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solv-int9411004.txt |@word secondly:1 partial:5 consider:1 proposition:9 follow:1 research:1 depend:13 finally:1 bqq:1 applied:1 straightforward:1 far:1 3ab:1 ankara:2 turns:2 notes:1 t2:1 harry:1 anal:2 consistent:1 nonautonomous:1 second:1 bilkent:1 further:1 substitute:1 scientific:2 will:2 what:2 nonlinear:4 xρ:1 3u:1 goes:1 new:4 method:3 coefficient:2 edited:2 hern:1 respectively:1 here:6 groups:2 xβ:1 along:1 equations:34 technical:2 ab2:1 products:1 divide:1 classification:16 total:1 derivatives:1 use:1 negative:1 next:1 comparing:1 xh1:1 therefore:1 type:18 more:1 started:1 fokas:1 operators:2 under:7 berlin:2 cases:3 iii:3 springer:2 equation:23 work:4 infinitesimal:1 following:12 example:2 proof:1 f1:2 f2:1 f3:2 give:9 sokolov:4 purposes:1 council:1 verlag:2 end:1 s2:2 s1:2 s0:2 maps:1 classify:2 fr:1 mat:1 faculty:2 compatibility:3 constants:3 andez:1 dynamical:4 third:2 explicit:2 generic:1 so:1 martina:1 definitions:1 order:7 over:1 mainly:1 russian:1 rσn:1 through:2 existence:2 satisfies:3 urses:2 before:1 forms:1 systems:1 derivative:3 decades:1 possessing:1 qq:1 non:4 introduce:1 they:2 nov:1 now:5 2u:1 february:1 2w:1 always:1 university:2 2d:1 2a:2 2b:8 2c:2 found:1 2h:8 mikhailov:1 arxiv:1 reduce:1 our:3 eq:21 out:2 furthermore:1 denotes:2 conjectured:1 supports:1 math:2 shows:1 linear:1 mσ:1 8b:2 surveys:1 dependencies:1 put:2 hc2:1 definition:2 r1:2 linearized:4 hence:1 first:4 symmetry:7 variables:3 utilized:1 done:1 xq:1 given:9 their:2 echet:1 siam:1 scheme:2 gives:2 2ab:2 2ac:1 exactly:1 differentiate:1 authors:1 x2:2 coefficients:2 outline:2 showed:1 integrability:3 classes:1 powers:1 symmetries:5 boston:1 any:2 relatively:1 lie:1 zero:1 depending:1 self:1 sciences:2 generalized:2 coincide:1 whe:1 shall:1 algebraic:1 nothing:1 class:4 physics:2 dot:1 quantity:1 cdf:1 show:3 supported:1 dependences:1 eaq:3 attempts:1 d2:1 d3:1 q2:2 based:1 parameters:1 2bq:2 analytic:1 only:13 integrable:18 local:1 2bb:1 2ba:1 above:1 means:1 dependent:2 db:3 dym:1 ones:1 dx:5 3b:2 dt:6 gen:1 dq:4 prime:1 evolution:4 differential:5 contain:1 view:1 set:4 exists:1 uu2:1 depends:10 decided:1 w2:2 its:3 state:1 determined:1 invariant:1 approach:1 recently:1 shabat:2 solv:1 both:3 σn:1 many:2 according:2 admit:1 8ab:1 among:2 point:2 simple:2 cb:1 whatever:1 mkdv:3 applicability:1 respect:1 turkey:3 arts:1 transformations:9 three:1 been:2 int:1 basic:1 6q:2 observe:2 olver:1 c2:3 c1:7 resultant:1 those:1 case:11 heidelberg:1 aim:1 procedure:1 coupled:2 almost:2 thus:1 ii:9 middle:1 df:2 containing:1 perform:3 recursion:7 dhb:1 same:5 proved:1 several:2 independent:3 investigated:1 upon:1 purpose:1 pde:4 programs:1 contact:1 coordinate:7 obtain:1 karasu:2 using:2 previous:1 infinitely:2 zakharov:1 tubitak:1 ease:1 belongs:2 transformed:2 east:1 transformation:9 eigenvalue:9 possible:1 department:2 integer:1 appearing:3 like:1 reduces:2 steps:1 arbitrary:5 mathematical:1 reidel:1 some:2 b0:3 b1:3 b2:9 kdv:2 provided:1 proceeding:1 dimensions:2 subclass:6 eliminate:2 algorithmic:1 ba:1 bb:1 equivalent:3 bh:1 bi:6 illustration:1 bq:3 simpler:1 world:1 most:1 important:1 introduced:1 inte:1 h2:3 h3:2 into:5 h1:2 functional:2 references:1 operator:6 utility:1 u4:1 there:2 transform:3 u3:4 u2:2 appl:2 way:1 ibragimov:2 function:6 transformable:2 aqq:1 complete:1 form:8 botti:1 sequel:1 but:2 ah2:1 properly:1 hb:1 hd:1 partially:1 uz:1 whether:2 up:6 us:7 below:1 autonomous:5 called:1 ac:1 ab:5 constant:2 choosing:1 ai:6 ah:3 abstract:1 general:2 aq:12 aw:2 ax:1 functions:5 differentiable:1 no:1 application:1 test:1 mathematics:1 conclusion:1 a1:3 a0:3 a2:4 variable:5 ago:1 dτ:1 together:1 4a:1
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solv-int9411005.txt |@word limited:3 partial:3 consider:1 results:3 fluids:1 leads:2 scalar:1 gm:9 layers:1 whose:1 quasi:1 edward:1 under:3 quarterly:1 suffered:1 include:2 presentation:1 sound:1 orthogonal:4 choice:1 difference:1 condition:9 riemann:1 presented:1 shock:1 solution:24 solved:2 vector:14 anal:1 ejs:1 equation:62 force:1 sign:2 zero:8 further:2 nonlinear:2 trivial:2 sum:1 expressed:1 thickness:1 reminiscent:1 poles:1 new:2 method:5 satisfy:4 27a:1 27b:1 simultaneously:3 respectively:1 here:1 tangent:3 19e:1 19d:6 equations:4 appears:1 19c:1 19b:1 obtained:1 41b:1 allows:2 action:1 auxillary:7 formulated:2 useful:2 9a:3 9b:1 decrease:1 unit:1 use:6 would:1 positive:1 contains:1 bundles:1 e0:2 therefore:1 more:4 initial:1 acceptable:2 apparent:1 particular:1 known:5 cases:1 maryland:1 must:10 md:1 account:1 inertial:1 work:4 deficiencies:1 ρu:5 following:4 atm:1 stream:1 pieces:1 indicates:1 assumptions:1 council:1 sense:3 sharp:1 isothermal:3 tan:2 end:1 ivy:1 dependent:1 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solv-int9411006.txt |@word yasuhiro:1 show:1 developed:1 over:1 find:1 obtain:2 nato:1 substituting:1 solutions:8 using:4 mentioned:1 existence:1 satisfies:2 still:1 exp:4 nov:1 τn:21 adding:5 derive:1 based:1 analytic:1 dividing:1 kagamiyama:1 technique:1 actually:4 lattice:3 only:2 potential:2 originally:1 systems:2 th:8 jacobi:1 integrable:1 nucl:1 transformation:2 weber:1 ser:1 ramani:2 them:1 dm:1 get:3 dependent:1 grammaticos:2 acklund:1 introduce:1 satisfied:1 ones:1 jp:3 dx:1 meguro:1 singularity:1 now:1 exact:3 geometric:1 condition:5 term:1 u01:1 semi:3 follows:1 university:3 arxiv:1 solution:10 iwanami:1 discrete:13 investigate:2 differential:1 arbitrary:1 relation:2 2n:4 reduces:2 dpi:12 trv:1 mathematical:1 multiplying:1 successively:1 methods:1 hν:2 haar:1 ed:1 τnn:49 some:2 direct:1 related:1 applicable:1 painlev:9 investigated:1 expect:1 eliminating:1 japan:3 quantum:1 terms:2 eq:3 v00:2 bilinear:11 shown:2 nonlinear:2 matrix:6 space:1 u2n:2 2c0:1 shenker:1 2c2:4 its:1 attracted:1 defined:2 investigation:1 above:3 between:1 formula:1 boundary:4 method:4 multiplied:4 recently:2 theory:1 douglas:1 kyoto:2 bn:10 attention:1 analogues:1 however:2 here:1 standard:1 v10:1 solv:1 article:1 asi:1 equations:12 properties:1 log:1 almost:1 arrive:1 parameters:2 question:1 column:8 similar:1 taking:2 studied:2 example:2 context:1 hence:2 introduced:1 expression:1 u02:1 unn:4 first:3 comment:1 among:1 useful:1 suffix:1 cc:1 hermite:2 into:1 integral:1 solve:2 system:2 dimensional:1 infinite:3 because:1 references:1 proved:2 u2:1 second:1 u0n:2 given:6 rewritten:1 decoupling:1 similarly:1 unknown:1 eqs:1 give:1 u1:2 u0:1 been:3 appears:1 few:1 difference:2 much:1 constants:1 way:1 taken:1 airy:2 was:1 komaba:1 naturally:1 function:8 determinant:5 form:2 4c2:1 continuous:1 essentially:1 japanese:1 confinement:1 understand:1 particular:1 c2:3 cases:1 c0:1 clarkson:1 applied:1 kind:1 applying:1 tokyo:4 kenji:1 equation:16 aan:1 casorati:3 painleve:2 um:1 un:7 limit:1 following:1 kurims:1 property:1 c1:5 hiroshima:3 proof:1 expressed:1 ac:3 2un:1 coupled:2 int:1 measure:1 kajiwara:5 contiguity:1 vn:9 resultant:1 ii:2 engineering:2 itself:1 variable:1 formalism:3 yet:1 physical:1 gives:1 satsuma:6 higashi:1 τ0n:1 corresponds:1 gravity:1 same:1 note:1 sciences:1 other:1 electrical:1 solitons:1 department:3 mathematics:2 dxx2:2 kluwer:1 applications:1 un0:2 extended:5 ku:1 hirota:1 derived:2 what:1 most:1 satisfying:2 lax:1 faculty:1 pair:1 structure:4 soliton:1 natural:2 auxiliary:1 considered:1 clear:1 partition:3 ohta:6 fundamental:1 tanabe:1 hn:1 model:5 furthermore:1 finally:2
