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solv-int9907001.txt |@word transitions:1 consider:4 brownian:1 results:12 proposition:2 expressions:5 replacements:1 calculate:1 show:9 γk:2 γj:2 uniqueness:2 present:1 under:1 analogous:1 presentation:1 mehta:4 ta:3 2rm:1 supported:1 wjk:1 straightforward:2 orthogonal:74 pichard:1 seemingly:1 choice:1 rm:2 matrices:16 school:1 presented:3 transmission:1 suffices:1 t2:1 applicable:1 louvain:1 science:1 eigenvalues:8 shows:11 noted:2 upper:2 facilitating:1 disordered:1 consistent:2 α2m:2 literature:1 sign:1 substitutions:1 zero:4 value:5 further:2 implemented:1 odd:10 zq:1 substitute:1 even:10 reconciliation:1 appear:1 giving:4 diag:1 sum:10 expressed:6 agrees:1 above:2 new:3 journal:1 multicritical:1 pioneering:1 degree:1 respectively:8 spacing:2 here:10 agreement:3 exceptions:1 expansion:2 represented:1 along:3 equations:1 transformation:4 knowledge:1 obtained:2 remark:3 generalizing:2 arc:1 allows:2 step:1 suggests:1 products:4 studies:2 involves:2 via:1 family:3 france:2 hermite:14 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solv-int9907002.txt |@word lagrangian:1 magnetic:1 results:2 scalar:1 commute:1 inverse:2 tu:1 editors:1 nonlocal:1 case:8 fax:1 rise:2 straße:1 dokl:1 choice:1 corollary:1 stays:1 discretizations:4 difference:5 matrices:1 condition:7 presented:1 solution:2 magnet:6 discrete:29 vector:2 der:1 upper:2 says:1 cfk:1 renormalized:1 takhtajan:1 sign:2 second:2 iσ3:1 iσ2:1 iσ1:1 theory:1 nonlinear:14 appear:1 giving:2 sum:1 version:3 above:3 new:1 ˆk:2 method:4 here:1 desired:1 groups:1 along:1 equations:10 implicit:1 obtained:2 shift:1 elaborate:1 vectors:2 periodic:3 resulting:1 smoke:1 fourier:1 via:2 projection:1 santini:1 unit:1 use:3 takes:1 would:1 nijhoff:1 next:1 ψj:6 ψk:51 therefore:1 associated:1 possible:1 more:4 linden:1 hoffmann:2 nkf:4 solitons:1 equipped:1 odinger:11 curvature:9 phone:1 berlin:3 basically:1 particular:1 known:2 hold:1 must:1 springer:1 ma:1 recall:1 equation:18 des:1 modified:1 mk:10 capel:1 following:8 modifies:1 proof:4 links:1 give:2 application:1 stereographic:1 tan:1 axis:1 normalize:1 needs:1 write:1 maps:1 instead:1 explains:1 sin:1 product:1 φ2k:1 derived:2 lax:1 date:2 fk:53 constants:1 introduced:5 natural:2 remember:1 korepin:3 su:3 sk:89 so:2 decreasing:3 representation:3 hashimoto:1 soc:2 interpreted:1 paper:1 japan:2 still:1 its:1 before:1 lf:2 derive:1 rapidly:3 thank:1 fix:3 lk:22 conjugation:2 writing:1 choose:1 covered:1 defining:1 acklund:1 sssr:1 they:1 oxford:1 rotation:5 now:4 february:1 several:1 always:1 university:1 hamiltonian:1 universit:1 2i:1 ifk:4 differential:1 doing:1 equivalence:8 literature:2 obtains:1 combining:1 our:2 extract:1 out:2 shown:3 jimbo:2 matrix:2 since:9 parallelogram:1 cancels:1 denotes:1 re:6 investigation:1 stud:2 ri:1 math:4 linear:2 normalized:1 diagonal:1 possibility:1 complicated:1 χ2n:1 van:1 r3:6 geometry:3 turn:2 technische:1 isotropic:6 view:2 first:3 initial:1 variables:5 another:1 ihm:6 ring:1 given:8 introduction:1 top:1 system:5 construct:1 their:3 normalization:1 scheme:1 gives:3 continuous:3 part:1 somewhat:1 showed:1 zero:10 preparation:1 doubly:10 were:1 curves:1 already:1 clearly:2 viewed:2 lie:1 angle:1 note:3 analogy:1 heisenberg:7 formulas:1 akad:1 multiple:1 most:1 pair:1 soliton:2 coincides:1 physica:1 points:1 χn:10 χm:11 χk:9 section:3 fact:5 show:2 rotating:1 miwa:2 gauge:14 solutions:2 find:1 writes:1 folded:1 written:3 should:1 going:1 factor:1 integrable:3 ksk:3 do:1 notation:1 get:5 de:1 famous:1 words:1 suris:3 lattices:1 geometric:2 quispel:1 evolution:6 arxiv:1 acknowledgments:1 twice:3 nauk:1 qk:2 qn:1 clarified:1 j0:4 see:4 result:2 discussions:1 forthcoming:2 bobenko:3 surfaces:1 state:1 ladik:9 between:1 boundary:3 conditions:4 email:1 terms:1 importance:1 attention:1 flow:1 comm:1 solv:1 jfk:1 both:1 cos:1 last:1 conclude:1 appeared:1 cf:2 quadrilateral:2 anti:1 lagrange:1 moreover:3 iψ:1 addition:1 been:1 reduction:1 pk:2 pn:1 ak:10 define:2 generating:2 sufficient:1 denote:1 irrelevant:1 applied:1 look:1 will:7 leaves:1 vk:40 thus:3 encouragement:1 iv:1 im:6 author:2 make:1 same:2 any:1 complex:3 modification:1 φk:1 independent:2 used:1 hand:4 v0:2 moment:1 purpose:1 ablowitz:11 identity:1 lower:2 schr:11 well:3 analysis:1 solve:2 model:18 possesses:1 usual:1 vˆk:3 less:1 being:3 underlying:1 identify:1 λk:6 λi:4 scattering:1 adding:1 nlse:8 sks:2 tim:1 point:1 seems:1 lattice:2 other:7 versa:1 theorem:9 solvable:1 transformation:5 iχ:1 iλ:6 around:5 term:3 period:1 background:1 press:1 using:1 aiming:1 helpful:1 like:1 yields:1 methods:1 seiler:1 some:1 transport:1 fachbereich:1 faddeev:1 slight:1 dropped:1 equivalent:9 although:1 substitution:1 identifies:1 chapter:1 getting:2 freedom:1 λsk:3 side:1 dependency:2 ensure:1 referred:1 slightly:2 discretization:4 into:1 integral:1 references:1 1lk:2 mkf:2 span:2 additional:2 there:3 transform:2 start:4 appl:2 way:4 function:1 complete:1 form:6 jun:1 triangular:2 but:7 russian:1 applying:1 versions:1 smooth:1 up:2 us:1 uk:7 problem:1 called:1 interplay:1 mechanics:1 constant:1 int:1 certain:1 abstract:1 singly:1 general:2 single:1 defines:1 again:2 functions:1 nk:3 no:1 mathematik:1 field:1 valid:1 izergin:1 juni:1 models:1 problems:1 prepared:1 gets:3 implies:1 vice:1 physics:1 required:1 time:6 once:1
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solv-int9907003.txt |@word limited:1 lakshmanan:1 represent:1 leads:3 eds:1 c2:1 guwahati:4 follow:1 inverse:5 technique:2 send:1 compensate:1 stable:4 include:1 fax:2 advantage:1 bilinear:1 electron:1 condition:1 unlike:1 transmission:5 turns:2 solution:20 solved:1 adjust:2 gauge:3 hasegawa:2 consistent:1 prediction:1 pulse:2 limǫ:1 rate:4 dynamics:3 odd:4 spectral:1 nonlinear:15 plays:1 indian:2 3m:1 3c:1 new:10 3a:1 solitonic:1 method:7 satisfy:4 simultaneously:1 respectively:1 gener:1 desired:1 operating:1 kilometers:1 along:2 equations:3 obtained:6 reshaped:1 institute:2 involved:1 leaves:1 studied:1 trial:1 makes:1 via:1 useful:1 ipx:1 conventional:1 takes:1 would:1 few:2 m3:1 m2:4 type:3 theoretical:1 more:4 successful:1 solitons:8 under:1 odinger:6 phone:2 springer:1 locked:1 equation:11 values:5 following:3 chosen:3 neglected:1 high:1 o:1 needs:2 ib:1 nontrivial:2 parameter:1 rise:1 may:3 earlier:1 containing:1 applications:1 plane:1 lax:1 short:1 dynamical:2 third:2 ss:1 light:2 spectra:1 so:1 sc:1 order:10 withing:1 indeed:1 over:2 satisfied:1 stability:2 paper:2 pulses:3 existence:2 ieee:1 group:6 thank:1 ln:1 interesting:3 stimulated:4 forms:1 absence:1 choose:2 mail:2 main:1 eventually:1 them:1 introduce:1 band:1 effects:1 now:2 discuss:1 dielectric:1 term:2 kerr:3 mode:1 found:2 2j:6 arxiv:1 financial:1 series:4 related:2 equivalence:1 frequency:1 quantum:1 operatorial:1 special:2 out:2 emerges:2 shown:2 since:1 rev:3 increase:1 fellowship:1 acting:2 daniel:1 math:1 8j:1 earns:1 telecommunication:1 envelop:2 quite:2 e0:5 care:2 hc1:4 impose:1 motion:2 gordon:2 already:2 cj:5 another:3 q02:4 given:3 kodama:1 needed:1 relations:2 their:1 tod:1 gives:1 optical:14 coefficients:12 distance:3 unfortunately:1 painleve:1 sech:5 india:3 enables:1 powers:1 function:1 motivation:1 vector:1 20a:1 20b:1 seen:1 zero:1 convenient:1 self:2 pivotal:1 take:1 even:4 play:1 added:1 electric:1 systems:1 thoroughly:1 most:1 significant:1 class:4 soliton:10 surprising:1 later:2 exp:2 physics:2 fact:1 nls:9 implying:1 attempts:1 relation:7 solutions:14 substituting:2 trivial:4 find:1 fibre:7 parameters:2 only:2 notation:1 remedy:1 cannot:2 words:1 3b:1 evolution:1 differential:1 qe:1 tappert:2 through:2 coefficient:4 set:1 exists:3 observed:1 namely:1 recently:1 subsequent:1 currently:1 propagates:1 pump:2 various:2 c2j:9 conditions:4 speed:1 notice:3 csir:1 terms:4 however:2 key:1 solv:4 providing:1 last:3 many:1 propagation:8 context:1 experimental:1 among:1 cm:3 cl:3 simple:2 pole:1 fibres:1 transformations:4 pz:1 three:2 been:3 acheived:1 interest:1 utilizing:1 lett:7 6a:2 6b:2 xxx:1 assert:1 observe:1 c3:1 2ǫm:1 c1:8 c0:3 present:2 case:2 stolen:1 laser:1 look:1 gnt:3 value:1 heidelberg:1 will:3 invoking:2 ultra:2 study:1 opt:4 jpn:1 almost:3 thus:4 itself:1 conf:1 ernet:2 technology:2 different:3 recursion:8 demands:1 same:4 unity:1 complex:1 several:1 higher:11 used:1 see:2 singapore:1 effect:5 hand:1 schr:6 analysis:1 solve:1 consistency:1 become:3 dimension:1 less:3 being:1 obtain:2 scattering:10 interestingly:1 conclude:1 smith:1 improvement:1 location:1 input:3 transformation:4 real:3 nandy:4 iη:1 govt:1 world:1 loss:5 like:3 signal:2 e02:2 arbitrary:6 multiplicative:1 output:1 stationary:1 reduces:2 methods:1 provided:2 describing:2 lead:2 propagating:1 proc:1 power:3 equivalent:1 shifting:1 explicitely:1 intense:1 commutative:2 kundu:1 scott:1 consequently:3 soc:1 localised:4 communication:4 into:1 h1:2 obtaining:1 due:1 references:1 determine:1 operator:1 additional:1 support:1 long:3 dispersion:3 appl:2 lot:1 raman:6 form:4 jun:1 but:1 hc:1 considerable:1 gedalin:1 made:2 consequences:1 us:4 liouville:1 verification:1 backlund:1 similar:1 called:1 int:5 abstract:1 direction:1 general:2 exist:1 satsuma:1 integrability:1 no:1 whereas:2 field:2 other:1 role:2 department:2 conclusion:1 time:3 important:2 structure:1 faster:1 assume:1 ghosh:4 investigated:1 sasa:2 hirota:1 starting:1
