories:2 expressions:2 canonical:3 spectral:6 established:1 nonlinear:7 plays:3 appear:1 witnessed:1 giving:5 deeply:1 section:1 celebrated:2 expressed:1 uniform:1 current:1 version:2 goes:2 droz:1 new:1 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