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solv-int9412001.txt |@word managed:1 consider:4 equalities:2 four:2 roy:2 analiz:1 relationships:3 whose:2 inverse:1 eˆ:3 nonlocal:1 those:2 excluded:1 under:1 andreev:1 worth:1 rise:1 p0:20 choice:4 trough:1 matrices:2 condition:9 riemann:3 sklyanin:1 solution:7 large:1 involution:3 upper:1 consistent:1 direct:2 sign:1 tex:1 fold:2 integrability:2 further:1 ba:2 even:1 nonlinear:5 ˆv:1 section:3 3p:4 poles:7 above:6 new:3 method:1 degree:1 respectively:2 modify:1 here:2 sinh:12 others:1 sine:1 equations:19 divisor:5 lomi:1 changed:1 amount:1 action:1 via:4 extra:2 derivatives:4 use:2 takes:1 sake:1 positive:1 give:1 next:2 comparing:2 therefore:2 more:2 becomes:1 operators:2 stable:2 enormous:1 uxx:3 known:1 hold:1 account:1 valued:1 dodd:6 equation:29 values:2 following:6 dec:1 specialized:1 proof:4 zametki:2 compare:1 do:1 preserving:1 sense:1 sought:1 exclude:1 axis:1 get:7 canonic:2 write:1 how:1 nontrivial:1 parameter:1 map:1 mat:3 algebra:1 may:3 algebro:5 after:1 derived:2 containing:1 plane:2 lax:2 d11:2 realized:1 third:1 light:1 spectra:1 explicit:2 correspond:1 so:1 order:5 restriction:2 help:1 developed:1 over:1 paper:1 london:2 its:4 derive:2 exclusion:1 fix:1 solving:2 forms:1 choose:1 derivative:1 defining:1 image:1 them:2 prevented:1 auto:1 acklund:15 processes:1 introduce:2 they:1 singularity:1 now:3 yu:2 realize:1 2u:8 inversion:1 several:1 equality:1 ux2:1 2eu:1 vt2:7 each:1 found:1 arxiv:1 doing:1 journ:1 reduce:1 applicable:1 constitute:1 equivalence:2 combining:1 eu:10 our:1 ev:3 extract:1 special:2 out:1 matrix:9 discrete:2 restricted:1 since:2 vectorial:1 ramified:1 math:2 linear:1 written:1 singularities:2 2h3:3 diagonal:3 quite:1 admits:1 base:2 pairs:2 r2:2 impose:1 gordon:1 consequence:1 first:4 initial:4 features:1 variables:7 number:1 zap:1 πd:4 similarly:1 introduction:1 system:1 construct:1 their:2 πp:2 intermediate:1 zeros:3 vxx:4 calculations:2 brevity:1 scheme:1 gives:2 lot:1 relationship:4 task:2 part:1 authors:1 cosh:1 kind:3 was:2 require:2 second:6 normalizing:1 bev:1 vx3:1 vx2:5 symmetries:1 rewrite:1 modern:1 spectrum:2 solitons:1 zero:1 depending:2 note:4 take:1 finding:1 algorithms:1 spectral:1 though:2 most:1 connected:2 utt:3 nothing:1 class:4 yamilov:4 branching:2 consequences:2 considered:2 typeset:1 points:4 physics:1 pril:1 notations:3 solutions:15 substituting:3 find:2 subtracting:2 enough:3 should:3 lemma:4 only:4 qx:1 integrable:9 local:1 abelian:1 means:3 vxt:6 ones:1 boundary:19 bˆ:1 qt:2 covering:2 conditions:6 differential:12 tarasov:1 qe:1 contain:2 analytical:2 scott:1 set:3 testing:1 turbulent:1 see:6 computer:2 surfaces:1 satisfying:1 symmetric:2 state:1 closed:1 between:1 invariant:2 geometric:5 approach:1 meromorphic:3 terms:2 shabat:5 solv:1 suggested:1 restrictions:2 last:1 taking:3 according:1 σd:3 fulfilled:1 passing:1 genus:1 point:3 polynomial:5 proved:1 considering:2 transformations:6 pt:1 addition:2 px:2 three:5 int:1 cauchy:1 interest:1 vtt:4 corresponding:1 gap:10 func:1 arisen:1 case:2 exception:1 exponential:1 originate:1 value:4 suppose:1 uxt:3 mclaughlin:1 non:1 surface:2 2ux:6 obstacle:1 vt:22 cone:1 vx:20 2ut:8 different:2 specialization:1 suggest:2 algorithmically:1 same:4 complex:1 finite:10 independent:3 infinity:1 singapore:1 moving:1 changing:1 opportunity:1 cycle:3 lower:1 σp:3 schr:1 well:1 thought:1 position:1 model:1 λp:1 unities:1 being:5 obtain:5 shape:1 λg:2 vˆx:1 vˆt:1 scattering:1 yet:1 functionally:1 previous:1 bullough:6 except:1 theorem:2 solvable:1 transformation:16 real:2 sharipov:6 background:3 using:3 ams:1 moreover:1 excluding:1 specific:1 arbitrary:1 essential:1 methods:2 deal:1 some:2 intern:1 mirror:2 proper:1 proc:2 limitations:1 obey:1 bl:1 equivalent:1 cλ:3 step:1 substitution:1 properties:2 world:1 getting:1 pλ:1 theorems:1 o:1 compatible:3 range:1 slightly:1 automatically:1 soc:2 h2:3 into:2 integral:1 bound:3 pair:1 appropriate:1 references:1 schrodinger:2 additional:1 vˆ:10 extraction:1 there:2 question:1 long:1 way:1 sections:1 function:6 complexified:1 complete:1 form:18 soliton:7 forming:2 triangular:2 but:1 construction:2 russian:6 2vx:1 divisors:9 ux:15 consist:1 ut:11 us:6 backlund:4 problem:8 similar:3 called:2 touchstone:1 constant:2 defined:4 abstract:1 scientific:1 commuting:1 check:2 constructed:2 functions:6 no:8 when:1 cˆ:1 virtual:1 reality:1 papers:1 theor:2 elements:1 problems:4 semin:1 polynomials:1 odinger:1 needed:1 structure:1 baker:4 d22:1 together:5 time:1 normalized:1
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solv-int9412002.txt |@word mγδ:1 partial:2 consider:1 similarity:2 series:1 results:3 illustrated:1 douglas:1 grateful:2 consists:1 follow:1 research:3 gr:1 whose:3 inverse:2 depend:1 schiff:1 fellowship:1 concerned:1 recurrence:2 those:2 under:1 characterised:3 deducing:1 applied:1 supported:1 stud:1 straightforward:1 very:1 rise:1 splitting:3 exact:23 condition:1 leads:1 school:3 riemann:1 presented:1 did:1 x3n:2 notes:1 t2:6 solution:25 t1:1 leave:1 discrete:45 math:8 science:1 anal:1 society:2 typified:1 linearizing:1 upper:1 zn:44 force:1 10b:1 10a:2 direct:2 sign:4 generalisations:1 painlev:30 further:11 odd:4 12z:4 substitute:1 theory:1 schlesinger:1 nonlinear:9 appear:2 ct2:1 incompatible:1 section:1 expressed:5 kent:1 version:2 poles:1 above:6 fractional:1 3b:3 3a:4 method:5 satisfy:1 κn:5 full:1 simultaneously:1 degree:3 respectively:9 here:3 papageorgiou:4 ranges:1 separation:1 address:4 alone:2 19d:1 equations:35 change:1 deduced:2 obtained:3 8z:3 remark:5 institute:1 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solv-int9412003.txt |@word secondly:1 partial:8 consider:6 illustrates:1 excellent:1 results:1 vr:4 kµ2:3 four:3 eds:1 during:1 go:2 3a2:1 remarkably:1 eη:1 localized:3 gr:3 whose:1 inverse:14 depend:1 calculate:4 integral:2 pb2:1 paris:1 33a:1 technique:1 acting:1 supported:1 finally:2 program:2 those:1 elliptic:1 under:2 exposition:1 analogous:3 include:2 presentation:1 kν:2 applied:2 conjecture:1 v11:2 g3:2 presently:1 straightforward:3 θz2:2 far:1 zˆ2:1 erale:2 reader:2 multi:1 wave:5 indication:1 georgia:1 putting:1 anonymous:1 nonlinearity:2 exact:13 condition:2 generalised:5 illustrated:2 xt2:2 34b:1 34c:1 notes:1 t2:5 solution:64 t1:4 large:2 solved:3 convenience:2 vector:6 scalings:1 small:1 relation:2 anal:1 optics:3 noted:3 akns:2 upper:1 review:1 des:1 computation:2 sin2:3 pulse:1 sign:2 generalisations:1 integrability:9 plenum:1 zz:2 zt:2 further:19 implemented:1 expressions:4 canonical:1 spectral:4 fr3:2 nonlinear:19 appear:3 sum:6 tabor:2 fr1:1 expressed:4 current:1 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solv-int9412004.txt |@word secondly:2 concept:1 consider:9 yasuhiro:1 results:3 grateful:1 gn:6 row:6 whose:6 inverse:1 terms:4 remarkable:1 γq:1 finally:5 th:16 analogous:1 kν:16 applied:1 orthogonal:1 far:1 putting:1 entries:4 difference:31 exact:3 condition:2 presented:1 notes:1 solution:8 discrete:32 convenience:1 anal:1 βx2:1 noted:1 wronskian:2 10n:2 ekvac:1 direct:2 matrices:2 painlev:19 pass:1 linear:8 bilinear:14 index:1 nonlinear:1 stands:3 d2:1 section:7 expressed:12 version:2 poles:1 3n:28 above:4 fractional:1 obvious:1 satisfy:2 degree:2 respectively:4 here:5 papageorgiou:4 asymmetry:2 cylindrical:3 concluding:2 quite:1 equations:40 obtained:4 technical:1 study:1 hiroshima:3 suitable:1 makes:1 appropriately:1 useful:2 br:1 zǫ:1 1st:2 use:2 prove:1 suppl:2 next:4 κx2:1 therefore:1 type:3 more:1 possession:1 transcendental:1 fokas:2 validity:1 particular:5 known:3 hold:1 iii:4 derivation:5 ramani:11 account:1 tokyo:2 equation:30 mn:3 modified:1 values:1 following:7 dec:1 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solv-int9412005.txt |@word since:4 homomorphism:2 consider:22 similarity:1 rev:3 global:5 dynamic:2 results:2 invent:3 commute:3 parameterization:2 sci:2 c1:1 1z2:1 scr:1 compact:11 whose:1 inverse:4 depend:18 calculate:4 forgoing:1 graph:18 description:3 technique:1 nonlocal:1 finally:4 program:3 tj:1 those:6 th:51 ti:23 semenov:1 tg:2 analogous:2 γg:1 hill:2 conservation:1 conjecture:1 labels:3 stud:1 very:6 frequencies:1 implicitly:1 ginsburg:1 springer:3 induce:2 geometrical:1 rl:9 corollary:1 crosses:1 formula:9 ui:1 exact:1 deformations:8 condition:27 groups:1 entire:7 dubrovin:4 riemann:89 solves:1 hamiltonian:17 positions:1 solution:5 t1:2 leave:2 admissible:1 vector:2 sine:1 small:1 eigenvalues:1 anal:3 rk:2 shansky:1 zn:3 zi:5 periodicity:4 alternating:1 arnimallee:1 direct:1 cosh:5 haak:1 integrability:1 manner:1 implemented:1 ode:5 obey:10 even:3 index:2 what:1 nonlinear:9 plays:1 cone:1 sum:2 foregoing:3 expressed:2 sheeted:1 poles:1 lptens:1 above:12 scientists:2 