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solv-int9907004.txt |@word homomorphism:1 consider:2 chain:19 localizes:1 madsen:1 global:2 sca:1 focus:1 existing:1 leads:2 scalar:2 follow:1 expressions:3 gl:2 m2l:27 preserves:1 inverse:4 terms:12 calculate:1 superspace:19 b389:1 posteriori:1 nonlocal:12 recurrence:4 tl:9 tk:11 th:28 dressing:11 analogous:2 presentation:1 case:11 conjecture:1 iul:4 abelian:2 very:6 account:6 wave:2 dzd:5 entries:2 difference:1 manin:5 condition:5 iuv:1 four:1 partially:1 hamiltonian:38 sdet:3 t2:4 solution:5 t0:1 t1:3 discrete:14 math:11 recall:3 indices:1 study:1 superalgebras:2 inspection:3 ρk:6 programme:1 work:2 force:1 jacobians:1 consistent:12 l2l:21 literature:1 second:12 folowing:1 j22:10 involution:4 concludes:1 rectangular:1 odd:2 theory:1 spectral:7 aim:2 what:4 nonlinear:3 t2l:1 brackets:5 trivial:1 section:31 toppan:2 brief:1 expressed:1 hereditary:2 a231:1 subspaces:1 krivonos:10 new:17 method:1 exercise:1 satisfy:4 q1:2 led:1 ibid:2 respectively:7 realizations:1 component:1 here:5 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solv-int9907005.txt |@word ito:10 evolutionary:1 oevel:1 proposed:3 hierarchy:3 pointed:1 supported:1 valuable:1 four:1 karasu:4 paper:1 relation:3 japan:1 satisfies:1 research:1 urses:5 fokas:1 nar:1 based:2 thank:1 infinitely:2 tubitak:1 actually:1 δhn:4 only:3 belongs:1 systems:4 easy:1 jacobi:1 integrable:3 east:1 scientific:1 therefore:2 bii:3 between:3 springer:1 admitting:1 choice:1 ankara:1 modification:1 made:1 dx:3 mathematics:1 using:1 dt:1 2nd:1 bringing:1 nor:2 possess:1 2v:4 like:1 semi:1 hamiltonian:18 δv:1 proc:1 university:1 arxiv:1 δh1:2 differential:1 either:1 arbitrary:1 found:1 its:1 right:1 density:1 drinfeld:3 δu:1 constitute:1 ara:1 second:1 result:2 discussions:1 kdv:1 out:3 given:2 gradient:1 abi:3 furthermore:1 new:1 rev:1 functionals:1 hereditary:1 symmetric:1 written:1 does:4 fuchssteiner:2 conjectured:1 prog:1 contrary:1 neither:2 ref:2 correct:1 math:2 satisfy:1 vx:3 recently:3 olver:3 degree:3 pletely:1 attention:1 bi:13 here:2 admits:3 reported:2 bv:1 york:1 although:1 solv:1 equations:2 fordy:4 stage:1 obtained:1 sobolev:1 applications:1 technical:2 many:3 studied:2 generated:1 side:1 ab1:2 admit:1 due:1 context:1 identity:1 texts:1 introduced:1 com:1 first:2 soc:1 groups:1 point:1 h2:2 h1:3 functional:4 system:30 infinite:1 bihamiltonian:1 been:2 novosibirsk:1 sov:1 operator:11 moreover:1 noticed:1 turkey:2 arts:1 rosenau:2 would:1 skew:1 there:2 three:1 u3:1 u2:1 vol:2 finding:1 proposes:1 observations:1 ed:1 was:2 gives:1 roy:2 form:2 2vd:2 quantities:3 operators:2 jun:1 but:1 construction:1 particular:1 known:1 2vx:2 vxxx:1 partially:1 multi:1 claims:3 ux:2 showed:2 dodd:2 ut:2 uv:3 6uux:2 2ux:4 value:1 work:2 printing:1 values:1 error:1 following:1 my:1 russian:1 claim:1 generate:1 4u:3 proved:1 coupled:1 int:1 abstract:1 sokolov:3 general:1 middle:1 conserved:4 vt:2 council:1 claimed:1 uxxx:2 check:1 ohs:22 incorrect:2 satsuma:6 wilson:2 author:7 recursion:8 pp:1 when:1 lett:10 same:1 graduate:1 note:1 sciences:1 other:1 hs:1 department:1 instead:1 theor:1 conclusion:1 references:1 rise:1 see:1 lie:1 i1:1 i3:4 i2:1 hand:2 most:1 wrong:1 lax:2 faculty:1 pair:2 structure:8 recent:2 observation:3 arising:1 later:1 well:1 physica:2 original:3 levi:2 points:1 expression:1 hirota:6 representation:1 physics:1 possesses:2 fact:1
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solv-int9907006.txt |@word neighbors:1 managed:2 chain:6 osp:10 results:5 four:6 scalar:1 follow:1 gl:2 contributions:1 row:1 devoted:1 content:1 pointing:1 prσ:6 irrelevant:1 concerned:3 finally:2 program:1 tk:1 th:1 fermionic:1 r12:7 zhang:5 far:1 implicitly:1 conditions:7 wave:2 electron:2 valued:1 difference:2 matrices:14 condition:5 leads:3 hamiltonian:5 tra:6 turns:2 sklyanin:3 t2:1 solution:7 t1:1 kondo:2 math:10 eigenvalues:1 superalgebras:1 configurations:2 possibility:3 jhep:1 specially:1 delius:1 sin2:1 literature:2 cosh:22 second:4 further:3 jilin:1 l207:1 spectral:2 index:1 r122:1 plays:1 brien:1 trivial:1 section:9 new:4 method:1 body:1 condensed:1 eikj:2 degree:1 exchange:1 respectively:1 here:2 behaviour:3 explore:1 bariev:1 china:1 ansatz:18 sinh:45 sine:3 equations:6 appears:1 obtained:3 remark:3 tunneling:2 study:3 allows:1 ourself:1 accomplished:1 periodic:1 permutation:1 identity:1 suitable:1 formulated:2 useful:1 extra:3 sgn:2 circumvent:1 denotes:3 use:1 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solv-int9907007.txt |@word consider:2 remarkable:1 fuctions:1 gx:4 four:1 commute:2 consists:1 scr:1 devoted:1 whose:1 inverse:2 depend:1 finally:1 those:2 dressing:18 very:3 3s2:1 putting:2 experimentally:1 exact:1 iut:3 generalised:1 bxx:2 presented:1 dif:1 ferential:1 solved:1 vector:2 plete:1 small:2 3b:1 akns:1 10b:1 consistent:1 10a:1 integrability:2 evaluated:1 zz:7 chen:2 further:3 substitute:1 zs:22 even:2 aim:1 nonlinear:7 appear:1 invertible:3 tsuchida:1 3s:1 section:11 expressed:1 current:1 above:1 3c:1 new:7 3a:1 solitonic:1 method:25 3d:1 satisfy:2 kaup:1 lee:1 degree:1 respectively:3 here:3 scribe:1 q14:2 ei:8 q11:2 q13:2 q12:2 concluding:2 sogo:1 marchenko:2 equations:40 obtained:2 luther:1 institute:1 birefringent:1 studies:2 9i:1 9h:1 9k:1 9j:1 useful:1 gluons:1 9a:2 9c:2 9b:2 9e:2 9d:2 9g:1 9f:1 propagations:1 apply:1 total:1 imaginary:1 unit:2 h1x:4 use:2 would:2 prove:1 eρ:4 eσ:2 next:2 therefore:2 iαk:2 means:1 volterra:1 type:26 theoretical:2 more:1 introducing:1 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solv-int9907008.txt |@word japan:1 consider:28 chain:1 similarity:1 rx:14 separates:1 commun:2 results:9 pfaffians:1 acad:1 leads:2 p02:3 p01:5 proposition:6 p07:1 p06:1 p05:1 edu:1 follow:2 alt:7 denotes:1 causes:1 row:3 relationships:7 certainly:1 dimensionality:1 referring:1 paris:1 financial:1 tr:5 contained:7 send:1 supported:2 finally:5 behave:2 tj:1 arisen:1 under:7 analogous:3 mehta:5 eliminate:2 alternating:2 p2:21 conjecture:3 random:19 2rk:8 straightforward:3 orthogonal:38 very:3 desired:2 end:1 keeping:1 choice:3 endpoint:8 every:7 additional:1 entries:3 affect:1 matrices:27 condition:1 χd:2 entire:3 gue:1 presented:1 induction:3 t4:2 dodd:4 solution:6 correct:2 vector:1 math:13 eigenvalues:35 20a:1 rk:5 noted:2 possiblity:1 uel:3 zn:3 uen:11 says:2 ten:1 sinh2:1 p04:1 direct:1 sign:6 fold:1 second:12 subtle:1 choices:1 ueq:2 expressions:1 quite:2 linear:26 spectral:1 what:4 goodman:1 stands:1 giving:3 diag:1 sum:5 bdi:1 symbolically:1 expressed:3 find:28 orthogonaux:1 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solv-int9907010.txt |@word consider:2 magnetic:2 global:4 results:1 four:2 eds:1 scalar:1 edu:1 gl:1 cases:1 whose:1 inverse:2 graph:1 kβ:2 quasi:7 kη:5 present:1 elliptic:2 under:2 worth:1 divergent:1 applied:2 r14:12 supported:1 r12:16 r13:16 zhang:11 rise:1 coloured:3 quesne:1 electron:1 entries:1 difference:14 matrices:14 condition:1 solves:1 hamiltonian:9 irreducible:2 solution:19 convenience:1 vector:1 demonstrated:1 section:2 indices:1 superalgebras:2 originally:1 qism:5 delius:3 integrability:3 value:1 odd:1 spectral:8 established:2 appear:2 sum:1 suspect:1 above:13 new:1 change:1 method:3 satisfy:2 full:2 degree:2 respectively:2 here:7 ansatz:2 groups:1 equations:6 appears:1 z2:7 obtained:8 remark:1 eij:1 shift:3 study:2 studied:1 allows:1 couplings:1 periodic:3 procedure:2 permutation:2 adopting:1 suitable:1 makes:1 via:1 mcguire:1 family:4 jrl:1 addressed:1 otherhand:1 research:1 use:1 charge:1 additive:1 eψ:5 would:1 commun:2 h0:4 stated:1 finally:1 next:1 nucl:3 m1:2 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solv-int9907011.txt |@word φ1j:4 consider:3 funct:2 induces:1 results:4 leads:3 scalar:9 proposition:7 types:1 follow:1 expressions:1 contributions:1 sung:1 localized:8 inverse:17 depend:1 analytic:1 uniqueness:2 those:1 under:6 include:1 norm:3 proved:2 string:1 orthogonal:2 implicitly:1 connects:1 wave:5 resonant:1 capillary:1 iut:1 condition:9 riemann:1 solves:2 presented:1 did:1 proc:1 applicable:1 large:1 discrete:10 rj:3 small:5 eigenvalues:15 anal:2 akns:1 zj:12 prediction:1 sign:1 rate:1 rigorous:1 dynamics:2 substitute:1 linear:2 spectral:30 established:1 nonlinear:7 appear:2 section:8 localization:1 near:2 expressed:9 henceforth:1 poles:1 above:3 sup:1 new:4 apply:1 method:1 contrast:1 satisfy:3 eikj:1 fiz:1 respectively:1 component:2 residual:1 here:8 water:1 reported:1 operating:1 free:1 concluding:2 ratio:2 along:1 equations:17 appears:2 obtained:2 weinstein:1 study:1 studied:2 products:3 identity:3 resonance:1 fourier:2 changes:1 private:1 uzz:1 support:3 establish:1 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solv-int9907012.txt |@word neighbors:2 represent:2 involutory:1 partial:1 consider:13 similarity:3 parallelogram:3 equalities:1 datum:6 results:7 leads:15 ψ1i:2 scalar:6 proposition:28 edu:1 consists:5 ward:2 row:1 devoted:2 whose:11 γy:1 inverse:1 depend:1 reformulate:1 tv:1 iii:7 subjected:1 equivalence:2 nonlocal:3 tn:6 γj:1 finally:11 chapt:1 tj:127 tk:34 th:9 ti:229 decomposition:3 analogous:3 presentation:1 norm:1 applied:3 belonging:1 proved:1 expressing:2 straightforward:3 orthogonal:10 very:2 bogolyubov:1 reader:1 translations:1 ρc:4 dokl:2 choice:6 corollary:16 under:1 kashiwara:1 formula:10 discretizations:1 ui:2 june:2 difference:6 matrices:4 rn:2 condition:21 arrange:2 four:2 dubrovin:2 riemann:2 solves:1 presented:6 turns:4 t2:4 solution:12 t1:10 large:5 discrete:20 vector:11 math:10 splitted:1 inscribed:3 gauge:1 warszawa:1 upper:2 zn:22 sapienza:2 evaluating:2 coordonn:1 transversally:3 conjugu:1 za:1 translating:1 go:2 integrability:13 cyclic:1 dordrecht:1 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solv-int9907013.txt |@word partial:1 pointing:1 results:4 four:2 eds:2 proposition:7 edu:1 follow:1 chain:1 reformulate:2 paris:1 segments:1 finally:1 tj:44 th:3 ti:48 orthogonal:1 erale:1 reinterpret:1 corollary:1 rm:1 difference:3 condition:1 presented:3 turns:1 t2:15 t1:14 deals:1 discrete:22 warszawa:1 des:1 za:1 imply:1 reine:1 linear:2 bilinear:1 nonlinear:1 section:2 version:2 sur:1 intersect:1 new:2 net:2 satisfy:2 notions:2 applies:1 component:2 here:2 l21:1 tangent:4 groups:1 q12:1 directions:1 teoretycznej:1 along:1 equations:13 z2:5 obtained:1 suitably:1 shift:1 vectors:5 allows:2 identification:2 a21:7 pinkall:1 scaled:2 santini:6 schief:1 would:2 coupled:3 negative:1 therefore:4 volterra:3 more:1 fokas:1 under:1 berlin:1 particular:1 known:1 projective:8 iii:3 springer:2 ma:3 ρi:8 equation:29 ρj:1 following:7 figure:6 give:2 egorov:1 degenerate:2 ratio:3 goal:1 darboux:2 orthogonality:1 pure:1 symposium:1 circular:2 lam:5 τij:1 mapping:2 applications:1 date:1 representations:1 data:2 lines:1 so:2 allow:1 representation:3 order:1 interpretation:6 hierarchy:3 indeed:1 soc:2 paper:2 through:1 mentioned:1 existence:1 nets:6 its:1 le:1 thank:1 la:1 chosen:1 interesting:1 affine:1 coordinates:1 forms:2 systems:2 tors:1 mail:1 defining:1 them:1 acklund:1 introduce:2 scaling:2 they:1 multidimensional:8 fizyki:1 invariants:4 level:1 each:1 found:3 uniwersytet:1 side:2 rims:1 mikhailov:1 differential:1 independent:1 related:1 elementary:6 toda:13 expect:1 quantum:1 out:2 shown:1 jimbo:2 space:2 since:2 denotes:1 aji:13 geom:1 formula:1 math:3 