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solv-int9412007.txt |@word results:4 gg:2 gf:1 expressions:3 dimensionality:1 depend:1 paris:2 finally:1 present:6 analogous:1 ramani:7 very:2 focus:1 wishes:1 difference:3 condition:1 leads:1 presented:3 turns:1 solution:18 discrete:15 further:2 relation:9 upr:1 upper:1 wronskian:1 cosh:1 painleve:1 zu:1 odd:1 bilinear:13 index:2 what:5 nonlinear:6 appear:1 expressed:3 d3:1 reminiscent:1 goes:2 kruskal:1 satisfy:2 κm:2 κn:17 full:1 respectively:1 here:3 papageorgiou:1 objects:1 sinh:2 ratio:2 quite:1 equations:17 obtained:9 5n2:1 shift:2 study:1 allows:3 minsk:1 usually:1 uniquely:1 useful:1 vii:1 plenum:1 establish:1 use:5 would:1 nijhoff:1 single:1 negative:1 next:4 comparing:1 m2:1 taken:1 associated:1 type:9 more:2 introducing:2 ecole:1 clearly:1 becomes:4 operators:1 factor:1 2w3:2 particular:5 known:5 must:7 me:1 account:1 tokyo:2 recall:1 equation:21 work:1 values:10 publications:1 following:4 dec:1 compare:2 sense:2 dependence:1 involve:1 14b:1 14a:1 14n:1 painlev:18 holds:1 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solv-int9501001.txt |@word represent:1 lakshmanan:4 consider:7 results:1 lancaster:1 edu:1 consists:1 partial:1 localized:1 inverse:1 depend:2 calculate:1 subjected:3 finally:1 th:3 under:1 string:1 orthogonal:7 rise:3 wave:1 rnew:2 entries:1 discretizations:1 parameter:4 matrices:3 qv1:3 condition:7 entire:1 level:2 turns:1 notes:1 specifies:1 solution:1 discrete:35 convenience:1 vector:9 math:10 dealt:1 solutions:1 throught:1 lecture:2 za:1 approximation:3 integrability:1 substituting:1 iσ3:3 iσ2:3 dynamics:19 zs:1 universities:1 what:1 nonlinear:3 appear:1 section:4 selected:1 3i:1 subspaces:2 3l:1 new:4 construction:1 method:2 era:1 κl:1 κn:1 respectively:2 even:2 modify:1 κb:1 tangent:1 free:1 sinh:1 q12:1 represented:1 const:2 along:6 sine:4 equations:17 change:1 obtained:3 remark:7 eij:1 institute:1 shift:2 study:1 vectors:2 allows:2 trautman:1 resulting:1 sci:2 define:3 nearest:1 requiring:1 pinkall:2 fm:1 first:5 santini:5 tools:1 select:2 use:4 takes:3 usa:1 remains:1 νr:1 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solv-int9501002.txt |@word sector:30 sci:1 consider:19 global:1 results:1 four:1 scalar:2 proposition:13 douglas:1 c2:3 follow:1 c1:10 polinomials:2 preserves:1 inverse:1 depend:4 semiclassics:7 re:9 graph:2 presents:1 finally:2 critical:4 petersburg:2 elliptic:5 under:1 brezin:1 analogous:1 norm:7 hill:1 case:8 conjecture:3 g3:9 string:6 g1:2 very:8 connects:1 corollary:7 orientations:2 difference:4 exact:25 deformations:2 condition:1 dubrovin:3 riemann:20 hamiltonian:2 t6:1 turns:1 t4:1 t2:1 solution:65 t0:4 large:6 solved:1 vector:3 indices:1 gauge:1 coinsides:3 straight:1 neighborhood:1 const:1 variables:4 direct:1 sign:1 approximation:3 painlev:2 pass:1 dynamics:1 odd:2 substitute:1 linear:13 even:4 established:1 nonlinear:2 plays:3 appear:1 invertible:1 d2:7 sum:2 find:1 version:1 poles:2 above:22 sup:3 obvious:5 increasing:7 method:6 coefficient:3 full:2 ǫu:4 degree:1 d1:7 never:1 here:18 desired:2 ihes:1 tangent:2 ru:1 others:2 directions:1 path:9 along:14 invented:1 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solv-int9501005.txt |@word miwa:1 minors:1 forget:1 yasuhiro:1 results:1 generalize:1 grateful:1 perturbations:1 gh:1 sogo:1 technique:2 under:4 must:1 applied:3 very:1 difference:1 condition:2 solution:5 relation:1 wronskian:3 10b:1 10c:2 10a:2 direct:1 cosh:1 painlev:1 chen:3 substitute:1 theory:1 bilinear:11 aim:1 nonlinear:4 ˆt:1 section:2 celebrated:1 shares:1 version:1 above:3 method:3 nakamura:2 satisfy:4 lee:1 even:1 here:2 expansion:4 represented:1 equations:16 change:1 obtained:2 remark:1 study:2 studied:1 matsui:1 suitable:1 9h:1 useful:2 9a:2 9c:1 vii:1 9e:1 9d:1 9g:1 9f:2 apply:1 ipx:1 univ:1 use:3 kundu:2 prove:2 eφ:1 suppl:2 next:1 ψj:5 type:7 becomes:2 odinger:4 ip2:1 appendix:1 normalized:1 known:3 cases:1 insights:1 tokyo:5 equation:16 mr:1 following:6 example:1 decoupled:1 f2:1 give:1 dnls:2 dxm:1 assumptions:1 get:3 far:1 pure:1 parameter:1 may:3 dx2:6 dx1:5 consequence:1 fg:2 revealed:1 constants:1 clarkson:2 explicit:2 bunkyo:1 so:1 order:3 talk:1 fγ:1 satisfied:1 paper:2 through:3 japan:3 cll:4 τm:3 chosen:1 solving:2 fruitful:1 choose:1 mail:1 setting:1 freeman:1 them:1 practice:1 effects:1 discuss:1 2t:1 hereafter:1 always:1 university:2 2f:1 2g:1 each:1 found:1 2n:5 2i:4 arxiv:1 reduce:1 society:1 owing:1 sectional:1 our:1 nonlinearities:1 special:1 shown:1 jimbo:1 δi1:1 δi2:1 denotes:1 wronski:2 rational:2 ref:3 math:3 linear:2 kaup:2 mmm:1 clarify:1 ψ2n:1 complicated:1 publ:1 log:1 impose:1 hence:2 first:2 xj:2 already:1 xn:2 symmetry:3 variables:3 faculty:1 xx:1 relations:3 1p:2 given:1 similarly:1 introduction:1 eqs:23 construct:4 their:1 assumption:1 listed:1 relationship:2 newell:2 authors:2 x2:9 x1:20 dtn:1 kenji:1 double:1 integrability:1 vx1:2 vx2:2 jpn:2 7b:1 7a:1 kajiwara:1 conjugate:2 any:1 latter:1 note:2 liu:2 generalized:3 meeting:1 formulas:1 scripta:1 kai:1 algebraic:1 phase:1 soliton:11 nonlinearity:1 clear:1 kn:5 physica:1 ohta:2 principle:1 exp:13 overdetermined:2 ϕ2n:1 physics:1 fact:1 nls:3 show:3 attempts:1 gauge:10 solutions:15 find:1 q2:1 jan:1 only:2 integrate:1 integrable:1 columns:1 means:3 dependent:1 dx:11 ϕj:5 meguro:1 dr:3 differentiating:1 determinants:2 qx:4 differential:1 set:4 hγ:3 depends:1 w2:6 w1:5 discussions:1 written:1 various:2 between:3 conditions:3 ima:1 rims:1 jp:1 however:2 p2j:2 solv:2 dx21:4 both:2 called:2 finds:2 among:1 conclude:1 proved:2 cp:1 consider:1 second:1 decoupling:1 equivalent:1 been:4 expressed:1 int:2 reduction:1 cosgrove:2 pj:4 pn:1 komaba:1 define:1 determinant:3 derivative:4 c1:1 case:9 multi:2 exponential:1 remaining:1 will:2 a20:1 ix:1 coupled:1 iq:1 generic:1 same:3 complex:4 physical:1 higher:2 independent:1 extended:2 ux2:1 ux1:2 hand:2 moment:1 uˆ:4 identity:3 schr:4 acknowledgement:1 2gh:1 left:1 proposed:3 obtain:2 abbreviation:1 integer:1 hongo:1 sciences:1 other:3 transformed:5 transformation:10 9b:1 iα:1 iβ:2 department:2 know:1 using:3 2q:3 modifications:1 helpful:1 28a:1 28b:1 arbitrary:2 rearrangement:1 qxx:5 reduced:1 mathematical:1 2iδ:1 some:1 2iγ:2 2qx:2 30a:1 30b:1 integration:1 comments:1 prog:2 kyoto:1 bn:1 bj:2 imaginary:1 properties:1 quotients:2 most:1 discussed:1 side:2 introduced:1 soc:2 into:8 22b:1 22a:1 nothing:1 references:1 operator:2 yajima:1 rows:1 additional:1 vˆ:4 there:2 u2:2 dispersion:1 start:2 appl:1 way:1 function:3 form:3 but:3 construction:1 october:1 applying:1 iqt:5 us:1 laplace:3 ac:1 constant:1 defined:3 abstract:1 aj:2 general:1 engineering:1 exist:1 formalism:2 check:1 constructed:5 satsuma:3 functions:3 eq:21 hybrid:1 reality:1 valid:1 test:1 theor:2 elements:1 ku:2 preceding:1 a1:1 wadati:1 variable:1 structure:6 auxiliary:1 assume:2 4q:1 4n:2 sasa:1 hirota:7 once:1
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solv-int9501006.txt |@word neighbors:1 gt:4 consider:19 priori:1 magnetic:43 lack:1 results:3 cosines:1 gx:5 leads:4 ginzburg:4 parameterization:4 go:1 follow:1 contributions:1 cases:4 gh:2 compact:1 whose:2 preserves:1 depend:2 segments:7 containing:4 presents:1 charge:1 does:6 tj:10 manifolds:5 th:1 under:10 connecting:2 analogous:1 norm:1 2lt:1 notations:1 orthogonal:4 far:2 translations:2 account:1 trigonometric:6 corollary:5 witten:1 difference:3 exact:5 condition:1 four:2 hamiltonian:5 induction:1 t2:2 solution:1 rationally:1 large:9 smale:1 vector:1 rj:13 small:37 shows:1 round:1 upper:6 smaller:3 neighborhood:12 nullity:2 zk:1 estimates:5 sign:2 approximation:10 consists:1 zero:11 alent:1 pass:2 turning:1 estimated:1 odd:1 linear:2 even:2 index:13 what:2 abc:1 morse:29 bdl:2 section:2 selected:1 δx2:4 cell:1 above:18 3l:1 obvious:6 coefficient:2 homology:3 led:1 κj:13 respectively:4 never:1 here:16 perpendicular:3 desired:2 tangent:6 groups:1 directions:2 along:13 equations:1 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solv-int9501007.txt |@word gw:2 represent:1 partial:1 consider:4 remarkable:1 results:1 commute:1 consists:1 expressions:1 gk:6 gj:8 gi:9 inverse:2 calculate:1 paris:1 λia:1 nonlocal:2 tq:1 tj:3 funk:1 th:2 dressing:16 analogous:1 include:1 g2:4 g1:4 dell:1 geometrical:1 difference:26 matrices:1 condition:1 notations:1 dubrovin:4 hamiltonian:1 did:1 dif:1 solution:7 dic:1 discrete:4 anal:1 diq:9 neighborhood:1 zero:1 canonical:1 bilinear:4 established:1 nonlinear:3 plays:1 section:1 maillet:1 version:1 poles:4 sur:1 establishes:1 scientists:1 new:2 method:12 intas:1 modify:1 equals:1 here:1 understanding:1 canonically:3 les:2 address:1 equations:25 change:1 institute:2 lomi:1 study:2 studied:3 published:1 usually:1 studies:3 exeter:1 via:5 extra:3 univ:1 unit:1 derivatives:1 use:3 would:1 intensively:1 remains:1 teor:1 physics:1 few:1 nucl:1 ψi:2 call:1 usp:1 type:5 theoretical:1 zeroes:1 formally:1 becomes:1 operators:11 ti:3 berlin:1 correspondingly:1 normalized:6 bogdanov:4 known:2 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solv-int9501008.txt |@word gu:2 partial:2 consider:1 results:2 scalar:1 consists:1 gk:3 gj:1 whose:4 inverse:11 depend:1 tt:2 equivalence:1 γk:3 tl:3 program:3 under:3 case:5 t12:3 very:1 dell:1 choice:1 putting:1 matrices:1 condition:2 turns:2 prolonged:1 vector:4 indices:1 still:1 application:2 direct:6 integrability:7 subordinate:1 β2t:1 linear:4 subscripts:1 established:1 t2k:1 nonlinear:16 stands:1 brackets:1 kamran:1 expressed:2 3i:1 above:1 3c:2 new:6 3a:2 method:11 implementable:1 3d:2 satisfy:2 respectively:2 realizations:2 component:2 here:3 leo:6 ansatz:3 groups:2 consideration:2 κv:1 equations:23 obtained:2 remark:2 involved:2 study:2 vectors:2 allows:2 akj:2 products:1 procedure:7 ifu:1 t21:3 adopting:1 birefringent:3 studies:1 quotient:4 emerge:1 formulated:2 family:1 put:1 analyzing:1 ai:1 apply:1 derivatives:1 ψx:1 6b:2 ψt:1 fordy:1 ψj:1 few:2 therefore:1 iαk:1 iαj:1 taken:1 type:7 theoretical:1 more:4 introducing:1 becomes:1 operators:1 odinger:3 berlin:1 normalized:1 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solv-int9501009.txt |@word represent:2 consider:3 illustrates:1 rev:5 magnetic:1 desirable:1 perelman:1 illustrated:2 roy:1 consists:1 clarified:1 integrity:1 causes:1 extra:3 whose:2 fg06:1 tr:4 γn:9 stable:1 embodies:1 straightforward:1 far:1 continues:2 myself:1 seemingly:1 wave:1 summarized:1 hannay:13 difference:1 entire:1 obvious:1 arnold:1 hamiltonian:11 did:1 forth:1 michael:1 intriguing:1 large:1 small:1 round:2 encloses:1 illustrating:1 second:3 eiαn:1 evaluated:3 concludes:1 further:1 linear:5 nen:2 what:1 adds:1 appear:4 rate:1 section:2 while:4 version:1 localized:6 goes:1 fractional:1 new:1 net:1 contributes:1 boost:1 evolving:1 degree:5 modify:2 here:4 atoms:2 behaviour:1 along:10 appears:3 change:7 obtained:1 wesley:1 institute:1 shift:8 study:2 reason:1 experience:1 suggests:1 amount:4 periodic:4 launched:2 action:4 makes:1 genuinely:1 useful:1 scales:4 namely:1 eiφn:2 glance:1 derivatives:2 feb:1 vivid:1 would:5 p0:5 calculation:1 iαn:2 examination:1 therefore:1 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solv-int9502001.txt |@word partial:1 consider:8 remarkable:1 directions:1 results:5 illustrated:2 per:1 localized:2 increase:1 depend:1 respectively:1 stably:1 γv:2 tl:5 stable:5 anharmonic:1 applied:2 very:6 rise:2 springer:1 wave:11 balancing:1 figs:1 venakides:2 difference:3 exact:2 condition:3 2γs:1 school:1 moderate:1 obvious:2 rtt:1 turns:3 shock:13 t2:1 solution:9 damped:4 large:3 discrete:4 adjust:1 science:1 small:7 infinities:1 upper:4 smaller:2 tel:1 specially:1 waveforms:1 dealing:1 pulse:1 sign:8 approximation:14 second:5 traveling:7 concludes:1 qualitatively:2 dynamics:1 estimated:1 goes:1 even:3 aim:1 what:3 nonlinear:3 section:3 above:4 deift:1 values:7 method:1 shocks:1 body:1 full:4 9th:1 relates:1 eksp:1 spacing:1 l21:1 free:1 others:1 represented:1 consideration:1 strong:2 equations:2 change:4 obtained:6 sending:1 noticeable:1 shift:2 study:2 adjusts:3 domains:2 suitable:2 changes:3 plotted:2 γp:1 mobility:1 explained:1 highly:1 logarithmic:1 visible:1 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solv-int9502002.txt |@word secondly:2 partial:3 consider:1 chain:11 illustrates:1 results:1 olive:1 scalar:1 consists:1 cases:3 depend:1 pointing:1 description:1 nonlocal:2 finally:2 th:1 dressing:1 analogous:2 worth:1 fuv:1 straightforward:1 very:1 wave:1 putting:1 difference:3 matrices:2 condition:5 presented:1 did:1 proc:1 notes:1 discrete:23 vector:1 der:1 upper:1 consistent:2 second:2 odd:3 theory:1 even:4 index:2 what:1 nonlinear:1 appear:1 diag:1 sum:1 expressed:1 version:2 above:2 consisting:1 full:3 spacing:1 here:2 papageorgiou:1 address:1 sine:2 equations:23 appears:1 z2:3 gibbons:2 obtained:4 institute:1 shift:1 periodic:1 resulting:2 via:1 replace:1 addressed:1 durham:2 unit:1 use:1 feb:1 takes:1 would:1 nijhoff:4 ψv:1 ψu:1 nucl:1 examination:1 therefore:1 3le:1 type:3 more:2 sort:1 labelled:1 particular:4 known:2 ward:1 topic:1 springer:2 equation:13 work:1 det:2 values:1 making:1 example:3 f0:1 f1:9 f2:4 saito:1 involve:3 cartan:2 rather:3 holds:1 parameter:1 fu:3 fv:3 algebra:7 diagram:1 levi:1 plane:6 lax:3 representations:1 fj:1 fk:13 fn:12 correspond:1 su:1 think:2 so:7 representation:4 order:1 ϕk:4 indeed:1 suris:6 satisfied:2 symbols:1 looks:1 its:3 roots:2 before:1 group:1 fit:1 affine:6 coordinates:2 permanent:1 systems:4 isaac:1 derivative:1 main:2 non:1 they:1 half:6 now:2 yu:3 maintaining:1 term:1 finite:4 preferable:1 university:1 each:3 2n:1 mean:1 mikhailov:1 differential:1 fairly:1 reduce:5 toda:19 laboratory:1 special:3 out:1 shown:2 matrix:6 since:1 denotes:1 stud:1 lecture:1 ref:2 math:4 linear:5 diagonal:3 quite:1 approaches:1 impose:5 motion:1 gordon:2 exhibited:1 first:2 symmetry:6 variables:3 dynkin:1 number:1 rank:1 another:2 open:1 interchange:1 similarly:4 unknown:1 system:5 least:1 zeros:1 constants:1 scheme:1 f1v:2 speaking:1 gives:1 exactly:1 kupershmidt:1 than:3 integrability:1 limiting:1 saitoh:1 dtp:1 seem:1 lie:14 wilson:1 latter:2 note:3 sciences:2 generalized:1 begin:1 continuous:2 olshanetsky:1 though:1 algebraic:3 involving:1 remarks:1 clear:1 physica:1 exp:23 usual:1 physics:1 quantity:1 reductions:1 purely:1 miwa:1 akns:1 corner:2 should:2 only:2 explicitly:1 a2n:1 integrable:9 capel:4 dn:4 do:6 notation:1 exceptional:2 syst:1 ones:2 words:3 ϕj:2 lattices:1 boundary:3 quispel:3 continuum:5 fields:1 arxiv:1 method:2 exists:1 imposing:1 depends:1 subject:1 ways:1 sites:2 symmetric:2 various:1 dynam:1 ladik:1 subscript:1 conditions:1 notice:1 terms:3 shabat:1 nature:1 restricting:1 however:1 comm:1 solv:1 fnv:1 fnu:2 taking:1 thinking:1 connection:1 f2u:2 unclear:1 cn:3 simple:4 others:1 cf:1 dimensional:10 appeared:1 described:3 equivalent:1 been:5 int:1 reduction:3 interest:1 basic:1 algebras:8 direction:1 corresponding:11 despite:1 those:1 case:4 unlike:1 examine:2 choices:1 dept:1 while:1 replaced:2 situation:1 region:1 jpn:6 refs:1 ir:1 vu:2 ie:1 cjk:5 different:4 etc:1 things:1 admit:2 same:2 turok:1 several:1 independent:4 literature:1 see:1 effect:3 hand:2 infinite:1 ablowitz:1 identity:1 lower:1 onedimensional:1 consistency:2 entry:1 dh1:1 left:1 restore:1 just:1 being:2 newton:1 integer:2 ergod:1 yet:1 multiples:1 zakharov:1 iϕ:1 lattice:9 lett:5 remaining:1 increased:1 period:1 immediately:1 appearing:1 like:1 follows:1 reduces:5 specific:1 santini:1 yields:1 arbitrary:1 δb:1 reduced:1 δa:3 mathematical:2 wiersma:1 right:1 often:1 namely:1 some:4 acad:1 b1:1 does:1 chains:4 bn:6 analysed:1 fordy:1 deriving:1 about:1 constraint:4 column:1 slightly:1 automatically:2 perelomov:1 soc:6 cambridge:1 letters:1 h2:11 into:1 integral:1 isomorphic:1 because:3 references:1 operator:1 leningrad:1 van:1 additional:1 strictly:2 there:9 question:4 long:1 appl:1 way:2 forward:1 function:1 hx:1 elsewhere:1 form:3 regard:1 but:9 he:1 made:1 versions:7 whether:4 uv:2 us:3 below:2 limit:4 uk:2 similar:2 examples:2 linden:1 ab:2 constant:2 defined:4 certain:2 abstract:1 general:3 single:1 exist:3 again:1 functions:2 locality:1 field:15 other:5 mathematics:1 conclusion:1 picture:1 elements:1 hirota:9 a1:3 cb3:1 variable:4 gets:1 structure:1 using:1 required:1 together:1 presenting:1 time:1 original:2