theory:7 governing:1 standard:1 proportionality:2 definition:5 geometry:6 manakov:1 int:3 invitation:1 consequence:1 first:2 xj:4 formulas:3 xi:6 conjugacy:1 interchange:1 given:9 rewritten:4 introduction:1 1x:1 adjoint:2 system:17 their:4 assumption:1 expand:1 calculations:2 alonso:1 coefficients:20 sections:1 second:1 collinear:1 jpn:1 generalization:1 conjugate:8 any:1 petviashvili:1 convenient:2 lij:33 potential:3 take:1 analogy:1 kac:1 schlesinger:2 opposite:1 instytut:1 but:1 acknowledgements:1 soliton:1 observation:1 fills:1 hi:7 ho:1 show:3 reductions:4 multicomponent:2 miwa:2 spaces:1 gauge:3 keywords:1 analogue:1 find:2 based:1 should:1 only:2 integrable:12 do:1 above:4 notation:1 de:2 cannot:1 lattices:18 kadomtsev:1 arxiv:1 roy:1 leur:2 london:1 isothermic:1 view:1 respect:2 warszawski:1 see:3 result:2 terms:3 bobenko:1 analog:6 surfaces:2 satisfying:2 nature:1 eorie:1 symmetric:2 various:1 between:1 invariant:4 geometric:9 notice:2 recently:1 missing:1 analogues:1 comm:1 solv:3 article:1 jetp:1 suggested:1 both:2 essentially:1 last:1 many:1 kji:2 according:1 laplace:29 became:1 among:1 point:2 simple:2 quadrilateral:30 dimensional:12 represented:1 sequences:1 moreover:1 basing:1 kp:3 pp:2 described:1 transformations:9 due:1 been:1 mart:1 defined:1 describes:1 basic:1 meeting:1 pl:1 define:4 direction:1 corresponding:4 ınez:1 present:2 fuw:1 nski:1 euclidean:1 sli:1 aij:9 property:1 ix:1 planar:3 studied:1 played:1 non:3 surface:1 iv:3 ii:2 ij:6 id:1 sauer:1 containing:1 author:1 formulations:1 cross:3 same:1 angew:1 rules:1 quadrilaterals:6 qji:6 singapore:1 hand:1 kij:10 potentials:1 identity:1 poland:1 kashiwara:1 solve:1 coordinate:1 position:1 dimension:1 reviewed:1 transforms:1 using:3 rotation:11 villars:1 zakharov:1 lattice:30 transformed:2 lett:5 transformation:11 generalized:2 read:2 know:1 integer:1 intersection:1 lji:2 like:1 right:1 classical:4 sequence:13 cons:1 cr:4 provided:1 describing:2 connecting:1 proc:2 scientific:1 equivalent:1 medina:1 gauthier:1 planarity:3 central:1 world:1 konopelchenko:1 organizers:1 discretization:1 doliwa:9 into:1 three:1 en:1 references:1 operator:3 proportional:3 k12:1 van:2 support:1 transform:1 quadratic:1 way:3 forward:3 was:5 function:12 form:10 jul:1 hj:4 construction:1 numeric:1 line:2 made:2 cie:1 versions:1 us:2 different:5 ul:1 submanifolds:1 pm:1 called:5 strongly:1 qij:27 homogenous:2 abstract:1 describe:1 general:1 defines:1 again:1 functions:4 integrability:1 nas:3 points:4 role:1 conclusion:1 a12:9 variation:2 meaning:2 important:2 sides:1 implies:2 factors:4 together:1 adam:1 hirota:16 backward:8 original:4
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solv-int9907014.txt |@word aided:1 partial:1 consider:8 chain:1 φ1c:1 results:7 segr:1 four:3 eds:2 proposition:15 generalize:2 edu:1 crete:1 2r2:2 row:2 polarity:1 whose:4 preserves:1 lkj:1 aji:3 paris:2 subjected:1 canonical:1 containing:1 tn:1 finally:4 tm:1 tj:44 tk:8 th:12 ti:90 must:1 xti:2 degeneration:1 summarizes:1 case:4 comm:1 string:1 orthogonal:4 preceeded:1 bilinear:2 translations:1 conditions:1 splitting:2 corollary:4 every:1 formula:3 discretizations:1 ma:3 difference:4 deformations:1 condition:5 arrange:3 identity:1 annihilated:1 presented:1 turns:3 t2:8 solution:7 t1:11 discrete:19 vector:10 math:4 indices:1 gauge:1 warszawa:1 rk:1 permutability:4 dis:1 zn:11 sapienza:2 coordonn:1 za:1 consists:3 integrability:12 cyclic:1 pass:1 reine:1 linear:9 spectral:2 3z:1 nonlinear:4 sub:1 dept:1 fact:1 section:8 analogously:1 rome:1 version:1 en:1 sur:2 above:6 new:13 net:6 congruences:5 method:2 sli:1 satisfy:10 notions:2 component:5 diagonal:3 june:1 objects:1 tangent:16 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solv-int9907015.txt |@word represent:1 partial:1 chain:3 funct:1 lagrangian:3 global:1 reversibility:1 eds:1 hurtubise:1 comments:1 go:1 expressions:3 gi:1 c0:1 remarkable:1 zone:1 tr:1 elliptic:7 under:7 geom:1 analogous:1 applied:3 conjecture:1 expressing:1 far:1 construction:1 springer:3 choice:4 entries:2 tridiagonal:1 difference:11 matrices:5 condition:2 generalised:1 dubrovin:23 riemann:4 level:2 notes:1 sklyanin:5 list:1 solution:1 formule:1 large:1 discrete:49 vector:6 interpolating:1 eigenvalues:1 anal:1 refer:1 des:1 periodicity:1 enti:1 consistent:1 seventies:1 direct:1 sign:3 integrability:4 perspective:1 incidentally:1 dynamics:6 odd:4 µg1:2 linear:3 even:5 trick:1 what:4 nonlinear:6 appear:2 brackets:2 giving:1 section:4 mechanics:1 expressed:3 poles:6 decade:1 reconstruction:2 new:2 3a:1 method:2 coefficient:1 evolving:1 full:2 respectively:1 here:2 papageorgiou:3 canonically:1 leeds:4 expansion:1 separation:20 consideration:2 along:3 equations:46 implicit:1 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solv-int9907018.txt |@word lakshmanan:1 consider:6 chain:2 vectorial:1 scalar:2 devoted:1 preserves:1 inverse:1 ver:1 tt:1 technique:1 helps:1 analogous:1 far:2 putting:1 matrices:7 condition:9 school:1 induction:1 applicable:1 discrete:4 math:6 gauge:8 anal:1 shows:2 noted:1 10b:1 takhtajan:1 consistent:3 10a:1 second:7 further:1 what:1 nonlinear:1 section:3 brief:1 xτ:1 agrees:1 version:5 above:2 new:3 satisfy:2 ichikawa:5 component:9 here:8 xξ:3 concluding:2 sogo:1 equations:1 galilei:1 obtained:3 study:1 vectors:1 regardless:1 9a:1 9c:1 9b:1 unit:1 clifford:2 ψx:1 prove:3 remains:1 jpn:7 ψt:1 ψn:4 type:4 known:2 derivation:1 jpsj:1 tokyo:3 science:2 equation:18 mn:4 14b:1 give:2 sokolov:3 sn2:2 14a:1 linearized:3 s3:3 s2:5 discussion:1 s0:26 sst:1 parameter:3 algebra:2 derived:2 lax:16 representations:2 parallel:1 λ2j:1 natural:1 outline:1 effective:1 explicit:2 st:3 sk:4 perform:1 so:1 sn:29 representation:9 order:1 noteworthy:1 hierarchy:9 satisfied:1 years:1 course:1 paper:4 through:1 differs:1 japan:1 satisfies:3 tsn:1 derive:1 ln:5 interesting:1 systems:13 mail:1 s1:7 correspondence:2 introduce:1 scaling:1 takayuki:1 eigenvalue:15 february:1 university:1 2f:1 each:1 2m:23 soc:7 difficult:1 2j:1 square:1 ei:7 ek:3 ej:3 ed:1 related:2 society:1 eq:20 shown:3 matrix:9 space:2 is2:2 since:1 rx:3 research:1 rm:2 ref:2 rj:4 rk:7 theory:1 found:3 approaches:1 e0:1 pairs:1 r1:1 starts:1 konno:5 ist:1 motion:3 manakov:1 promotion:1 first:1 variables:3 xx:6 2δij:1 open:1 size:1 given:9 checked:1 rewritten:1 introduction:1 eqs:6 system:27 construct:1 compatibility:7 their:2 appl:1 brevity:1 identity:1 statement:1 scheme:1 gives:1 way:1 recursively:4 continuous:2 17b:1 17a:1 authors:1 x2:1 x0:2 x5:1 kulish:1 sections:1 integrability:1 preparation:1 powers:1 sty:1 generalization:12 manner:1 any:1 bunkyo:1 sj:4 k3:1 instance:1 take:1 heisenberg:6 begin:1 takhtadzhyan:1 multiple:3 shall:1 s30:6 connected:2 remarks:2 why:1 yamilov:1 soliton:1 pohlmeyer:1 clear:1 coincides:2 typeset:1 ku:1 physics:2 fact:4 laws:2 probl:1 show:1 reductions:1 relation:3 expressed:3 keywords:1 substituting:2 find:4 q1:1 should:3 experiment:1 integrable:7 do:3 ssx:1 viewpoint:1 meanwhile:1 familiar:1 dx:1 interpreted:3 qr:1 continuum:1 qx:3 arxiv:1 yield:1 investigate:1 semidiscrete:1 iqt:1 qk:7 qj:4 qm:2 view:1 set:3 clarified:1 ishimori:2 irt:1 various:1 between:4 progress:1 boundary:1 choose:1 terms:2 jp:1 however:1 solv:1 uτ:1 ferromagnet:6 received:1 essentially:1 last:1 0b:1 chosen:1 connection:1 arbitrarily:1 among:1 point:1 simple:6 anti:2 constant:1 considering:2 jetp:1 commutative:2 basis:2 due:2 been:3 reduction:4 define:1 corresponding:1 xxx:1 miki:1 func:1 olver:1 spin:2 present:2 case:3 multi:15 novel:1 cast:1 wki:17 coupled:8 iq:1 ir:1 thus:2 ii:4 examined:1 vx:2 s2j:1 s2k:2 same:1 s2m:10 pauli:1 higher:7 independent:4 singapore:1 flows:4 purpose:1 infinite:1 expand:1 recent:1 acknowledgement:1 well:2 s20:2 i2m:13 components:3 monet:1 just:1 being:1 obtain:7 world:1 hongo:1 previous:1 k2:2 zakharov:1 except:1 lattice:1 transformed:3 lett:3 easy:1 5a:1 transformation:11 5b:1 explained:1 easily:1 iζ:2 using:1 vξ:1 semi:8 follows:2 reduces:1 yields:1 reduced:1 replacement:1 because:2 often:1 2iζ:1 some:1 l15:1 does:1 scientific:1 use:3 substitution:1 fordy:2 integers:1 extension:1 constraint:5 λsn:1 wadati:12 o:12 extensions:1 introduced:1 discretization:7 into:8 appropriate:2 sov:1 there:5 u1:1 noticed:1 dispersion:3 conservation:2 lot:1 call:1 was:2 function:1 complete:1 form:1 jul:1 hf:12 commun:3 ut:2 up:1 us:2 limit:1 problem:15 ac:1 proved:2 int:1 flow:10 fellow:1 single:1 formulation:6 sxx:3 check:1 constructed:1 no:1 graduate:1 field:7 other:1 department:1 theor:2 elements:1 hirota:1 problems:2 15a:1 sx2:2 15b:1 generalized:3 rq:1 assume:2 time:3 tsuchida:7 4b:1 original:6 4a:1
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solv-int9907019.txt |@word consider:5 results:2 invent:1 leads:2 eds:1 scalar:1 row:3 inverse:2 calculate:3 paris:1 description:1 tu:3 tr:4 tn:4 tm:1 those:2 lkp:19 p2:2 straightforward:2 g0:1 very:1 αri:1 αrk:1 αrn:2 entries:4 difference:2 matrices:2 school:1 solves:3 hamiltonian:33 turns:2 discrete:2 science:1 unifying:1 abbreviated:1 work:2 concise:1 dealing:1 direct:1 second:13 further:1 canonical:16 residue:3 nonlinear:1 plays:1 letts:1 invertible:1 section:7 celebrated:1 rm:16 version:4 above:5 international:2 method:1 respectively:3 here:1 desired:1 china:3 address:1 represented:1 equations:7 obtained:1 shift:5 studied:1 poisson:8 dickey:3 hospitality:1 via:1 use:2 prove:6 next:1 comparing:1 linear:3 therefore:2 memory:1 means:3 type:1 theoretical:2 more:1 introducing:2 qdn:5 sokolov:1 operators:6 qdm:1 known:1 cases:3 hold:1 permits:1 recall:1 equation:3 mn:5 modified:2 salam:2 following:8 proof:3 beijing:2 calculation:1 organized:1 trieste:1 sense:1 rather:1 di:2 how:1 ordinary:1 parameter:2 map:23 fr:1 intended:1 algebra:2 may:1 bkm:3 lax:3 fordy:1 natural:1 lou:1 so:4 pleasure:1 holds:1 hierarchy:37 indeed:3 satisfied:1 paper:4 mentioned:1 irene:1 its:5 le:2 thank:2 maps:2 ln:18 interesting:1 solving:1 lt:1 systems:2 derivative:1 main:1 conjugacy:1 asterisque:1 introduce:5 they:1 identically:1 now:5 easily:1 university:1 presented:1 found:3 baxter:1 differential:1 kℓ:2 extended:5 our:4 ew:11 out:3 shown:2 matrix:10 since:3 denoted:1 formula:2 rn:31 ri:5 math:10 rk:2 foundation:1 theory:1 standard:1 complicated:1 starts:1 could:1 omit:1 turn:1 int:1 ltn:2 first:17 miura:22 variables:1 clear:1 done:1 another:1 given:6 introduction:1 