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solv-int9502003.txt |@word proposition:1 secondly:1 similarity:1 comparatively:1 results:13 gy:1 gx:1 commute:1 follow:1 excludes:1 inverse:1 alamos:1 tt:1 recurrence:1 γj:2 charge:8 tm:1 th:3 under:3 analogous:1 p2:1 1pn:1 straightforward:2 very:1 implicitly:1 wave:2 suggesting:1 wishes:1 fall:1 redefinition:1 condition:1 generalised:2 dubrovin:2 riemann:2 hamiltonian:13 solution:14 t0:3 involution:1 adjust:1 mulvey:1 gauge:3 permutability:1 strachan:2 degeneracy:1 l95:1 coordinate:1 2k2:1 sin2:1 direct:4 approximation:1 fold:1 second:5 zx:2 zt:2 dynamics:1 linear:3 spectral:1 3z:1 plays:1 ufn:1 section:8 favour:1 expressed:1 version:1 above:3 new:5 coefficient:1 degree:2 q0:1 respectively:1 l1:3 here:2 cos2:1 groups:1 strong:1 equations:10 appears:2 change:5 obtained:2 antisymmetric:1 weinstein:2 study:2 studied:3 suggests:1 poisson:2 suitable:1 makes:1 involves:1 ne1:1 pxx:1 followed:1 family:3 logarithmic:1 why:1 durham:3 total:1 tn:5 use:4 feb:1 would:2 prove:1 remains:1 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solv-int9502004.txt |@word quebec:1 partial:2 gr:1 remarkable:1 global:1 results:6 leads:1 infinitesimally:1 generalize:1 meinel:2 consists:1 oldest:2 heid:1 reparameterization:1 consider:1 kh:1 whose:1 isometric:1 depend:1 circ:1 paris:1 technique:1 intensive:1 finally:1 those:1 excluded:1 dressing:1 division:1 conjecture:1 straightforward:2 very:1 translations:1 choice:1 entries:1 matrices:8 deformations:2 condition:2 dim:1 school:1 presented:2 turns:1 notes:1 solution:8 large:1 discrete:1 vector:1 indices:2 der:1 upper:1 lecture:3 za:2 sign:2 integrability:5 plenum:1 displays:1 pass:1 iσ3:2 further:2 linear:20 spectral:3 what:2 nonlinear:3 dei:1 annali:1 sum:2 celebrated:1 umbilic:3 reconstruction:1 new:3 method:2 satisfy:1 palmer:1 ichikawa:2 respectively:1 certainly:2 here:1 8d:3 sinh:6 const:2 xf1:1 sine:1 equations:5 implicit:1 logarithmic:2 obtained:1 great:1 institute:3 study:3 studied:1 suggests:1 resulting:1 published:1 usually:1 resonance:2 studies:3 uniquely:2 formulated:1 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solv-int9502005.txt |@word partial:3 consider:8 equalities:2 results:9 lr2:7 row:1 devoted:1 whose:1 γj:4 tl:1 tk:1 xti:1 applied:1 very:1 dokl:1 putting:1 difference:2 matrices:2 condition:11 entire:1 wetensch:1 solves:1 t2:32 solution:24 t1:127 integro:1 vector:5 cooke:1 math:4 eigenvalues:2 biorthogonal:8 linear:37 established:1 appear:1 trivial:3 section:1 uniform:1 current:1 above:1 new:5 method:3 chose:1 xλ:2 objects:1 equations:14 obtained:6 remark:1 vectors:9 contr:7 fourier:1 uniquely:6 identification:1 bounds:1 vij:1 limj:1 analyzing:1 apply:1 linearly:2 use:4 feb:1 prove:4 positive:1 γi:1 properties:5 therefore:2 criteria:1 vectorvalued:1 theoretical:1 more:2 zeroes:1 nauka:1 israel:1 becomes:1 operators:4 distribution:1 levin:1 berlin:1 virtue:1 particular:2 known:5 cases:1 hold:2 iii:6 must:1 springer:1 valued:5 science:1 equation:58 det:2 values:1 publications:1 following:1 trans:3 root:2 example:2 proof:8 control:12 theorems:3 purposes:1 bellman:1 numbers:5 absolute:1 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solv-int9502006.txt |@word consider:1 leads:1 eds:1 providence:1 tn:10 tm:1 under:2 orthogonal:4 choice:2 corollary:1 wishes:2 entries:3 tridiagonal:4 matrices:2 condition:1 hamiltonian:1 bn:6 notes:1 t2:1 solution:4 t1:4 large:1 eigenvalues:11 anal:1 upper:2 work:1 eλt:1 direct:1 integrability:1 further:2 dynamics:1 theory:1 plays:1 appear:1 cˆi:2 diag:8 section:1 ak0:1 expressed:2 symes:5 version:1 expresses:2 method:6 nakamura:2 satisfy:1 full:7 here:6 separation:1 along:1 equations:5 appears:1 obtained:5 remark:2 weinstein:1 studied:1 orthogonalization:7 periodic:1 permutation:1 action:1 relation:2 via:2 φkm:3 sgn:2 establish:1 feb:1 asymptotic:1 usa:1 distinct:2 contains:1 ψj:4 ψi:12 call:3 introducing:1 initial:8 ti:1 eξ:21 normalized:1 particular:1 φk0:1 cases:1 potential:1 evolves:1 springer:1 ρi:4 equation:11 ρj:2 det:2 modified:1 flaschka:1 publications:1 following:3 proof:3 lφ:2 tau:2 give:5 expanding:1 permutations:1 sense:1 verlag:1 information:1 verify:1 holds:1 orthogonality:5 nyu:1 pure:1 ordinary:1 may:1 suppose:1 collection:1 consequence:4 lax:1 fi:2 data:1 compatibility:1 constants:1 ψi2:3 dynamical:1 explicit:4 summing:1 so:1 fundamental:1 decreasing:2 lλ:1 hierarchy:10 developed:1 over:2 interpreted:1 course:1 paper:1 satisfies:1 its:1 diagonalized:1 thank:3 ln:12 solving:1 2λi:1 writing:1 systems:2 schmidt:1 arguments:1 non:1 framework:1 they:1 now:5 φj:7 eigenvalue:2 february:1 finite:5 dirac:1 university:1 l0:6 each:1 2m:4 ℓn:1 cˆij:1 differential:1 arbitrariness:1 ed:1 toda:19 yield:1 measure:2 out:1 leave:1 shown:2 matrix:30 since:2 denotes:1 orthonormalized:1 reader:1 formula:10 math:3 linear:2 diagonal:6 completely:1 kodama:2 york:1 e2:2 derivation:2 applications:1 geometry:1 motion:1 turn:1 δij:5 signature:1 hence:3 generalizations:1 first:4 xi:1 xn:2 variables:2 encouraging:1 ℓj:3 ℓi:6 relations:7 directly:1 given:7 necessarily:1 fascinating:1 introduction:1 system:4 construct:2 1i:5 ordered:2 final:1 gives:2 immediate:1 part:1 authors:1 x1:2 siam:1 finitely:1 mclaughlin:1 showed:1 sections:1 imply:2 kth:1 were:1 1n:1 say:1 any:1 viewed:1 angle:1 zero:1 general:1 szeg:4 converges:3 note:7 k0:4 coincide:1 collaboration:1 molecule:2 formulae:5 nothing:1 flow:1 physica:1 order:3 bracket:1 diagonals:2 exp:4 fact:1 selection:1 show:6 text:1 supported:1 percy:2 spaces:1 gauge:1 guidance:2 written:3 should:1 lemma:4 only:1 indeed:2 integrable:5 moser:3 dn:6 dominant:3 dk:3 di:19 new:1 compute:1 him:1 evolution:1 qr:5 qt:2 arxiv:1 factorization:6 gram:1 ohio:1 set:1 constructing:1 exists:1 see:4 lec:1 result:2 λi:6 subject:1 eigenfunctions:3 symmetric:18 state:1 invariant:2 conditions:1 terms:2 numer:1 points:1 however:1 comm:1 solv:1 amer:1 c21:1 many:1 according:1 chosen:1 colloquium:1 symplectic:1 otherwise:1 comment:1 ci:12 cn:1 point:1 quantizations:1 respect:1 li:1 pp:1 described:3 skew:1 been:1 int:1 pn:5 define:2 determinant:6 corresponding:1 tomei:2 quantities:1 observe:2 determination:1 denote:1 case:7 main:1 classifications:1 exponential:1 value:3 will:1 contemp:1 aii:2 aik:4 aij:8 property:6 procedure:6 vol:2 thus:2 ii:1 ij:1 rii:1 vanish:1 containing:2 φt:2 grant:1 generic:3 split:1 φi:17 proved:2 φk:2 φm:7 φn:6 independent:1 extended:1 maeda:1 i0:5 viewing:1 identity:1 eigenvectors:6 lower:2 band:1 well:1 solve:2 components:1 sets:1 just:1 λt:1 obtain:4 immediately:1 λk:17 λj:8 alternative:3 scattering:1 λn:17 apple:1 lattice:5 book:1 easy:1 theorem:6 diagonalization:1 c11:5 nanda:2 transformation:1 eigenfunction:1 deift:5 φ0m:1 φ0n:16 φ0i:11 term:4 φ0k:3 φ0j:7 using:3 ams:1 unique:1 helpful:1 c1k:1 c1i:8 sorting:6 c1n:2 yields:2 arbitrary:2 become:1 e2ξ:2 replacement:2 classical:1 sequence:1 some:4 nonzero:2 integration:1 omori:1 decomposition:1 prog:1 prof:4 columbus:1 equivalent:1 properties:1 would:1 world:1 oh:1 column:2 freedom:2 o:7 nonvanishing:1 greatly:1 soc:1 into:1 functional:1 nsf:1 nonperiodic:1 references:1 span:6 log:3 strictly:1 there:1 transform:1 ψn:1 was:1 naturally:1 function:2 complete:1 form:3 enough:1 triangular:3 but:1 line:1 partially:1 arranged:2 cij:6 us:1 problem:5 eigenvector:1 mechanics:1 associated:1 defined:3 likewise:1 abstract:1 influence:1 ordering:2 dλ:1 a1i:1 dα:3 functions:4 compared:1 fixing:1 when:2 setting:1 role:1 becomes:1 department:1 mathematics:2 theor:1 calculating:1 preceding:1 polynomials:1 includes:1 a1:1 acknowledgment:1 implies:4 algorithm:1 assume:1 orbit:1 together:4 mass:1 time:2