system:4 construct:1 echet:1 intermediate:1 calculations:1 structures:19 gives:1 ictp:1 mining:1 continuous:3 kupershmidt:10 part:3 coefficients:1 cheng:1 marshall:1 zero:1 were:2 seam:1 boston:1 need:3 seen:2 cumbersome:1 constrained:1 orders:1 wilson:1 liu:3 take:1 jacobian:1 new:3 coincide:1 δni:1 calculus:4 exactly:1 trace:1 centre:2 reach:1 birkh:1 algebraic:1 but:4 formulae:2 acknowledgements:1 professor:1 tensor:3 soliton:2 δn0:1 considered:2 calculated:1 flow:3 yang:1 mailing:1 oevel:10 show:3 supported:1 notations:3 substituting:1 find:3 just:1 should:1 only:4 explicitly:1 integrable:2 dn:4 dm:5 dk:2 notation:2 get:2 hopefully:1 suris:3 during:1 gen:2 qq:1 evolution:1 qt:8 approach:2 arxiv:1 summary:1 qa:1 drinfeld:1 δa0:3 δa1:2 δji:1 national:1 see:3 projections:1 eliminating:1 discussions:3 terms:1 αq:2 αr:1 αu:1 αt:7 symmetric:1 various:1 between:17 invariant:1 conditions:1 recently:1 attention:1 wt:4 solv:1 δam:1 tensors:5 both:2 dorfman:1 last:2 context:2 expression:1 relevant:1 conclude:2 mkdv:1 proved:3 kp:30 considering:1 transformations:2 skew:1 defined:3 abdus:2 kronecker:1 expected:1 abstract:1 define:1 present:1 case:10 p1:2 unify:1 value:1 remaining:2 will:3 aid:1 property:4 metric:2 thus:5 reads:2 ij:1 converts:1 dual:1 aspects:1 technology:1 different:3 italy:1 shaw:3 author:1 make:1 same:1 any:1 modification:2 hierarchies:5 development:1 used:3 singapore:1 hand:2 parametrized:1 purpose:1 identity:1 recent:1 well:1 sets:1 soviet:1 gelfand:2 proposed:2 obtain:3 feher:1 identify:1 using:1 scattering:1 like:1 conclusions:1 auser:1 point:1 seems:1 lattice:8 other:3 lett:2 easy:3 theorem:2 transformation:4 generalized:2 bij:5 read:1 background:1 integer:2 bit:1 formal:1 helpful:1 follows:2 δu:1 δq:1 either:1 δh:10 arbitrary:1 δa:1 kdv:1 provided:1 lead:2 prob:1 scientific:1 power:1 slight:2 bi:8 although:1 properties:2 central:1 world:1 column:1 commun:4 aℓ:2 important:1 αai:1 αak:1 into:4 isomorphic:1 qrn:2 references:2 operator:11 there:1 u0:2 noticed:1 way:1 mkp:3 was:4 complete:1 form:1 jul:1 construction:1 hn:1 hl:3 level:1 he:3 ut:1 us:2 un:2 ui:1 uj:7 called:1 constant:1 ai:20 ak:16 aj:4 am:45 single:1 exist:1 constructed:4 functions:1 amounts:1 when:2 graduate:1 field:2 setting:1 role:1 fokas:1 symbol:1 stay:1 a1:1 a0:16 ξj:1 a2:1 variable:1 sides:1 structure:6 lm:6 harnad:1 physics:2 time:2
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solv-int9907020.txt |@word sector:3 partial:1 sch:2 alg:1 concern:2 trigonometric:1 foy:2 interpret:1 eds:1 proposition:8 torii:1 computation:1 c2:21 go:1 gn:41 gl:15 worked:1 nakayashiki:3 row:6 devoted:1 whose:1 inverse:6 depend:1 calculate:1 combinatorial:21 b389:1 stably:1 ts:8 uniqueness:1 behave:1 those:3 stable:4 connecting:1 analogous:1 fukuda:1 ıl:53 applied:2 conjecture:14 stud:2 very:1 assuming:1 translations:1 multi:1 choice:3 corollary:1 balls:1 cellular:19 summarized:1 experimentally:1 matrices:8 condition:4 annihilated:1 squares:3 tns:4 gebra:1 irreducible:4 anisotropy:1 sklyanin:2 list:2 solution:1 t0:6 hereafter:1 large:16 discrete:3 vector:1 phase:1 min:4 indices:2 noted:1 related:4 upper:2 smaller:1 consistent:1 b22:1 b21:1 b20:1 fold:2 second:2 insertion:1 further:2 odd:2 d4:1 linear:3 even:4 index:2 what:4 nonlinear:1 plays:1 appear:2 invertible:4 3r:1 section:25 brink:1 consistently:1 above:11 bm:11 3c:14 suppose:3 learned:1 solitonic:2 method:5 ˆn:5 viii:5 body:1 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solv-int9907021.txt |@word replacing:5 represent:1 iθ:1 homomorphism:1 consider:4 chain:15 localizes:1 global:1 results:5 leads:1 scalar:2 generalize:1 follow:1 expressions:2 gl:7 content:1 preserves:1 inverse:3 calculate:1 longstanding:1 superspace:25 b389:1 xiong:1 subjected:1 nonlocal:8 presents:1 finally:5 tk:10 th:15 dressing:11 analogous:3 must:2 presentation:1 conjecture:1 very:2 dq:2 conjectured:1 focus:1 dzd:2 bihamiltonian:1 entries:2 ui:4 manin:12 special:2 symplectic:1 hamiltonian:36 ref:1 sdet:3 t2:4 solution:4 t0:1 t1:3 large:1 discrete:14 recall:3 gauge:2 becker:2 hospitality:1 inspection:1 equation:24 inconsistent:1 jacobians:1 consistent:14 l2l:20 literature:1 modified:9 past:1 zero:10 mφ:1 displays:2 j21:6 concludes:1 further:1 rectangular:1 odd:11 linear:5 even:4 will:2 what:6 nonlinear:1 appear:4 brackets:6 d2:3 section:10 3v:2 expressed:2 hereditary:2 consistently:4 version:4 suspect:1 fuchssteiner:1 above:3 krivonos:1 new:29 acknowledgments:1 exercise:1 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solv-int9908005.txt |@word customary:1 consider:2 pointing:1 funct:1 equalities:1 focus:1 leads:5 eds:1 proposition:5 edu:1 go:1 sci:1 research:2 whose:1 inverse:5 chinese:1 aug:1 tu:2 δhn:8 δhm:4 those:1 under:2 zhang:5 very:1 rise:1 2ra:1 choice:5 manipulated:1 affect:1 associated:3 condition:6 tri:12 hamiltonian:54 bn:3 notes:1 solution:1 δh1:2 δh0:2 integro:2 commute:1 harry:2 anal:1 noted:2 programme:1 δu:20 direct:1 zero:20 rrx:1 further:1 spectral:4 established:3 what:2 nonlinear:6 sub:1 invertible:5 brackets:2 section:9 shares:1 consequent:1 fuchssteiner:3 above:4 new:2 public:1 satisfy:1 respectively:1 objects:1 china:3 concluding:2 equations:13 z1:6 z2:6 obtained:1 search:1 vectors:2 allows:2 example:6 resulting:2 poisson:2 pick:2 usually:1 ask:1 total:1 establish:3 select:1 derivatives:1 nonlinearization:1 would:2 prove:1 contains:2 next:1 few:1 noting:2 ψn:1 therefore:11 taken:1 qci:2 type:3 qcn:3 decomposable:1 more:4 separated:1 pavlov:1 becomes:2 operators:22 apparent:3 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solv-int9908006.txt |@word represent:1 gt:1 gr:2 remarkable:1 excepting:1 edn:1 results:1 gx:1 four:1 ge:1 generalize:2 consists:1 research:1 consider:2 whose:1 inverse:10 depend:1 calculate:1 aug:1 fellowship:1 tt:1 young:1 finally:1 those:3 under:1 include:1 straightforward:1 far:1 conditions:5 choice:1 putting:1 entries:2 difference:1 matrices:17 condition:5 school:1 list:8 solution:9 large:1 discrete:1 convenience:1 vector:2 math:9 small:1 relation:2 anal:1 noted:2 employing:1 ze:3 consistent:2 direct:1 throughly:1 integrability:19 zy:1 rrx:1 chen:6 further:1 choices:7 spectral:2 what:1 nonlinear:18 invertible:1 3r:1 section:16 brief:1 expressed:3 version:3 above:8 capital:1 new:7 beukers:1 scr:1 method:7 satisfy:3 lee:6 exchange:1 respectively:6 component:2 here:11 following:9 groups:1 address:1 concluding:2 path:2 strong:1 equations:32 appears:1 change:4 obtained:5 generalizing:1 study:1 changed:1 approaches:1 products:1 fourier:1 york:1 limx:5 via:1 explained:1 lillo:1 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solv-int9908007.txt |@word consider:4 yasuhiro:1 funct:1 results:1 scalar:2 gn:2 gk:1 gj:1 gi:4 row:2 c0l:10 aug:1 ty:1 tr:1 recurrence:4 th:7 dressing:1 tb:1 case:13 g0:1 putting:2 matrices:2 condition:3 presented:2 suffices:1 t2:2 solution:8 t0:1 t1:1 discrete:14 indices:2 gauge:1 anal:1 equation:66 wronskian:1 ekvac:1 direct:1 painlev:38 zz:1 schlesinger:2 established:1 3y:1 nonlinear:2 funkcial:1 annali:1 section:4 expressed:1 above:1 sixth:2 new:1 nakamura:1 3d:1 satisfy:3 κn:3 respectively:2 here:2 equations:29 change:4 obtained:3 remark:2 example:1 p2:3 masuda:2 suitable:1 studies:4 involves:2 uniquely:1 yamada:2 apply:1 tn:13 prove:3 suppl:2 next:5 paramater:1 therefore:2 ψl:21 associated:2 type:1 introducing:1 odinger:1 s3:3 known:3 iii:2 recall:1 ε2n:2 work:1 det:2 ρl:4 ρn:6 obvious:1 following:6 hiroshima:2 stimulating:1 proof:8 f2:1 give:2 calculation:1 carroll:1 arise:1 provide:1 verify:1 discussion:1 acts:6 recovers:2 leznov:1 pura:1 fourth:3 symposium:1 parameter:4 product:2 derived:1 hence:5 representations:1 constants:1 natural:1 third:4 explicit:1 darboux:2 so:3 s2:10 s1:8 ito:1 holds:1 spectral:1 paper:2 through:1 existence:1 satisfies:3 s4:2 its:3 τn:36 cln:31 group:1 cli:1 clk:5 δgn:1 actually:2 forms:1 systems:2 jacobi:2 them:1 acklund:7 introduce:1 2p:1 αq1:1 they:2 half:1 φj:1 similarily:1 2t:2 term:1 equality:2 2q:1 university:3 hamiltonian:6 2y:3 l0:1 each:1 2n:10 cl0:8 cl1:8 cl2:3 differential:1 ed:1 reduce:1 applicata:1 toda:39 expect:1 eq:5 special:6 canada:1 shown:2 matrix:3 space:1 since:3 denotes:3 rational:4 conjectured:1 formula:14 induction:1 math:5 theory:1 standard:3 hankel:3 put:2 e2:1 definition:1 derivation:5 geometry:1 omit:1 int:2 consequence:1 first:4 xa:1 s0:8 directly:1 kobe:2 xxxiv:1 taniguchi:1 given:17 checked:2 rewritten:1 similarly:1 introduction:1 system:1 construct:1 their:5 normalization:6 structures:1 1n:2 recursively:3 translation:6 completes:1 coefficients:1 kenji:1 piii:4 second:3 determined:1 gives:3 symmetries:1 rewrite:2 ann:1 kajiwara:5 generalization:1 discussions:1 manner:2 any:2 viewed:1 vgn:1 zero:5 general:7 note:1 εn:3 completed:1 bilinear:5 shall:1 molecule:3 polynomiality:2 algebraic:1 appear:1 soliton:1 ckl:5 professor:1 physica:2 proceedings:2 ohta:4 exp:1 kx:1 sequence:4 dli:1 noumi:3 show:3 lewis:1 relation:6 solutions:15 d2:1 fifth:2 parameters:1 lemma:9 only:1 transcendental:1 factor:2 a2n:7 integrable:1 umemura:6 columns:2 dl:6 dk:1 hiv:1 get:1 ones:1 dy:2 ds:3 determinants:1 qt:2 πs2:1 c2n:4 arxiv:1 πs3:1 crm:1 κl:14 clarified:1 j1:2 j2:1 namely:1 japan:4 αp2:1 recently:1 αp1:1 cofactor:2 2αp:1 dlk:2 review:2 written:1 πs1:1 conditions:1 2pq:1 multiplied:3 terms:1 shabat:1 vertical:1 however:1 veselov:1 2αf:1 concentrate:1 jk:2 solv:2 thank:1 both:1 essentially:1 σn:48 dl2:1 dl1:1 dl0:1 contribution:1 expression:3 ck:1 cj:2 ci:1 cn:18 cl:40 cf:1 2nd:1 dimensional:1 cy:1 sequences:2 polynomial:2 moreover:1 d73:1 considering:1 pq:5 pv:7 transformations:6 pt:1 been:1 defined:6 describes:1 pj:3 define:4 masatoshi:1 direction:1 corresponding:1 gen:1 δtn:1 c1:1 c0:1 present:2 applied:3 will:6 aij:2 di:1 procedure:2 jpn:2 thus:4 non:5 iv:2 ii:7 ik:2 ij:3 higashi:1 cjl:1 generic:1 recursion:3 proved:5 φl:11 independent:1 see:2 i1:2 i0:1 i2:1 hand:1 v1:11 v2:9 a232:1 changing:1 identity:1 schr:1 well:2 montreal:1 arising:1 usual:2 obtain:3 4v2:1 integer:3 yamamoto:1 adding:1 lattice:2 add:2 transformed:4 lett:2 theorem:18 transformation:3 bij:2 possible:1 immediately:2 c1l:6 follows:4 δp:1 δq:1 yields:1 arbitrary:4 works:1 right:1 classical:1 formulas:10 okamoto:9 b0:1 b1:1 choosing:1 integration:1 okada:1 prog:2 miraculous:1 chains:2 saveliev:1 workshop:1 scientific:1 derivatives:3 kyoto:1 bn:2 bi:1 bj:1 world:1 column:4 2h:5 discussed:1 side:1 soc:2 transcendents:1 nagoya:1 appropriate:1 references:1 operator:1 ψj:1 rows:1 log:18 painleve:1 removing:1 initial:4 δσn:1 appl:1 function:3 form:6 hv:1 but:1 matematica:1 adler:1 applying:3 wish:1 up:1 us:3 below:2 limit:1 similar:8 called:4 pii:5 constant:6 b2:1 ai:3 certain:1 abstract:1 aj:1 determinant:23 determinantal:1 engineering:1 proves:1 ay:2 piv:3 satsuma:1 functions:13 completeness:1 nn:2 no:1 detail:1 application:3 setting:1 electrical:1 department:3 mathematics:2 theor:2 conclusion:1 denote:1 polynomials:9 a1:13 a0:10 a3:2 a2:9 structure:3 acknowledgment:1 hiii:1 using:3 interval:1 hirota:3 n1:2 n2:2
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solv-int9908008.txt |@word forger:1 consider:1 qdq:1 results:1 leads:2 gb:4 ga:6 row:1 inverse:4 const:2 aug:1 technique:1 tj:1 th:2 under:1 γb:3 γa:11 must:2 tb:5 tc:1 ta:7 p2:17 orthogonal:2 very:1 fab:2 matrices:3 condition:2 pbp:1 presented:1 did:1 solution:6 try:1 solved:4 vector:1 pba:1 abµ:1 indices:2 levicivita:1 possibility:1 ifab:1 sign:1 civita:2 second:1 nonhomogeneous:1 linear:2 bilinear:7 nonlinear:3 invertible:2 diag:4 expressed:1 version:1 above:2 method:1 satisfy:2 respectively:1 fields:4 lem:1 ansatz:10 others:1 equations:17 xη:1 obtained:4 rdp:1 ab0:2 ab1:2 products:1 poisson:1 action:5 proof:1 via:2 useful:1 highly:1 first:1 summation:1 unit:1 would:1 prove:1 fbc:1 next:2 comparing:2 taken:1 means:2 type:1 more:2 introducing:1 zuse:1 operators:1 g123:2 berlin:1 qdp:1 varying:1 known:1 cases:2 hold:2 easiest:1 δca:1 equation:6 work:1 det:3 remain:2 following:3 example:2 numbers:1 define:5 f1:1 f2:2 f3:2 relativistic:1 permutations:2 2la:4 uai:2 konrad:1 dropped:1 hearn:1 r22:3 goal:1 vielbein:1 fpb:1 rather:4 six:1 maps:1 fpq:1 instead:1 field:3 parameter:4 wolfram:1 tried:1 algebra:3 may:1 lab:8 levi:2 lax:18 faculty:1 g312:3 quasiclassical:2 grant:2 explicit:1 su:12 so:4 holds:1 indeed:1 paper:1 through:1 mentioned:1 find:6 derive:1 group:5 lc:2 la:5 chosen:1 pcp:2 pcq:3 lj:2 pab:3 coordinates:3 forms:3 systems:4 pcb:2 mail:1 xyz:1 them:1 cvut:1 p12:7 they:4 identically:3 now:1 february:1 university:1 hamiltonian:2 l2:21 l3:20 l1:22 found:1 side:3 constraints:1 baxter:1 mikhailov:1 reduce:3 allan:1 related:1 quantum:2 our:1 special:1 zentrum:1 simplify:1 matrix:19 admissible:1 rev:1 math:2 theory:2 diagonal:15 free:3 completely:1 complicated:3 r11:2 g213:2 e1:2 e3:2 e2:2 pairs:3 interaction:1 chiral:12 r2:1 ministry:1 motion:2 relativistically:3 done:2 another:1 impossible:1 given:5 rewritten:1 adjoint:2 their:2 calculations:2 john:1 editor:1 academy:1 serve:1 immediate:1 jordan:1 natural:1 than:1 unfortunately:3 cyclic:2 namely:2 were:2 generality:2 generalization:3 lbc:1 lbd:1 seem:1 any:3 lie:3 hopelessly:1 zero:1 note:3 sciences:2 generalized:10 coincide:1 spectral:3 towards:1 shall:4 bordemann:1 algebraic:1 fcd:1 pair:12 sufficient:1 why:1 r33:3 qbp:1 satisfied:2 exp:1 sigma:3 gabc:1 fact:1 spaces:1 relation:1 solutions:2 keywords:1 d2:2 principal:13 q1:5 q3:3 q2:3 only:4 wood:1 subsection:1 integrable:9 local:1 get:6 dependent:5 solvability:3 combinations:1 aν:1 determinants:1 arxiv:1 yield:1 set:4 exists:2 prague:1 see:6 computer:1 p22:7 tensor:1 nondegenerate:1 nuclear:1 symmetric:4 written:1 invariant:6 conditions:11 terms:4 transpose:1 however:1 killing:3 comm:1 δab:3 solv:1 lb:6 xlab:1 limits:1 acknowledge:1 equal:1 admit:1 solving:1 simple:1 cb:4 harmonic:1 lk:2 dimensional:3 cz:1 respect:1 considers:1 ǫabc:2 pq:3 transformations:1 basis:5 three:3 anisotropic:3 θi:3 corresponding:1 restrictions:1 25b:1 25a:1 curves:1 nonconstant:4 case:5 p3:16 p1:17 look:1 solvable:1 while:3 rba:2 metric:21 non:1 reads:2 ia:1 containing:1 author:1 connection:3 same:2 antisymmetry:1 diagonalize:1 qab:3 proved:1 gets:1 lqc:1 independent:4 used:1 dimg:4 hand:9 totally:1 identity:1 lower:1 preceeding:1 variety:1 well:1 without:3 solve:2 coordinate:1 model:8 dimension:1 left:4 flat:1 manifold:2 just:1 less:1 obtain:3 immediately:2 scattering:1 multiples:1 christoffel:1 conclusions:1 zakharov:1 seems:2 lett:2 easy:2 adj:7 transformation:1 references:1 sums:5 lcd:1 press:1 using:5 unique:1 loss:2 necessary:2 follows:1 imposes:2 yields:1 arbitrary:2 δg:1 right:2 formulas:1 czech:3 b1:9 b2:9 both:1 expressing:1 prob:1 inserting:5 ba:5 bb:4 bc:14 step:1 bq:1 br:1 p32:7 fordy:1 most:1 column:1 dependence:1 o:1 extensions:1 introduced:1 block:5 cambridge:1 previously:1 into:6 due:1 coefficients:4 because:3 wherefrom:1 lund:1 log:1 support:1 there:1 u1:3 u3:3 u2:2 start:1 quadratic:1 tg:1 way:2 was:4 form:23 but:2 pj:1 aµ:4 russian:2 msc:1 up:2 limit:1 ud:1 ua:5 called:1 uc:1 ub:2 aa:1 ab:5 constant:9 ad:1 int:1 abstract:1 general:7 ap:1 engineering:1 exist:2 formulation:6 education:1 identities:2 check:3 physical:1 tedious:1 again:1 functions:1 eventual:1 no:8 mathematica:2 when:1 defined:3 other:6 republic:3 department:1 theor:2 elements:9 models:19 symbol:3 replace:1 important:2 variable:1 sides:2 structure:5 implies:1 auxiliary:1 assume:4 physics:1 cherednik:1 requires:1
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solv-int9908009.txt |@word represent:1 dimentional:1 chain:1 four:2 scalar:1 proposition:1 gn:10 gm:1 gl:7 gj:1 nakayashiki:3 consider:5 θq:1 aug:1 z1r:1 those:3 elliptic:4 case:4 g1:2 orthogonal:1 regional:1 presented:2 large:1 admissible:2 commute:1 math:6 science:3 small:1 round:1 encloses:2 zj:34 sign:2 fold:7 zero:4 further:1 spectral:1 appear:1 abf:1 section:10 expressed:1 poles:9 method:1 satisfy:7 κj:4 exchange:2 respectively:1 here:4 zz12:9 expansion:1 groups:3 directions:2 equations:1 z1:21 z2:15 vectors:1 kubo:2 periodic:1 products:2 akm:1 permutation:1 formulated:1 fµ:7 family:1 wii:39 sgn:5 clockwise:3 virasoro:5 use:6 would:1 prove:14 probabilities:3 abbreviations:1 next:2 nucl:3 m1:1 therefore:1 ψm:1 taken:1 type:39 duality:6 operators:45 particular:3 hold:3 tokyo:1 feigin:1 aµν:10 equation:2 work:1 ρl:3 mj:1 fock:3 following:14 example:1 proof:9 claim:4 theorems:1 xz1:1 organized:1 πj:7 states:2 allowed:1 νm:4 µj:4 νj:6 s1:2 holds:1 located:1 rsos:5 parameter:2 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solv-int9909001.txt |@word ψ1x:2 gu:2 sci:1 results:1 leads:2 φ1x:3 commute:1 ψ1m:1 grateful:1 edu:2 constants:1 gn:1 research:3 inverse:1 aug:1 technique:1 tr:2 finally:1 under:4 g2:16 g1:16 zhang:1 springer:4 matrices:1 deformations:1 condition:1 tri:1 hamiltonian:45 solution:1 vector:3 science:1 inspection:1 solutions:1 employing:1 force:1 zero:2 further:1 dψ2:1 dψ1:1 ackel:1 spectral:30 employ:1 what:1 nonlinear:6 g22:5 appear:1 section:3 fuchssteiner:1 above:3 new:3 acknowledgments:1 satisfy:1 edited:2 degree:1 respectively:1 guangzhou:1 china:4 concluding:2 along:1 equations:3 appears:1 search:1 study:1 resulting:2 poisson:1 usually:1 geng:1 studies:1 palais:1 tu:2 hamiltonians:1 ψx:1 handled:1 γi:1 ψt:1 ψi:3 therefore:3 associated:3 type:3 more:1 integers:1 becomes:1 operators:1 odinger:1 curvature:1 berlin:3 normalized:1 known:3 cases:1 hold:1 ramani:1 keeping:1 valued:1 ma:8 recall:1 equation:4 work:1 cao:2 three:2 following:3 example:7 proof:1 wojciechowski:1 f1:2 f2:1 f3:1 f4:1 process:1 council:1 confocal:1 guarantee:1 fortunately:1 discussion:1 enl:1 feature:1 fourth:1 answer:1 acta:1 verlag:5 parameter:1 product:1 binary:2 fx:1 hong:4 isospectral:1 lax:6 fi:2 fj:1 φ2x:3 fn:1 natural:2 dynamical:1 third:1 explicit:1 yielding:4 st:1 provide:1 si:1 so:3 g12:5 ding:1 hierarchy:10 indeed:1 move:1 soc:2 kong:4 course:1 paper:3 through:3 lattices:1 japan:1 satisfies:1 still:2 its:4 chosen:1 interesting:3 solving:1 actually:1 lu:1 degrees:2 systems:43 derivative:1 non:17 acklund:1 they:2 now:2 discuss:1 fields:2 eigenvalue:1 term:2 2q:5 2r:4 university:3 presented:1 theory:1 each:3 found:3 side:2 constraints:32 arxiv:1 directly:1 σ2t:1 independent:1 ed:2 energy:1 related:1 operator:2 toda:2 ey:2 our:5 operation:1 special:1 out:1 shown:2 matrix:1 gradient:1 res:2 rep:2 since:2 rx:1 denotes:2 particles:1 may:1 math:7 shows:2 foundation:1 ψ2x:3 kaup:3 standard:1 york:1 put:1 generate:2 pairs:4 sinica:1 linearized:4 motion:5 hence:1 trv:1 βi:1 first:3 xj:1 xi:2 xn:3 symmetry:36 variables:3 powerful:2 strategic:1 xx:1 another:1 city:2 given:2 similarly:1 introduction:1 1x:1 adjoint:11 system:41 assumption:1 xiu:1 exactly:1 newell:3 part:1 authors:1 x2:1 x3:1 x1:4 x4:1 zsu:1 kind:1 cimento:2 second:2 aims:3 project:2 were:1 symmetries:5 contradict:1 mind:1 ming:1 say:1 any:3 lie:1 calogero:1 note:1 k2:2 k0:5 take:4 finding:1 birkh:1 involving:2 connected:1 remarks:2 class:5 interacting:1 soliton:10 don:1 especially:1 kn:1 physica:1 bracket:1 hietarinta:1 physics:2 think:1 oevel:1 show:3 supported:1 akns:31 find:2 believe:1 just:1 basel:1 only:2 going:1 integrable:35 moser:1 do:1 means:1 grammaticos:1 valuable:1 dx:4 zhu:1 σ1t:2 qr:4 qx:2 differential:2 yield:2 involutive:1 contain:2 grad:1 body:3 ser:1 reference:1 national:1 j0:2 j1:2 j2:2 see:2 result:1 eigenfunctions:4 functionals:1 irn:4 between:3 conditions:2 email:2 notice:1 terms:1 extend:1 transpose:1 however:2 ji:1 solv:2 uφ:1 both:1 last:1 many:3 taking:2 according:1 symplectic:1 comes:1 cn:1 point:1 corresponds:1 2nd:2 dimensional:9 analyzed:1 grants:1 anti:1 kowloon:1 polynomial:3 moreover:2 li:4 pp:2 amer:1 observing:1 due:2 int:2 much:1 algebras:1 eφ2:3 generating:2 commutes:1 func:1 bull:1 present:1 case:5 arnold:1 will:1 ir2:1 coupled:1 vol:1 φix:3 ir:5 thus:1 them:1 equal:1 reads:2 il:1 vx:1 2g1:3 2g2:3 φt:2 grant:2 φx:1 recursion:1 parts:1 emphasize:1 φi:3 φj:1 finite:2 φm:2 φn:2 difficult:2 evolve:1 hand:1 auser:1 potentials:7 changing:1 ablowitz:1 schr:1 well:1 analysis:1 solve:1 left:1 λr:1 λq:1 λu:1 λt:1 being:3 dφ1:1 obtain:1 competitive:1 dφ2:1 yes:1 scattering:1 functionally:1 wen:1 lattice:1 potential:2 transformed:1 lett:4 solvable:1 transformation:1 advances:1 possible:1 αj1:1 like:1 follows:3 δu:7 specific:3 yields:2 either:1 δh:4 arbitrary:3 become:1 qxx:2 mathematical:1 right:1 methods:1 classical:3 some:5 qφ2:1 choosing:1 kdv:2 generates:1 nonzero:2 provided:1 provides:1 prof:1 integrals:1 equivalent:1 nonlinearization:9 although:1 properties:1 comparison:1 constraint:8 freedom:2 mixes:1 introduced:2 perelomov:1 rφ1:1 h2:6 into:5 h1:6 integral:4 negative:1 because:3 references:1 qrx:1 φj1:1 there:3 question:1 appl:1 inner:1 was:1 function:6 form:2 hs:3 but:3 hk:1 construction:1 hn:2 segur:1 illustrative:3 compute:1 whether:1 ut:3 us:3 different:1 excitement:1 liouville:1 jψ:1 problem:23 similar:1 mechanics:2 interchanges:1 constant:2 defined:8 eφ1:2 abstract:1 zeng:1 general:2 exist:2 dλ:1 functions:5 integrability:2 no:2 when:3 other:4 solitons:1 department:2 mathematics:2 kinds:2 βj2:1 zhou:1 problems:10 generated:5 structure:1 implies:1 assume:1 time:1 requires:2 nuovo:2