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solv-int9503001.txt |@word consider:2 leads:2 dα:9 presentation:1 γd:1 very:2 manin:3 four:3 school:1 hamiltonian:3 dαx:2 convenience:1 harry:5 ten:1 consistent:3 zero:2 further:1 odd:3 even:3 index:1 nonlinear:1 wxxx:1 version:3 suspect:1 above:2 fractional:1 method:1 respectively:3 here:3 china:3 address:1 consideration:1 sine:1 equations:5 knowledge:1 box:1 remark:1 kanno:2 involved:2 study:3 suggests:1 u3x:1 formulated:1 useful:1 projection:1 would:1 commun:3 suppl:1 next:1 taken:1 type:2 more:2 particular:1 known:5 cases:8 fermionic:2 science:1 equation:11 work:2 following:6 my:2 proof:2 beijing:3 calculation:1 cited:1 sense:2 occur:1 end:1 darboux:2 verify:1 di:1 pure:1 sato:1 mas:1 mar:1 may:9 applications:1 lax:8 lhd:2 natural:1 dynamical:1 kulish:1 kersten:1 so:1 pleasure:1 order:3 hierarchy:1 inami:2 pointed:1 years:1 paper:1 including:1 mentioned:1 still:1 thank:2 interesting:3 fix:1 lt:7 systems:6 supersymmetry:1 them:1 greater:1 propose:1 kiso:2 noticing:1 mention:1 they:1 yu:1 term:1 name:1 always:1 university:2 arrested:1 each:1 found:2 side:1 subsystem:1 related:1 aim:1 laboratory:1 out:1 since:2 rev:3 get:1 math:9 shows:2 foundation:1 reformulated:1 standard:2 ramos:1 hand:1 beginning:1 8u:2 feasible:1 βd:1 gordon:1 consequence:1 first:2 roelofs:1 variables:4 number:1 given:1 system:15 construct:3 1a:1 superintegrable:1 statement:1 popowicz:1 structures:1 gives:1 mining:1 progr:1 relationship:1 kupershmidt:7 part:1 than:1 kind:1 skdv:1 argument:3 any:1 petviashvili:1 greek:1 note:3 liu:2 analogy:1 algebraic:1 representation:3 remarks:2 class:1 rogers:1 dordrecht:1 mailing:1 oevel:3 phenomenon:1 reductions:1 supported:1 notations:1 gauge:1 decompositions:1 kadanoff:1 figueroa:1 based:1 just:1 should:1 only:4 integrable:5 boris:1 means:2 de:2 dym:5 during:1 du:9 dr:2 kadomtsev:1 consist:1 fields:5 arxiv:1 shd:8 set:5 national:1 see:5 w2:1 terms:1 nonstandard:2 best:1 subject:1 αt:1 αx:8 78b:1 between:2 αi:1 approach:1 αn:2 latin:1 recently:1 rims:1 attention:1 however:3 wt:1 solv:1 recall:1 restrictions:1 last:3 taking:1 etc:1 context:1 conclude:1 simple:1 corresponds:2 mkdv:1 mathieu:1 transformations:1 three:3 been:1 dux:2 reduction:1 much:1 basic:1 referee:1 supersymmetric:6 case:19 will:3 while:1 thus:5 uxx:5 reads:1 itself:1 uxxx:2 technology:1 generic:1 same:2 physical:1 difficult:2 flows:2 publ:1 recent:1 acknowledgement:1 well:3 model:3 possesses:1 proposed:1 facts:1 preprint:1 candidate:2 mathematically:1 interested:1 lett:4 easy:1 mod:1 transformation:1 lacking:1 five:2 know:1 press:1 world:1 apart:1 like:1 follows:1 manifest:1 communications:1 korteweg:2 inter:1 reidel:1 right:1 some:1 kdv:4 ccast:1 lead:2 comments:1 αxx:2 power:1 kyoto:1 bi:1 super:10 o:2 2i:2 deserves:1 extensions:3 konopelchenko:1 letters:2 references:3 operator:9 bosonic:1 schrodinger:1 u1:1 u0:4 noticed:1 102a:1 was:1 form:2 regard:1 denoting:1 but:1 link:1 hd:9 ux:14 embedded:1 ut:2 us:3 considered:2 un:3 ui:2 detailed:1 proved:2 int:1 abstract:1 general:5 exist:1 our:3 commuting:1 constructed:1 when:1 graduate:1 field:2 other:1 department:1 mathematics:1 theor:1 conclusion:1 elements:1 models:1 radul:2 important:1 variable:3 implies:1 vries:2
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solv-int9503002.txt |@word consider:1 induces:1 global:1 results:6 consists:1 amplified:1 contributions:1 localized:1 inverse:2 zone:1 γq:1 γt:1 th:1 stochastic:1 analogous:1 indicating:1 very:1 wave:5 figs:2 resonant:1 exact:2 al0:4 carman:2 level:1 ref:1 tanh:1 t2:2 solution:14 t0:3 t1:2 large:2 discrete:2 scalings:1 small:4 optics:1 equation:1 application:2 zh:1 discover:1 pulse:5 sign:5 rate:1 value:8 choices:1 expressions:1 linear:3 spectral:5 what:1 nonlinear:8 appear:1 ct2:3 reminiscent:1 wenzel:4 above:5 new:1 principal:1 method:1 coefficient:1 led:1 fiz:2 eksp:1 never:1 here:5 reported:1 amplification:2 active:2 path:2 equations:5 change:4 obtained:4 remark:3 balance:2 shift:3 study:2 studied:1 allows:1 approaches:1 through:2 resulting:3 published:1 fourier:4 studies:2 hump:1 via:1 montpellier:3 linde:2 namely:1 scaled:1 decrease:2 total:1 readily:1 use:1 would:1 positive:2 continuous:1 eφ:2 predictions:1 france:1 process:1 call:2 chu:2 spike:23 taken:2 survive:1 theoretical:2 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solv-int9503003.txt |@word consider:5 remarkable:1 priori:1 alg:3 magnetic:3 splitting:1 leads:1 proposition:3 computation:1 gl:1 gi:1 devoted:1 preserves:4 superspace:1 funct:2 pˆt:33 under:3 anharmonic:11 tb:6 g2:1 g1:1 g0:7 print:4 corollary:1 perihelion:1 govern:1 deformations:2 dubrovin:1 hamiltonian:11 t2:10 t1:12 vector:1 splitted:1 bxa:1 relation:1 anal:1 superalgebras:2 approximation:2 dynamics:22 odd:2 even:2 nonlinear:4 ˆt:41 appear:2 brackets:6 sum:1 expressed:1 abp:2 abq:2 version:3 subspaces:1 ˆg:1 international:1 t2s:2 respectively:2 here:2 behaviour:1 objects:3 equations:9 appears:1 remark:1 institute:2 shift:1 poisson:7 superalgebraic:1 hospitality:1 via:2 classification:1 ii2:2 apr:1 marked:2 juriev:6 aˆt:33 austria:2 univ:3 use:1 commun:1 m1:2 therefore:3 m2:2 type:4 operators:3 ti:1 pairs:4 central:1 hold:1 analogous:1 springer:2 car:2 equation:1 superstructure:1 theories:1 erwin:2 ere:2 values:2 mp:2 following:2 example:3 proof:1 f1:4 f2:3 december:1 lorentz:2 nonhamiltonian:4 axiomatization:1 needs:1 end:2 straightforward:1 rather:1 hom:2 ryz:4 hi:1 verlag:3 parameter:1 sin:9 product:2 algebra:4 may:6 oscillators:25 after:1 xzy:1 applications:1 produce:1 physik:1 fi:2 data:1 compatibility:1 constants:1 realized:1 natural:1 dynamical:5 maybe:1 explicit:1 so:7 sl:1 definitions:1 operations:1 dx:1 course:1 its:2 relativity:1 forms:2 defintion:1 systems:9 jacobi:1 hidden:8 deformation:1 texas:2 non:1 combination:1 introduce:1 yz:1 they:1 now:1 easily:1 2q:1 2s:1 always:1 realistic:1 iff:5 2b:1 each:3 2l:1 associative:1 differential:1 related:3 quantum:20 special:1 shown:2 rp:62 matrix:1 rr:2 space:9 crucial:1 investigation:1 ra:2 rb:1 rc:9 denoted:1 fomenko:1 math:6 semidirect:2 linear:6 interactions:2 karasev:1 standard:1 admits:4 difficulty:1 put:9 βt:2 definition:4 xuv:1 interaction:6 geometry:2 phrases:1 re0:1 motion:6 explored:1 derivations:1 hence:3 generalizations:1 first:2 there:4 number:1 xy:1 another:1 representations:2 xt:3 mercury:1 arch:6 system:6 relations:6 their:1 statement:1 zxy:1 structures:1 part:3 kind:1 polarized:6 determined:1 w2:7 nonabelian:1 any:3 lie:23 mappings:3 convenient:3 note:5 potential:1 εi:3 forces:1 heisenberg:1 shall:1 ıve:3 most:3 letter:2 representation:10 pair:18 acknowledgements:1 commutation:1 isotopic:21 considered:4 sometimes:3 possesses:1 axb:1 bracket:1 realised:1 physics:1 arnol:1 spaces:3 gauge:1 superalgebra:9 principal:4 q2:11 parameters:1 commutators:1 should:3 integrable:2 hamiltonians:9 interested:1 do:1 above:1 means:1 between:1 words:1 dt:7 cˆt:33 continuum:1 qv:2 arxiv:1 qa:3 qb:3 integr:1 set:1 physically:1 namely:3 arc:2 result:1 w1:6 subject:1 interacting:2 αx:1 state:1 difficulties:3 closed:3 simplest:1 subscript:2 conditions:1 preserve:1 terms:3 however:3 wi:3 key:1 solv:3 amer:1 suppressed:1 both:3 cos:6 quantization:6 etc:1 appeared:1 character:1 cf:5 2i1:1 dimensional:1 anti:7 asserted:1 xay:1 described:2 pt:1 basis:1 wien:1 mark:1 int:2 reduction:1 faulkner:1 algebras:2 abstract:1 important:2 define:1 modern:1 families:1 yzx:1 sufficient:1 c2:1 denote:2 case:4 cbr:2 intriguing:1 will:4 coupled:19 vi:7 thus:2 quantize:1 itself:1 triple:7 ax:1 verified:1 author:1 generic:2 media:1 i22:3 renormalize:1 same:4 split:4 several:1 higher:1 meets:4 investigated:1 spectively:1 i1:7 i2:8 effect:2 hand:1 v1:42 v2:41 birkhauser:1 identity:1 schr:2 well:7 mathematische:1 quantitative:1 dimension:1 bodies:1 charged:1 maslov:1 just:1 less:2 fˆt:1 underlying:2 thanks:1 preprint:1 conclusions:1 nilpotent:1 seems:1 mathematically:1 belongs:2 formal:2 solvable:1 unravelled:1 march:1 spanned:3 harmonic:10 amp:2 ruled:1 sissa:1 integrals:3 arbitrary:3 denis:1 mathematical:2 often:2 classical:19 examples:1 though:3 provides:1 closely:1 esi:1 obey:1 bt:1 bv:2 bp:1 become:1 super:7 zuv:1 extension:1 algebraic:4 novikov:1 dependence:1 compatible:2 acp:1 obeys:1 t1s:2 perelomov:1 duke:1 soc:1 h2:9 xyz:7 h1:9 integral:2 isomorphic:2 references:1 operator:5 methods:2 span:1 support:1 initial:6 quadratic:2 way:2 resulted:1 was:1 vienna:1 complete:1 form:9 but:2 construction:2 russian:2 illustrative:1 gravitational:1 uv:1 ur:1 called:6 mechanics:4 associated:2 defined:8 certain:2 universal:1 describe:2 general:3 aq:1 exist:1 formulation:4 corresponding:4 identities:1 defines:2 no:3 na:3 whereas:4 field:1 other:2 mathematics:1 theor:1 elements:7 thirring:1 odinger:2 generated:3 a2:3 rqc:2 structure:3 rq:56 lanl:2 modules:1 i12:4 4l:1 ternary:1 time:1