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solv-int9909002.txt |@word precise:1 consider:7 global:2 results:2 sergey:1 proposition:15 computation:4 talks:1 gn:36 expressions:2 disk:1 centers:6 rigidity:1 devoted:1 preserves:1 m2m:1 tu:2 tr:5 finally:3 those:1 γg:1 case:11 conjecture:3 labels:1 r12:5 already:1 straightforward:2 orthogonal:2 very:2 keeping:1 corollary:2 putting:1 lecture:1 difference:8 matrices:3 deformations:1 condition:4 induced:1 obvious:1 riemann:5 presented:5 turns:1 notes:1 integrating:1 july:1 solution:30 integrated:1 large:1 discrete:77 differential:2 science:1 inscribed:1 equation:64 cfn:2 zn:2 nonautonomous:1 direct:3 literature:1 painlev:7 korteweg:1 further:2 reine:1 odd:2 4x2:3 linear:3 even:1 established:4 what:1 plays:1 combined:1 section:9 purdue:1 http:1 reasoning:2 schwarzian:1 version:1 above:5 fractional:2 deal:1 aii:3 net:1 connected:1 method:6 contrast:1 satisfy:9 respectively:5 never:1 here:3 packing:2 tangent:3 inversion:4 address:2 consideration:1 along:1 equations:29 z2:19 celebration:1 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solv-int9909003.txt |@word partial:1 consider:9 pointing:1 funct:1 results:1 invent:1 leads:3 scalar:4 proposition:6 generalize:2 follow:1 expressions:1 research:1 reasoning:1 gi:2 devoted:2 whose:1 inverse:1 depend:1 turkish:1 nonlocal:6 tn:2 under:1 applied:1 belonging:1 r12:2 r10:7 r11:6 very:1 dokl:1 choice:1 ankara:2 entries:1 difference:1 matrices:1 condition:3 hamiltonian:4 turns:1 applicable:1 ri:2 eigenvalues:2 anal:1 12v:2 direct:2 10d:1 sign:2 second:2 bilkent:1 further:1 dynamics:1 odd:6 vun:2 eigenspaces:1 theory:2 even:2 aim:1 gibbons:1 nonlinear:5 sub:4 contemp:1 section:11 3v:7 expressed:2 symes:6 above:2 illustrations:1 new:2 method:4 3d:2 satisfy:1 relationships:1 27d:1 respectively:2 here:7 5u2:4 ansatz:8 groups:2 sawada:4 consideration:1 standard:7 equations:14 transformation:1 obtained:2 remark:2 sobolev:1 technical:2 allows:1 resulting:2 published:1 g0:2 suitable:1 u3x:9 projection:2 texts:1 santini:2 total:1 establish:1 use:18 takes:2 would:2 prove:1 remains:1 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solv-int9909005.txt |@word partial:1 consider:4 results:2 scalar:3 3a2:3 denotes:1 inverse:2 depend:2 calculate:1 tj:2 present:2 applied:2 string:3 very:1 riemann:1 did:2 list:1 solution:3 vector:2 indices:1 integrability:1 subscripts:1 nonlinear:3 appear:2 gβα:1 section:1 expressed:1 above:1 new:2 method:3 satisfy:1 here:5 groups:1 consideration:1 november:1 equations:4 obtained:2 search:1 studied:1 ku1:1 ψu1:2 published:1 classification:2 summation:1 total:1 derivatives:1 takes:2 covariant:1 ψv:1 ψw:1 ibragimov:1 uγ1:2 type:1 const:1 nauka:2 operators:2 curvature:1 known:1 must:1 equation:5 det:1 obvious:2 following:12 example:2 f1:1 f2:1 nontrivial:3 3w2:1 fu:1 fv:1 fw:1 may:1 earlier:1 dx2:1 4th:4 representations:1 constants:1 fundamental:1 order:16 fα:1 fβ:1 over:1 symbols:2 group:1 writing:1 systems:16 vtx:1 defining:1 them:2 acklund:3 mention:1 uν1:3 they:1 possess:1 2u:12 university:1 each:1 found:1 homogeneous:1 bw2:1 differential:1 w12:3 investigated:2 meth:1 out:1 reseach:1 matrix:1 3rd:6 space:7 lagrangian:1 research:1 formula:1 foundation:1 linear:1 admits:9 completely:1 besides:1 chiral:1 ds2:3 u21:3 first:2 xi:2 symmetry:14 u1:2 variables:2 another:1 u2:4 moskow:1 jet:1 introduction:1 5th:8 system:17 too:1 calculations:1 ψv1:1 moscow:1 part:2 authors:2 translation:1 believe:1 than:1 coefficients:2 accordance:1 zero:1 uβ1:3 were:5 russia:1 w2:2 function:7 symmetries:20 rewrite:1 cumbersome:1 any:3 lie:3 take:2 gα:2 shall:1 twodimensional:1 metrics:1 preliminary:1 reducible:3 dordrecht:1 calculated:1 ku:1 physics:1 laws:1 v12:1 supported:1 spaces:1 solutions:2 substituting:1 find:1 only:5 going:2 integrable:5 local:1 do:2 u31:1 dependent:1 dx:5 report:1 dt:4 aν:3 densities:1 fields:5 arxiv:1 investigate:1 sep:1 see:1 computer:1 w3:1 differentiable:1 w1:10 sem:1 uν:2 tensor:1 uα:5 state:1 simplest:1 αj:1 wtx:1 wt:2 solv:1 article:3 tensors:1 wx:2 many:3 admit:6 σv:1 ci:1 2nd:1 dimensional:4 polynomial:7 moreover:2 throughout:1 meshkov:1 three:1 int:2 abstract:1 corresponding:9 quantities:2 kw1:1 c9:2 c8:2 c3:2 c2:2 general:3 c7:1 c6:1 c5:3 c4:2 case:2 du2:1 metric:3 av:5 vm:4 vv1:1 vt:2 vw:6 vx:2 vanish:1 grant:1 same:1 proved:2 higher:13 independent:3 used:1 v1:7 v2:6 v3:3 uαi:2 center:1 english:1 parametric:4 manifold:1 differentiation:2 scattering:2 preprint:1 infinitely:2 versa:1 theorem:6 solvable:1 transformation:1 dvdw:3 vβ:1 unique:3 like:3 follows:1 integrals:1 arbitrary:4 mathematical:1 reidel:1 methods:1 deal:1 some:3 dimensions:1 lead:1 2c5:1 does:3 proc:1 scientific:1 aαβ:2 bw:3 about:1 tomsk:2 constraint:1 aαβγ:1 statements:1 christoffel:1 into:1 integral:2 references:1 wβ:1 additional:1 there:4 3th:1 u0:8 u3:1 3u:1 conservation:1 was:2 therefore:3 2vc:1 complete:1 form:6 but:3 repeated:1 russian:1 ux:4 ut:4 us:2 below:1 ui:1 utx:1 more:1 ab:3 constant:1 semicolon:1 ai:1 configurational:2 bβγ:1 denote:1 conserved:1 exist:1 kv1:1 functions:6 no:2 uµ:1 when:4 field:4 other:1 theor:1 exp:17 models:1 a1:2 a2:5 structure:1 acknowledgment:1 vice:1 assume:1 rule:1 implied:1 time:1 gαβ:5
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solv-int9909007.txt |@word partial:2 consider:1 primed:1 four:1 research:1 inverse:1 under:17 include:1 case:3 provides:1 trigonometric:1 witten:1 emphasized:1 condition:2 notes:1 solution:9 leave:1 discrete:4 math:4 eigenvalues:1 subindex:1 10b:2 10a:2 sign:2 second:1 b135:1 chen:2 nonlinear:3 section:4 celebrated:1 henceforth:2 poles:1 above:3 3c:1 3b:3 3a:4 method:10 contrast:1 satisfy:5 supporting:1 ibid:1 respectively:5 cylindrical:1 address:1 concluding:1 sine:4 equations:27 obtained:1 institute:2 drs:1 suggests:1 products:1 stressed:1 changes:1 jalan:1 followed:1 9a:1 9b:1 apply:3 derivatives:1 use:2 proceed:1 would:1 remains:2 next:1 comparing:1 nucl:1 m1:8 m3:8 m2:9 australian:1 theoretical:1 solitons:1 odinger:3 particular:1 known:4 cases:1 hold:2 iii:1 must:1 springer:1 dodd:2 pursue:1 equation:46 mi:3 mk:1 remain:1 obvious:1 following:11 claim:1 αm1:2 allowed:2 tan:2 verlag:1 respective:2 nontrivial:1 parameter:10 sin:6 wave:1 express:1 may:3 after:2 derived:4 fi:1 derives:2 constants:1 introduced:1 explicit:1 su:1 secs:1 so:5 pleasure:1 conjugation:3 sg:10 order:3 itb:1 canberra:1 zen:1 held:3 paper:1 through:2 mentioned:1 satisfies:2 its:4 derive:5 thank:2 acknowledge:1 chosen:2 fix:2 solving:1 decreases:1 suspicion:1 choose:4 derivative:2 13b:1 non:2 auto:5 acklund:16 anticipated:1 they:2 front:1 eigenvalue:1 2v:2 university:1 2a:6 2b:3 degasperis:1 side:1 mean:1 financial:1 another:2 ed:1 reduce:1 related:6 constitute:3 static:1 connect:1 our:6 pseudopotentials:1 eq:14 special:1 shown:2 space:1 nuovo:1 since:8 rev:3 denotes:2 looking:1 re:6 lecture:1 ref:4 c33:1 shows:1 foundation:1 linear:1 8b:2 8c:1 8a:3 8d:1 reason:1 york:2 derivation:2 could:2 konno:3 gordon:4 ism:1 first:4 symmetry:1 miura:1 variables:3 number:2 xx:4 directly:1 precisely:1 interchange:1 given:4 introduction:1 eqs:7 1a:5 their:7 1b:4 zeros:1 convention:2 final:3 gives:5 progr:1 exactly:1 62a:1 optical:1 x2:11 kept:1 x1:11 cimento:1 project:1 minus:1 symmetries:11 unchanged:6 discussions:1 conjugate:7 self:1 able:1 note:3 sciences:1 potential:3 take:1 data1:1 shall:1 riccati:21 pair:3 acknowledgements:1 32b:1 soliton:1 prolongation:5 considered:4 part:1 usual:5 vries:1 fact:3 12a:1 nls:11 directorate:1 show:2 cpt:19 relation:7 solutions:8 substituting:1 wahlquist:7 find:1 devries:2 should:1 only:4 explicitly:2 factor:1 integrable:4 familiar:1 de:1 overall:1 reversal:1 new:13 dr:1 alexander:1 fields:3 arxiv:1 yield:1 twice:1 comma:2 fixed:1 set:2 bts:2 sep:1 national:1 differs:1 sec:2 result:3 eliminating:2 operated:1 78a:1 between:6 invariant:7 subscript:1 approach:1 email:1 preserve:1 terms:3 august:1 however:2 vanishing:1 key:1 solv:1 c22:3 both:1 cos:2 cot:1 according:5 ernst:15 finds:1 otherwise:1 comment:1 simple:1 corresponds:1 dimensional:1 coordinates:5 respect:2 cp:3 considering:2 transformations:15 pt:8 due:1 been:2 cosgrove:1 substraction:1 6a:2 6b:1 6c:2 corresponding:11 c23:1 xxx:1 essentially:1 observe:1 irrelevant:1 present:1 applied:1 eigenstate:1 will:7 euclidean:1 while:2 neugebauer:5 iz:2 thus:4 13a:1 encouragement:1 iv:1 ii:2 dual:1 technology:1 id:1 different:2 pseudopotential:15 d19:1 same:8 beside:1 rules:1 complex:17 resulting:2 prerequisite:1 higher:1 used:1 ni:3 i1:1 hand:2 purpose:2 potentials:1 hans:1 identity:1 schr:3 studies:2 indonesia:2 well:4 analysis:1 academic:1 solve:1 calogero:1 left:1 obtain:1 transforms:1 scattering:2 12b:1 conjugates:1 bullough:1 application:1 had:1 iψ:2 add:2 other:3 transformed:1 lett:3 versa:1 c13:1 republic:1 c11:3 5a:2 transformation:19 5b:2 real:3 iλ:4 australia:1 manton:1 read:1 harmonic:2 increases:1 press:1 using:5 advanced:1 like:1 bobby:1 follows:1 performing:1 specific:1 korteweg:3 either:1 arbitrary:1 popular:1 become:1 stationary:1 essential:2 gauge:1 parity:1 right:1 some:2 examples:1 kdv:7 lead:2 centre:1 manipulations:1 does:3 eliminate:5 expressing:1 prof:1 11d:1 11a:2 obey:1 11c:1 11b:2 equivalent:2 bt:21 freedom:1 wadati:3 referred:1 into:4 within:3 integral:2 nothing:2 appropriate:1 references:1 vii:1 ricatti:1 support:1 there:1 transform:8 accordingly:1 was:2 function:12 αn1:1 form:3 differences:1 but:2 sdm:1 applying:1 characteristic:1 gravitational:1 uv:2 up:2 us:5 freddy:1 similar:1 ac:1 int:1 abstract:1 general:1 exist:1 rule:8 laboratory:1 6d:1 education:1 simplest:1 sasaki:1 again:1 functions:5 nk:1 rederive:2 when:1 field:13 valid:1 remarks:1 holding:1 department:1 mathematics:1 theor:1 conclusion:1 a12:1 preceding:2 deriving:1 generated:1 n2:9 l67:1 vice:1 assume:1 physics:2 required:1 together:2 estabrook:7 time:2 n1:9 4d:1 n3:9 4b:2 4c:3 4a:5
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solv-int9909008.txt |@word partial:1 consider:6 remarkable:1 similarity:3 proposition:4 generalize:1 gn:11 devoted:1 whose:2 inverse:1 calculate:2 producing:1 tu:8 presents:2 tm:6 tj:13 under:3 iui:1 case:8 conjecture:1 straightforward:2 p0:1 ovsiannikov:1 corollary:1 putting:1 exact:1 nijenhuis:1 bn:15 turns:1 t4:2 t2:21 solution:2 t1:3 solved:1 convenience:1 vector:13 anal:1 noted:2 lk1:1 upper:2 consistent:1 zero:2 dynamics:1 linear:7 spectral:2 what:6 nonlinear:1 t2n:9 diag:2 hereditary:3 fuchssteiner:1 above:2 replaced:1 method:3 coefficient:1 notions:1 respectively:2 component:1 here:6 galilean:2 groups:4 bk:2 equations:15 galilei:6 box:1 eij:1 institute:1 shift:3 allows:1 p2:1 simultaneous:2 action:1 suitable:1 u3x:1 uniquely:1 useful:2 family:1 requiring:1 replace:1 texts:1 addressed:1 apply:1 establish:1 unit:1 derivatives:3 use:1 prove:2 positive:1 next:3 comparing:2 explicitly:1 ibragimov:1 characteristics:2 associated:1 more:2 introducing:1 operators:1 ti:8 odinger:2 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solv-int9909009.txt |@word represent:1 gt:3 consider:7 gv:1 depends:1 induces:1 desirable:2 results:4 fluids:1 scalar:4 consists:2 gk:62 gj:1 gi:2 certainly:1 calculate:1 tu:1 tr:18 finally:2 present:5 under:9 semenov:1 tg:4 lh:1 presentation:2 ingredient:1 case:19 g2:4 g1:4 far:1 translations:2 multi:3 choice:1 mps:2 discretizations:2 difference:1 matrices:3 notations:1 hamiltonian:9 die:1 list:3 solution:1 t0:3 t1:3 leave:1 discrete:42 vector:3 science:1 manifestly:1 reyman:3 shows:1 originally:1 application:2 dealing:1 direct:3 translating:1 integrators:2 integrability:5 further:6 dynamics:2 hopefully:1 theory:9 bilinear:3 established:2 nonlinear:1 plays:1 appear:3 invertible:3 diag:1 section:3 probably:1 expressed:5 19th:1 version:2 en:1 above:6 new:1 body:25 notions:1 orpers:1 respectively:1 even:1 here:3 delivering:1 identifications:1 tangent:4 symm:4 groups:5 represented:1 ratio:1 along:1 extrema:2 equations:32 implicit:2 obtained:4 shansky:1 remark:2 weinstein:1 remarks:1 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solv-int9909010.txt |@word neighbors:1 precise:1 miwa:1 ams:1 consider:3 remarkable:1 global:1 leads:6 scalar:4 ψ1n:1 edu:2 follow:1 remarkably:1 gl:1 contributions:1 compact:1 whose:1 preserves:1 iii:2 equivalence:1 canonical:2 m2n:1 trivial:3 tn:15 finally:3 tj:3 tk:14 ti:103 λs1:2 mehta:1 fay:9 string:2 straightforward:2 orthogonal:6 very:1 construction:3 translations:1 wave:11 corollary:7 valued:5 every:6 entries:2 exact:1 condition:7 four:3 riemann:10 induction:2 notes:1 tokyo:1 t2:1 solution:8 t1:8 deals:1 solved:1 vector:6 louvain:3 recall:2 small:1 zl:1 upper:3 mn:13 zi:45 zj:22 zk:10 haar:1 ψi:2 consistent:1 zg:16 morozov:1 sign:7 rate:1 evaluated:1 gn:1 further:1 odd:9 expressions:2 eigenspaces:3 theory:7 bilinear:13 dissertation:2 nonlinear:1 appear:5 moments:2 giving:1 diag:2 section:6 near:3 find:1 reminiscent:1 birkhoff:1 annals:1 poles:6 establishes:1 replaced:2 wn:5 subtracting:1 codimension:1 coefficient:6 q2k:4 led:1 degree:6 exchange:2 respectively:6 aij:3 equals:5 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solv-int9909011.txt |@word since:1 partial:4 being:1 satisfied:1 dy2:1 infeld:2 x2:30 scalar:1 relation:1 solutions:4 questions:1 amp:1 y1:37 y2:40 scattering:1 ihep:1 note:1 number:1 how:1 explain:1 solving:1 encompasses:1 assertion:1 universal:3 only:1 other:1 what:1 mail:2 solvable:1 hope:1 real:5 them:1 yj:1 return:1 differentiation:1 dependent:1 dg:2 implicitly:3 results:1 yg:1 choice:1 additional:1 shown:1 using:1 bogoliubov:1 now:1 condition:1 insert:1 february:1 kα:2 equality:1 called:2 follows:1 university:2 arxiv:1 solution:8 b373:1 separately:1 solved:2 token:1 differential:2 announced:1 arbitrary:6 found:1 govaerts:2 introduce:1 lines:1 mathematical:3 shock:1 deal:1 sep:1 energy:1 identifying:1 some:2 morozov:1 inhomogeneous:1 depends:2 result:2 choosing:1 rigorous:1 laboratory:1 special:1 out:1 surfaces:1 fails:1 describing:1 dimensions:2 twice:1 though:1 consequence:1 denotes:1 geometry:1 written:2 above:1 replaced:1 expect:1 journal:1 minimal:1 shows:1 satisfy:1 gives:1 terms:2 linear:2 whose:1 equivalent:2 little:1 here:1 however:1 admits:1 completely:1 references:1 solv:1 preprint:1 along:1 dubna:1 equations:10 implicit:1 deduced:1 obtained:2 both:1 about:1 dtp:1 last:1 carried:1 extension:1 institute:1 many:1 region:2 similarly:1 dy1:1 equal:1 david:1 covariant:1 admit:1 resulting:1 theory:1 together:2 hence:1 regarded:2 automatically:1 first:6 generalisation:3 xi:1 russia:2 variables:3 xf:1 functional:1 dimensional:3 variable:1 linearization:1 durham:4 simply:1 protvino:1 monge:1 respect:3 total:1 linearly:1 readily:1 derivatives:4 given:3 jetp:1 eye:1 log:5 fairlie:6 introduction:1 unknown:2 question:1 three:2 been:1 properties:1 nucl:1 jinr:1 3le:1 type:2 theoretical:1 recovered:1 define:1 function:10 field:3 arises:1 relationship:1 generalisations:1 conclusions:1 moscow:2 pairs:1 aware:1 derivative:3 known:1 x1:30 spirit:1 those:1 case:1 caveat:1 born:2 equation:22 det:1 second:2 involved:1 barbashov:1 will:1 ere:1 near:1 future:1 obvious:1 uk:1 cavalier:1 problem:1 more:1 similar:1 mx:1 proof:1 point:1 ac:1 constant:1 eliminating:1 int:1 implications:1 abstract:1 mixed:1 general:5 high:1 himself:1 analysis:1 further:3 constrained:1 any:1 constructed:1 again:1 functions:7 verified:1 form:4 integrability:1 depending:1 write:2 differentiability:2 when:2 cross:1 same:1 clearly:1 leznov:4 sciences:1 complex:8 arguments:2 department:1 plus:2 parameter:1 higher:1 differentiable:1 chernikov:2 imply:1 investigations:1 may:7 act:1 upon:3 dx2:1 dx1:1 hand:1 constraining:1 plane:1 cup:1 purpose:1 pair:1 wave:2 implies:1 proceed:1 third:1 assume:1 soviet:1 space:2 well:1 su:1 bateman:16 points:1 so:2 principle:1 physics:6 order:3 dh1:1 usual:1
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solv-int9909012.txt |@word represent:1 partial:2 equalities:2 results:2 leads:2 commute:1 follow:1 expressions:1 research:1 devoted:1 calculate:1 equivalence:1 contained:1 finally:2 under:3 applied:1 straightforward:1 very:2 implicitly:1 corollary:2 manipulated:1 condition:1 immediately:1 solution:12 solved:3 convenience:1 proposition:3 indices:1 upper:2 direct:2 second:10 pass:2 further:1 theory:1 index:3 what:1 section:4 version:1 above:1 new:3 method:1 satisfy:2 compact:1 simultaneously:1 degree:1 respectively:6 here:1 them:2 represented:1 consideration:1 equations:22 implicit:2 institute:2 involved:1 dru:1 hospitality:1 zhdanov:1 transformations:1 editors:1 durham:2 protvino:1 derivatives:10 ψy:4 takes:1 remains:2 next:2 comparing:1 taken:2 3le:1 type:3 theoretical:2 separated:1 introducing:3 ua:1 operators:3 known:2 cases:1 must:1 keeping:3 defines:1 augment:1 equation:24 work:1 det:4 ere:4 obvious:1 following:10 arrive:1 ay1:2 compare:1 process:1 preserving:1 monge:6 high:1 effectively:1 want:2 end:1 mutually:1 divided:1 means:1 leznov:2 antiholomorphic:3 instead:1 may:4 different:4 third:2 explicit:1 summing:2 φy1:1 so:2 fundamental:1 definitions:2 order:2 ry1:5 uvx:1 unsolved:1 help:2 indeed:2 satisfied:1 combinations:1 paper:4 y1:48 satisfies:1 y2:23 its:6 before:2 coordinates:2 systems:3 main:2 defining:1 yi:5 yk:3 they:1 bogoliubov:1 now:2 february:1 equality:4 university:1 2a:2 each:4 found:1 side:4 homogeneous:2 another:1 energy:1 inhomogeneous:1 quantum:1 our:3 beyond:1 extract:1 special:1 er:1 ru:14 rv:1 matrix:3 space:11 crucial:1 publish:1 denotes:1 acting:1 equate:2 ra:2 reader:2 evaluation:1 shows:1 foundation:1 linear:5 dubna:1 definition:2 pairs:4 βyi:1 geometry:1 determining:1 turn:1 consequence:2 cc12:1 βi:1 first:7 indebted:1 there:2 symmetry:1 researches:1 variables:3 supplement:1 directly:1 checked:1 rewritten:2 introduction:1 unknown:2 achieved:1 system:20 relations:1 assumption:1 calculations:3 scheme:1 final:2 holomorphic:3 moscow:2 crucially:1 part:3 authors:1 determines:1 sections:1 depends:1 aims:1 future:1 tion:1 russia:2 uy1:2 uy2:2 rewrite:3 anl:1 qy1:2 argument:1 qy2:2 morelos:1 orders:1 rαi:1 zero:2 able:1 sciences:2 jacobian:1 xi:1 shall:1 algebraic:1 pair:7 acknowledgements:1 consequences:2 considered:1 coincides:1 uru:3 barred:3 usual:1 physics:5 fact:1 solutions:5 substituting:5 d2:1 find:1 knowledge:1 dividing:1 aψ:1 only:7 going:1 generators:2 inami:1 integrable:4 columns:1 notation:3 di:1 df:8 ones:1 nearly:1 dv:1 du:1 dp:2 dq:2 qy:1 arxiv:1 hydrodynamic:7 contain:1 fixed:2 multiplying:3 exists:1 sep:1 mongeamp:1 facts:1 namely:1 result:6 best:1 written:2 between:2 αi:2 progress:1 conditions:3 terms:5 uψ:2 solv:1 solu:1 come:3 last:8 similar:2 region:2 etc:1 connection:2 expression:2 vux:1 comment:1 among:1 ci:1 dimensional:8 distinguish:1 respect:6 considering:2 commutative:1 fairlie:3 py:5 three:1 been:1 defined:2 reduction:1 interest:1 determinant:1 arises:2 corresponding:1 mind:1 θa:8 selfconsistency:5 gap:1 finished:1 θy:2 understand:2 c2:1 present:4 case:2 multi:1 value:2 remaining:1 will:3 near:1 suppose:1 mexico:1 thus:3 non:1 ii:1 middle:1 vr:2 vt:1 vv:4 vy:1 vanish:1 vy2:4 containing:1 vy1:3 grant:1 journal:1 φy:8 complex:7 arguments:4 proved:1 fill:1 higher:1 calculation:1 see:1 upon:1 hand:6 concluding:1 center:1 analysis:1 concrete:1 solve:1 sets:2 position:1 arising:1 dimension:3 dh1:1 left:3 manifold:2 less:1 obtain:6 amp:4 differentiation:4 previous:2 vψ:2 attractive:1 theorem:1 transformation:1 real:2 rules:2 using:4 like:1 follows:2 either:1 arbitrary:4 mathematical:2 right:3 methods:2 some:1 rffi:1 pψ:3 dimensions:2 investigations:1 integration:1 kyiv:1 does:1 connecting:4 assuming:2 equivalent:2 step:1 properties:2 ruu:3 comparison:1 central:4 dependence:3 recalling:1 mixed:4 automatically:1 into:6 obtaining:1 unbarred:3 references:1 realisation:1 rows:2 prepare:1 support:1 initial:1 way:1 jinr:1 was:4 function:14 form:14 analyse:1 but:5 russian:1 encoded:1 uy:7 annihilate:1 ut:1 us:3 below:1 limit:1 subclasses:1 constant:2 int:1 abstract:1 general:10 engineering:1 au:7 dθ:1 laboratory:1 check:2 sasaki:1 constructed:2 functions:17 field:1 other:1 remarks:1 department:1 mathematics:1 conclusion:2 separate:2 models:1 backbone:1 important:3 qψ:3 dψ:2 assume:1 values:3