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solv-int9504001.txt |@word magnetic:7 dynamic:1 analiz:1 whose:5 const:2 calculate:3 presents:1 under:2 spec:1 conjecture:1 jack:3 summarized:1 affect:1 school:1 dubrovin:2 solution:7 admissible:1 vector:8 quasiperiodicity:2 shows:1 miller:1 direct:2 second:3 correlator:1 rigorous:3 even:5 selected:1 liberty:1 sheeted:1 above:14 new:9 notions:2 here:4 reported:2 fairly:1 q13:19 q12:7 represented:2 obtained:17 rigorously:1 study:3 stressed:1 fourier:1 b342:1 total:1 univ:1 linearly:1 would:6 substitutions:1 tm:2 therefore:1 unfortunately:1 type:6 separated:20 odinger:7 warn:2 berlin:1 continual:1 outdated:1 must:1 springer:3 feigin:3 mo:1 work:5 theories:2 flaschka:1 my:1 example:8 give:3 relativistic:6 validates:1 generically:1 caution:1 degenerate:4 guarantee:2 hoc:1 provide:3 verify:5 feature:1 how:5 nontrivial:3 ordinary:2 frenkel:3 classify:1 lam:1 replacing:2 tsiganov:4 lax:2 summarize:1 attempt:1 third:3 davies:1 correlation:2 order:11 interpretation:1 sanchez:1 over:1 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solv-int9504003.txt |@word gt:1 consider:3 results:2 2c1:1 leads:2 follow:1 gh:1 inverse:2 tt:2 under:2 applied:1 g4:1 g3:1 6p3:1 far:1 ginsburg:1 wave:4 exact:5 condition:6 school:1 hamiltonian:2 shock:1 guo:1 solution:14 δh1:2 convenience:1 gauge:1 linearizing:1 painlev:10 pass:2 chen:1 further:2 ode:1 linear:2 even:3 what:2 nonlinear:5 u31:1 3c:2 new:2 method:5 coefficient:1 full:2 notions:1 inviscid:4 component:1 here:1 china:3 expansion:3 address:1 consideration:2 sine:2 equations:7 box:1 remark:2 geophys:2 drs:1 resonance:1 useful:1 2φt:1 apr:1 ghil:2 use:1 would:2 next:2 therefore:2 taken:1 type:4 more:5 solitons:2 2w3:2 mansfield:1 particular:1 known:3 hold:2 must:2 nutku:2 science:1 equation:60 work:1 modified:4 obvious:1 following:7 example:2 beijing:3 give:3 calculation:1 indicates:1 performed:1 sense:3 tan:2 information:1 boussinesq:4 straightforward:1 rather:2 get:4 sic:1 very:2 3w2:1 sin:3 singular:6 may:12 wiley:1 derived:1 dx2:1 fluid:2 explored:1 lax:1 ff:1 φ2t:1 xxxx:1 fj:2 maj:3 compatibility:2 constants:2 stress:1 natural:1 clarkson:2 effective:1 explicit:2 perform:1 so:1 order:3 typical:1 indeed:1 satisfied:2 produced:2 course:1 paper:1 existence:1 still:1 its:2 roots:1 before:1 solitary:4 group:2 thank:1 interesting:5 fruitful:1 systems:4 derivative:1 travelling:1 decades:1 into:2 them:2 acklund:4 introduce:1 landau:1 scaling:1 identically:1 front:1 now:4 easily:1 term:1 university:2 2c:1 found:2 referred:1 em:1 ej:2 doing:1 series:1 our:1 extract:1 out:1 since:2 denotes:1 investigation:1 math:8 shows:3 achievements:1 foundation:1 provide:1 theory:2 39d:1 york:1 beginning:1 definition:1 pairs:1 impose:2 counterpart:1 gordon:2 first:1 symmetry:1 waves:2 transform:1 xx:10 long:1 another:1 clarity:1 given:3 φ2x:2 leading:2 carnevale:2 system:5 construct:1 fm:1 vxx:1 vxt:1 siam:1 cite:1 gives:1 mining:1 whitham:1 segur:1 coefficients:1 kind:1 double:1 iteration:1 second:2 w2:7 rewrite:1 seen:2 any:2 lie:1 zero:2 thorough:1 note:2 k2:2 take:1 finding:1 rediscovered:1 bilinear:1 philadelphia:1 though:1 riccati:3 importantly:1 but:1 remarks:1 soliton:2 laurent:3 considered:2 calculated:1 later:1 flow:1 physica:2 vtx:1 principle:1 kx:2 mailing:1 fact:1 particularly:1 show:1 supported:1 relation:1 solutions:10 astrophys:2 substituting:2 d2:1 find:5 proposed:1 should:1 vxxx:1 integrable:5 he:1 hopf:1 meant:1 do:2 dm:1 dj:2 above:4 means:3 dc:3 dyn:2 during:1 dt:3 gen:2 prime:1 liu:1 evolution:1 approach:1 arxiv:1 zhu:1 musette:2 satisfy:1 exists:1 national:1 see:7 w4:1 w3:1 truncating:1 w1:1 discussions:1 vvx:1 case:4 difficulties:1 various:1 conditions:1 available:1 notice:1 recently:1 utt:1 wtx:1 weak:3 however:3 jm:2 wtc:7 solv:1 wx:3 cos:3 last:1 wv:1 taking:1 wt:7 expression:1 cos2:1 cj:2 ci:1 cm:1 point:1 dimensional:1 respect:2 bξ:2 gxx:1 transformations:2 three:2 been:1 int:1 reduction:2 pi:1 choose:1 conte:2 describe:1 quantities:1 xxx:1 great:2 gx2:1 olver:2 c3:1 c2:6 c1:4 c0:1 present:2 p2:2 p3:1 p1:2 p4:1 will:7 suppose:1 property:2 procedure:1 coupled:1 thus:3 uxx:3 vt:2 vw:1 vx:5 technology:1 φp:1 φt:3 φx:3 problems:1 tells:1 φj:2 several:2 higher:1 used:1 equalizing:1 cubic:1 numerical:1 interscience:1 ablowitz:2 literatures:1 acknowledgement:1 well:2 analysis:9 burgers:4 without:1 solve:2 model:1 manifold:6 φtt:1 just:1 among:1 3p4:1 obtain:1 using:3 scattering:2 letting:1 density:1 extra:1 weiss:4 other:1 easy:1 kuramoto:1 transformation:2 real:2 press:1 world:1 helpful:1 like:1 success:1 qualitative:1 collect:1 δh:1 arbitrary:3 δg:1 stationary:1 interestingly:1 methods:1 classical:2 some:7 b2:3 kdv:2 ccast:1 happens:1 sivashinsky:1 describing:1 lead:3 resonances:2 integration:2 2c2:1 2c3:1 does:2 eliminate:1 provides:1 power:2 tabor:3 bm:1 kruskal:1 bj:2 bt:5 properties:1 about:1 constraint:1 o:1 compatible:1 carrier:1 consequently:2 automatically:1 cambridge:1 φxx:6 h2:1 h0:1 h1:1 references:2 there:1 u1:6 u0:3 u3:3 u2:1 quadratic:1 way:2 lou:1 was:1 function:3 hx:1 form:1 ht:1 hu:1 reminds:1 truncation:2 made:1 applying:1 us:9 um:8 below:1 uk:6 uj:28 problem:1 similar:1 constant:3 defined:1 recognize:1 abstract:1 aj:7 am:1 general:1 conserved:1 arises:1 exist:1 laboratory:1 constructed:2 compared:1 integrability:1 wxx:3 detail:1 graduate:1 book:1 test:6 conclude:1 nonclassical:1 important:2 nonintegrable:3 required:1 together:1 hirota:1
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solv-int9505001.txt |@word consider:16 chain:3 funct:1 magnetic:6 global:1 dynamic:2 probl:1 bc:1 ga:1 compact:2 certainly:1 aug:1 kβ:1 th:1 under:3 semenov:2 analogous:1 ra:1 p2:1 string:1 kω:2 2rc:6 denoted:1 matrices:7 deformations:1 condition:1 2rp:1 dubrovin:2 hamiltonian:13 t2:5 t1:5 admissible:2 bxa:1 anal:2 shansky:2 oscillator:2 sin2:4 second:1 booth:2 rrx:1 dynamics:13 theory:1 nonlinear:8 brackets:7 d2:2 associate:1 l0:11 current:3 version:1 subspaces:1 new:1 exercise:1 simultaneously:1 respectively:5 here:3 mab:3 cos2:12 represented:1 equations:15 change:1 tian:2 antisymmetric:1 receive:1 lomi:2 changed:1 mx:1 periodic:2 products:1 poisson:5 via:3 family:2 marked:4 juriev:2 2bp:1 use:4 next:1 ψi:4 m1:16 m0:11 m2:2 nonpotential:7 themselves:1 type:6 theoretical:1 more:2 sort:1 introducing:1 duality:3 becomes:1 operators:4 dressing:1 particular:1 known:1 foundations:1 cases:1 hold:1 iii:1 springer:5 equation:2 mi:2 mj:1 values:1 mp:1 following:3 my:1 example:2 mz:1 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solv-int9505002.txt |@word partial:3 maciejewski:2 rev:1 lack:1 rod:1 four:1 supplement:1 sci:4 consider:2 copernicus:3 editors:1 dz2:1 those:1 elliptic:1 under:2 worth:1 p2:8 global:1 springer:1 valued:1 putting:1 skii:2 presented:3 irreducible:9 notes:1 solution:2 eigenvalues:3 anal:1 ρk:1 strachan:1 zn:3 zi:4 takhtajan:3 direct:2 integrability:5 rouen:2 ode:4 zs:1 appear:2 section:2 expressed:1 xvii:1 sur:3 above:4 new:4 method:5 pioneering:1 degree:12 respectively:1 component:3 here:2 modular:2 l22:2 equations:12 appears:1 z2:19 z3:18 obtained:2 great:1 institute:1 study:2 allows:1 contradiction:2 poisson:1 permutation:1 hospitality:1 deg:6 churchill:1 tau:1 sincerely:1 jouanolou:4 apply:1 univ:2 linearly:2 use:2 proceed:1 working:1 prove:4 negative:4 france:2 comparing:1 call:1 associated:1 2y2:2 more:3 fractions:1 alg:2 almost:1 definition:1 tested:1 berlin:2 excellent:1 known:3 iii:1 must:1 nutku:1 account:1 mf:1 ρi:1 equation:10 work:2 ematiques:2 publications:1 following:9 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solv-int9505003.txt |@word represent:2 partial:4 consider:3 scd:1 dynamic:4 results:3 four:2 scalar:2 proposition:10 