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solv-int9909013.txt |@word represent:1 partial:1 consider:5 equalities:4 results:6 leads:3 scalar:2 commute:1 go:1 minors:1 expressions:5 row:3 inverse:2 calculate:2 technique:1 finally:2 present:2 th:1 under:2 analogous:1 δsn:1 straightforward:1 implicitly:4 keeping:1 geometrical:2 corollary:5 matrices:2 condition:2 obvious:2 solution:19 solved:2 proposition:3 indices:5 specially:1 consistent:1 direct:5 integrability:1 follow:1 further:4 ues:1 index:1 what:4 appear:1 giving:1 sum:1 above:5 new:3 d1:1 satisfy:1 simultaneously:1 respectively:5 here:2 represented:1 consideration:3 equations:36 implicit:2 obtained:2 institute:1 p2:1 resulting:1 suggestion:1 symmetrical:1 cancellation:1 uniquely:1 durham:2 protvino:1 inverses:1 summation:1 readily:1 derivatives:8 use:1 ψy:2 takes:1 recalling:1 contains:1 next:1 comparing:1 m1:1 therefore:1 3le:1 ψa:2 type:3 theoretical:1 more:5 separated:1 introducing:4 initial:3 operators:4 particular:1 cases:1 must:4 account:4 recall:1 equation:31 det:4 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solv-int9909017.txt |@word ψ1x:2 now:1 construct:1 manifold:21 help:1 when:2 over:1 obtain:8 vanishes:1 pxx:4 through:1 solutions:13 c2:1 constants:3 substituting:1 trivial:1 find:1 previous:2 seminal:1 pde:2 termed:1 ln:2 temporal:1 jap:1 should:1 simple:1 must:2 setting:1 coefficients:1 constitutes:2 integrate:1 integrable:2 te:1 transformation:3 generalized:1 musette:1 non:3 sonia:1 handle:1 izv:1 salamanca:2 means:4 far:1 de:3 martinez:1 february:1 results:1 define:1 private:1 dx:1 invariant:1 resonant:1 using:3 pxt:1 yu:2 condition:3 easily:1 term:4 2w:1 level:1 fields:1 calvo:1 aez:1 expansions:4 solution:4 ussr:1 yields:5 arbitrary:3 analytical:1 leaves:1 soc:1 2h:1 arxiv:1 sep:1 series:2 special:1 some:1 related:1 nski:1 isospectral:1 painlev:6 used:2 c1:1 combining:1 terms:2 dynamics:1 weiss:2 appropiate:1 neighbourhood:2 2pt:1 spectral:3 given:3 est:5 dimensions:7 interaction:2 section:3 shall:2 integration:3 state:1 eliminate:1 provides:2 between:2 αi:5 new:1 problems:1 conditions:1 method:6 math:5 satisfy:2 probl:1 matveev:1 recently:1 hern:1 usal:1 2py:1 2px:2 restricting:1 ısica:2 ψx:10 expansion:3 conde:1 inverse:2 substitution:3 solv:3 jour:1 equations:14 p2x:4 wy:1 wx:3 obtained:2 linear:1 perform:1 rederived:1 many:1 taking:2 o:1 called:1 f2:2 konopelchenko:1 due:1 universidad:1 hence:2 coefficents:1 pickering:1 expression:1 px:6 first:1 among:2 pxy:1 py:6 φxx:1 h2:6 communication:1 h1:4 corresponds:1 tabor:1 system:3 dimensional:3 linearization:1 xx:2 set:2 references:2 ψt:4 fi:3 polynomial:3 moreover:2 ψxx:2 consider:1 second:1 derivatives:2 use:2 ψy:6 transformations:11 pt:1 area:1 introduction:1 leading:3 eqs:2 truncated:4 u0:1 been:2 defined:1 reduction:1 ψi:2 facultad:1 m0:1 way:1 call:1 themselves:2 branches:1 start:1 more:1 function:4 conte:1 arises:1 βi:14 solitons:2 tool:1 vpx:2 but:1 part:2 because:1 generalization:1 mail:1 implies:1 line:2 denote:1 spain:1 truncation:2 case:3 springer:2 uy:6 ux:6 integrating:1 sections:1 equation:20 expanded:1 iteration:3 see:2 us:2 mj:2 will:1 manifolds:1 represents:1 iterated:1 uj:2 following:2 orica:1 problem:1 property:2 my:3 mx:1 procedure:1 myy:1 f1:2 uxt:2 later:1 constant:1 satisfying:1 coupled:2 int:3 abstract:1 vw:2 them:4 uxx:2 uxy:5 itself:1 vt:1 a12:3 sense:2 vx:3 vy:2 ci:1 constructed:1 functions:2 generic:1 φt:1 zero:1 no:1 darboux:11 φy:2 fukuyama:2 eigenvalue:3 cross:1 same:1 ourselves:1 write:1 alonso:1 build:1 potential:1 p2y:1 es:1 spatial:1 φi:1 hi:1 defines:1 parameter:3 difficult:1 salle:1 bilinear:1 calculation:1 acklund:2 exp:3 singular:18 ψ2x:2 carnevale:1 singularities:2 movable:2 medina:1 v2:2 nonlinear:4 lax:12 ht:1 potentials:1 pair:12 ψyy:2 compatibility:2 expand:1 eigenfunctions:6 soliton:6 laurent:1 longer:1 toda:2 considered:3 4w:1 pilar:1 analysis:5 order:2 φx:4 kp:1 verlag:1 allow:1 hirota:5 definitions:1 requires:1 having:1 fact:1
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solv-int9909018.txt |@word partial:8 consider:13 remarkable:1 12a:5 t2i:1 commun:2 focus:1 extensively:1 gg:1 bringing:1 scalar:24 computation:1 follow:4 expressions:13 gl:2 ψdx:1 devoted:1 whose:2 isometric:15 inverse:4 terms:2 calculate:1 advantage:1 paris:1 tw:1 financial:1 nonlocal:1 tn:1 finally:1 manifolds:2 θg:2 under:7 γb:1 analogous:1 te:1 chirally:1 t11:9 witten:1 string:3 straightforward:3 very:1 erale:1 translations:1 springer:1 induce:2 geometrical:8 isomorphism:2 additional:1 entries:3 exact:2 eisenhart:3 condition:11 dubrovin:1 riemann:5 exits:1 presented:3 turns:5 notes:2 nucl:1 july:1 solution:36 deals:1 solved:1 vector:10 phase:2 interpolating:1 gauge:5 referred:1 equation:53 degeneracy:1 upper:5 des:1 10b:2 10c:4 consistent:1 10a:6 transform:1 sin1:1 second:3 progress:1 concludes:4 further:3 dynamics:1 cat:2 quite:1 linear:22 spectral:4 will:8 what:4 disk:3 g22:3 appear:4 invertible:3 section:17 codazzi:3 expressed:2 uniform:2 ǫl:8 en:1 sur:1 above:39 new:2 3a:7 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solv-int9909019.txt |@word represent:1 minoru:1 consider:2 trigonometric:1 four:1 commute:1 higher:1 grateful:1 edu:1 expressions:1 replacements:1 const:2 th:6 under:7 string:1 interpreting:1 matrices:1 condition:15 dim:12 solution:25 try:1 discrete:1 guiding:4 zn:1 periodicity:1 consistent:3 direct:1 sin1:39 sergeev:5 integrability:1 further:2 even:1 xω:1 section:1 above:8 new:8 satisfy:6 full:2 here:3 understanding:1 cos1:51 strong:1 change:6 obtained:1 vectors:1 periodic:1 changes:3 composed:1 useful:1 support:1 unit:1 use:8 prove:1 next:8 m4:2 noting:1 m1:2 therefore:2 m3:2 m2:2 taken:1 until:1 becomes:2 iii:1 must:11 equation:29 work:1 values:1 following:7 root:3 example:2 proof:3 korepanov:1 give:18 calculation:2 sense:1 sphere:1 arise:1 rather:1 write:1 how:1 instead:1 nara:1 sin:78 arcs:6 may:3 after:2 plane:1 faculty:1 date:1 attempt:1 explicit:4 su:2 so:3 fundamental:3 sl:2 representation:3 order:4 prefactor:2 satisfied:8 course:1 paper:4 statistical:6 japan:2 satisfies:8 before:2 chosen:1 interesting:1 forms:1 fig:5 mail:2 cef:1 non:2 propose:1 they:2 bazhanov:25 easily:1 e2πi:1 university:3 identified:1 found:3 x12:7 x13:20 x14:13 constraints:1 baxter:26 financial:1 weight:18 series:1 ef:2 principles:1 our:1 eq:23 special:1 really:1 large:1 shown:3 jimbo:1 space:1 projected:1 research:1 replacing:3 formula:2 math:5 reformulated:1 given:11 quite:2 clarify:4 approaches:4 complicated:1 x24:11 interaction:3 chiral:2 language:2 impose:5 transfer:1 iβ2:1 first:4 xi:2 xn:20 symmetry:10 variables:7 xij:3 construct:1 another:4 little:1 checked:1 similarly:1 introduction:1 eqs:17 relations:12 attach:2 too:1 potts:2 speaking:1 gives:6 progr:1 completed:1 part:2 authors:1 x2:16 x3:26 x1:31 than:1 x4:15 kind:1 showed:1 likely:1 ia3:17 symmetries:29 rewrite:3 zamolodchikov:7 few:3 generalization:1 conjugate:2 their:3 lie:1 horibe:4 take:6 circles:1 opposite:2 boltzmann:20 abc:1 multiply:1 acknowledgements:1 parametrize:8 especially:1 partition:2 points:4 principle:5 exp:35 hietarinta:1 physics:2 fact:2 fukui:3 show:1 colors:1 relation:22 solutions:6 substituting:4 trivial:2 find:16 behind:1 only:3 factor:2 integrable:11 do:2 cube:10 triangle:6 notation:1 dependent:1 de:2 overall:1 despite:1 stroganov:7 approach:9 arxiv:1 summary:1 investigate:2 pioneering:1 exists:3 sep:1 clarified:1 2dim:1 w1:47 w0:2 review:1 symmetric:1 state:6 between:1 progress:1 conditions:1 x23:17 restricting:1 jp:2 however:1 key:1 solv:1 come:1 cos:113 cubes:1 last:1 2n:4 many:5 taking:5 according:2 connection:1 expression:1 comes:1 point:1 simple:3 cf:2 ce:2 ωx2:2 ab:2 considering:1 second:2 addition:3 been:2 int:5 abstract:1 θj:8 θk:8 θi:6 corresponding:1 sufficient:2 miki:1 fund:1 understand:7 external:1 angles:15 c3:9 c2:9 c1:9 spin:12 c6:9 c5:9 c4:9 applied:1 tetrahedron:29 will:3 while:1 situation:1 jpn:1 vi:2 thus:1 them:1 ii:6 ij:2 df:2 make:1 same:4 any:1 complex:2 difficult:1 independent:2 used:4 cubic:29 assignment:1 numerical:2 functions:1 parametrized:2 v1:11 v2:12 v3:35 v4:20 normalization:2 mangazeev:8 well:1 academic:1 without:2 solve:1 model:47 spherical:33 proposed:2 obtain:1 assigned:1 scattering:1 preprint:1 candidate:10 vω:1 seems:1 parametrization:18 lattice:2 ade:1 transformed:2 lett:4 gave:1 around:3 possible:1 know:1 using:14 mod:6 necessary:3 systematically:1 follows:1 separately:1 become:2 works:3 essential:4 spins:1 replacement:1 mathematical:3 kashaev:7 some:1 b4:13 b1:12 b2:14 b3:13 proper:1 though:1 does:1 miwa:1 refer:1 bd:2 bf:2 power:3 bc:2 equivalent:2 perpendicular:1 restrictive:1 fermat:1 properties:1 bdf:1 x34:8 constraint:5 commun:5 automatically:4 soc:1 into:7 functional:2 references:1 proportional:3 additional:2 comparing:1 iβ0:1 iβ1:1 strictly:1 there:10 start:1 way:8 was:2 function:5 form:15 but:3 properly:2 ωx:2 intuitive:5 whether:1 us:1 ωv:1 trigonometry:24 examples:1 detailed:1 ac:4 later:2 ae:2 ad:2 ai:4 ak:2 aj:2 denote:3 engineering:1 exist:6 formulation:2 check:2 triangles:2 constructed:1 ni:2 nj:1 boos:1 detail:1 rewriting:1 other:1 branch:3 papers:2 department:2 theor:1 stat:2 star:2 a10:1 models:4 a1:49 a3:60 a2:49 a4:13 a9:1 generalized:2 structure:13 assume:1 factors:1 weights:2 time:2 original:6
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solv-int9909020.txt |@word sci:1 consider:14 chain:5 gp:2 comparatively:1 results:11 invent:2 integration:1 leads:7 eds:2 scalar:4 generalize:1 br2:1 consists:3 minors:6 expressions:10 contributions:1 compact:2 whose:6 preserves:1 depend:3 calculate:4 paris:1 tt:6 γp:5 trivial:2 γk:15 γj:2 γi:100 investigation:1 those:2 th:24 under:1 semenov:1 tg:4 analogous:4 include:2 γg:9 ωp:15 applied:4 belonging:1 g2:10 advantage:2 orthogonal:3 2re:1 p0:1 choice:1 print:1 kuznetsov:1 putting:1 allowed:1 stays:1 word:1 zeitschrift:1 difference:4 matrices:3 condition:18 treating:1 dim:2 34a:2 34b:1 presented:6 bn:1 turns:1 notes:2 criterion:1 list:1 solution:27 large:10 solved:1 convenience:1 vector:9 2κr:7 indices:19 eigenvalues:12 reyman:1 shows:3 ρk:1 bases:1 configurations:1 upper:1 work:1 grateful:1 ζik:2 eigenmatrix:1 lecture:2 direct:1 b21:1 sign:2 approximation:1 go:2 second:5 value:3 44c:1 qualitatively:7 44a:2 odd:1 gm:2 44e:1 44d:1 spectral:1 aim:4 what:6 nonlinear:3 stands:2 minami:2 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