expressions:2 gj:1 analiz:1 certainly:1 depend:8 tu:1 acting:1 those:1 th:5 under:7 g2:1 g1:13 zhang:1 urel:2 choice:2 every:1 difficult:1 emphasized:2 difference:2 exact:1 deformations:1 condition:36 leads:2 solves:1 presented:1 bn:2 turns:3 notes:1 sklyanin:1 t2:1 solution:7 try:1 solved:2 vector:2 math:3 harry:1 small:3 degeneracy:1 dx:3 eλx:1 const:2 consistent:4 direct:3 cosh:1 integrability:6 zy:1 further:4 dynamics:3 odd:5 zs:8 even:2 16r2:2 t2k:1 nonlinear:2 plays:1 appear:2 section:9 bdn:1 expressed:2 reasoning:1 above:6 new:13 method:3 satisfy:3 respectively:4 drew:1 provides:1 sinh:4 others:1 represented:2 consideration:2 along:1 standard:2 equations:20 appears:2 change:6 obtained:8 remark:1 singapore:2 institute:1 shift:5 study:1 allows:1 contradiction:1 periodic:2 action:1 conveniently:1 makes:1 involves:1 formulated:1 useful:1 classification:1 santini:1 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solv-int9505004.txt |@word minors:1 consider:5 results:6 leads:5 proposition:12 edu:2 consists:2 gn:2 gi:4 row:5 particles:1 inverse:9 noncompact:1 tn:28 tl:3 tm:7 tk:3 under:4 presentation:1 g3:1 g2:2 g1:2 orthogonal:5 very:1 removing:2 choice:4 corollary:2 p1:1 entries:7 tridiagonal:10 little:1 matrices:2 condition:2 entire:1 hamiltonian:3 turns:1 notes:1 t2:2 solution:15 t0:10 t1:10 large:3 solved:3 convenience:2 commute:1 λnk:4 eigenvalues:25 noted:2 upper:2 wronskian:2 eλt:1 direct:1 itive:1 sign:1 eλn:1 zero:4 odd:1 canonical:1 bilinear:7 appear:2 diag:20 section:8 expressed:6 symes:3 binet:1 above:10 aii:1 d1:8 method:10 nakamura:2 3d:1 satisfy:6 full:10 symmetrizable:1 eλ2:2 here:11 pumping:1 b2k:4 groups:1 equations:10 change:3 obtained:4 remark:4 generalizing:1 study:6 studied:2 reason:1 orthogonalization:6 suggests:1 periodic:1 permutation:1 correct:1 studies:1 g2i:1 schur:1 useful:1 projection:2 limt:1 replace:1 separation:1 decrease:1 sgn:2 readily:1 derivatives:1 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solv-int9505005.txt |@word represent:1 concept:1 partial:7 consider:8 subindices:1 caused:1 dynamic:1 results:9 leads:1 scalar:1 expressions:10 compact:1 preserves:1 gazizov:2 depend:2 tx:5 2b12:1 alamos:1 tt:5 technique:1 finally:2 prolonging:1 preserved:1 under:3 nodes:3 case:19 b22:1 springer:2 unstructured:3 discretizations:2 difference:9 exact:1 deformations:1 condition:1 harlow:2 t2:2 solution:3 t0:6 t1:3 leave:2 discrete:9 small:8 application:2 illustrating:1 oscillation:1 cfd:2 direct:1 approximation:12 zero:13 design:1 kx1:2 further:2 dynamics:1 substitute:1 theory:1 even:1 index:1 nonlinear:8 cell:1 establishes:1 new:2 contributes:1 method:5 satisfy:4 here:1 groups:23 galileo:1 consideration:1 along:1 equations:24 τ1k:1 obtained:3 institute:1 leaves:1 studied:2 allows:2 resulting:8 procedure:2 action:1 composed:1 followed:1 family:9 εh1:1 total:2 select:1 derivatives:8 would:1 remains:1 continuous:1 contains:2 calculation:1 therefore:5 survive:1 const:1 introducing:1 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solv-int9505006.txt |@word partial:4 consider:6 desirable:1 results:2 computation:1 sci:3 expressions:2 inverse:1 tu:1 acting:1 quasi:1 th:1 under:30 aux:2 include:1 applied:4 very:3 rise:3 translations:2 choice:1 ovsiannikov:1 nonlinearity:2 exact:7 condition:5 groups:1 solution:6 leave:1 involution:1 vector:8 gruyter:1 application:1 specially:1 direct:1 cosh:4 second:1 value:1 further:1 dynamics:1 ode:4 canonical:1 even:1 established:3 what:1 nonlinear:19 stands:2 giving:1 fuchssteiner:1 above:13 new:6 method:3 clausthal:2 modify:1 here:5 pioneered:1 γx:4 ansatz:9 sinh:3 represented:2 consideration:1 sine:2 equations:24 logarithmic:1 ukraine:2 remark:2 institute:3 involved:1 study:4 contradiction:2 rosenau:1 principally:4 hospitality:1 zhdanov:5 technique:1 classification:1 substitution:2 total:1 establish:2 linearly:1 derivatives:4 use:1 takes:1 would:3 prove:3 contains:2 next:2 comparing:1 approach:1 call:1 ibragimov:1 criteria:1 type:4 more:2 operators:1 odinger:2 berlin:1 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solv-int9506005.txt |@word partial:1 consider:9 gp:2 results:4 leads:3 proposition:8 generalize:1 edu:2 constants:1 follow:1 row:3 compact:1 whose:1 inverse:15 pb2:2 similarity:6 noncompact:1 tn:3 finally:1 tm:1 those:2 th:4 under:8 cahn:1 include:2 tb:3 ingredient:2 applied:1 orthogonal:2 very:1 choice:4 corollary:2 wishes:1 entries:3 tridiagonal:1 matrices:17 deformations:1 convexity:1 cmn:2 exponential:1 hamiltonian:2 bn:2 induction:2 notes:1 t2:3 solution:22 t0:8 large:1 solved:3 convenience:1 vector:2 indices:1 eigenvalues:17 anal:1 noted:2 upper:5 zh:1 eλt:10 direct:3 behave:1 eλn:4 second:2 odm:3 theory:3 spectral:4 dissertation:1 plays:1 appear:2 norris:1 diag:16 section:18 expressed:11 symes:1 binet:2 above:4 new:4 construction:1 principal:2 consisting:1 publications:1 satisfy:4 full:11 symmetrizable:1 exchange:1 respectively:5 eλ2:3 here:25 eii:4 b2i:1 address:2 represented:3 ocm:6 equations:13 obtained:12 remark:2 generalizing:2 study:3 studied:3 commonly:1 glg:4 akj:1 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solv-int9506006.txt |@word partial:1 results:3 eds:1 go:1 whose:1 inverse:5 tr:3 finally:1 tk:24 analogous:2 applied:1 conjecture:1 supported:1 very:1 conjectured:3 associated:1 difference:1 matrices:1 t5:2 t3:6 t1:39 large:1 solved:1 math:3 cosh:1 painlev:6 further:2 dynamics:1 odd:2 invertible:2 brackets:1 giving:1 sum:3 above:2 u30:3 new:1 method:1 satisfy:1 equals:10 here:2 desired:1 sinh:12 others:1 sine:1 equations:13 remark:1 institute:1 study:1 products:4 suitable:1 changes:1 useful:1 plenum:1 total:1 univ:1 derivatives:2 use:5 usa:2 prove:1 positive:1 negative:1 nucl:2 noting:1 therefore:1 taken:1 themselves:1 theoretical:1 more:3 becomes:1 operators:3 apparent:1 particular:1 cases:1 hold:1 iii:2 ii:1 science:1 equation:4 work:3 det:7 mk:1 values:2 proof:7 arise:1 david:1 end:1 holds:2 write:1 how:2 mccoy:3 sato:2 express:1 algebra:1 may:2 philosophy:1 applications:2 levi:1 multiplication:1 third:1 lemmas:1 korepin:2 so:4 allow:1 correlation:6 representation:1 dorfmeister:1 hierarchy:10 developed:1 over:1 years:1 e2φ:15 paper:2 through:1 statistical:2 satisfies:5 its:4 derive:2 rapidly:1 thank:1 bringing:1 systems:3 ri:1 them:1 integral:1 introduce:2 scaling:2 bogoliubov:1 now:4 developments:1 university:2 2d:2 2n:1 side:7 domain:1 arxiv:1 ei:16 ej:8 series:2 related:2 elementary:1 fs:2 quantum:5 our:2 special:1 jimbo:2 matrix:2 space:4 since:3 rev:1 denotes:2 reader:1 formula:4 induction:1 integrated:5 rj:1 shows:1 foundation:1 harold:1 earlier:1 theory:2 written:1 josef:1 free:1 completely:1 california:2 york:1 definition:1 keep:1 inverts:1 u20:2 gordon:9 davis:1 first:6 xk:2 xi:1 omitted:1 variables:3 exact:1 temporarily:1 precisely:2 illustrate:1 given:2 rewritten:1 similarly:1 introduction:1 relations:1 their:2 transcendent:1 1d:1 statement:3 convention:1 gives:8 exactly:1 albert:1 immediate:1 required:1 part:2 differentiate:1 authors:2 kind:1 second:2 winternitz:1 were:1 fashion:1 craig:1 zamolodchikov:2 mind:1 generalization:1 take:2 formulas:7 begin:3 fundamental:1 trace:1 investigations:1 decreasing:1 connected:1 jul:1 tracy:5 acknowledgements:1 class:5 especially:1 ke:3 t2n:1 km:1 exp:1 mechanical:1 left:5 physics:1 fact:6 quantity:2 show:4 random:1 miwa:2 relation:1 find:6 fifth:1 q0:3 assertion:1 lemma:10 factor:1 constant:1 moser:1 establishes:1 means:1 simplest:1 closely:1 determinants:8 widom:3 fields:2 differential:7 twice:2 qi:6 qj:8 kernel:4 set:1 smooth:1 national:1 correlations:2 see:2 theoretic:1 techniques:1 bernard:1 subsequent:1 review:1 symmetric:2 state:1 various:1 between:3 limit:1 boundary:1 conditions:1 notice:1 terms:2 kei:4 rims:1 attention:1 wi:3 wu:2 solv:1 bose:1 both:3 last:1 v02:4 taking:1 equal:2 etc:1 connection:4 holonomic:2 relevant:1 point:3 simple:1 ca:2 dimensional:1 mkdv:7 grants:1 respect:2 throughout:1 slavnov:1 three:1 int:2 combined:1 interest:1 basic:1 expected:1 pi:4 b426:1 define:1 direction:1 quantities:3 gas:1 observe:4 denote:2 spin:3 present:1 case:3 p0:3 single:1 will:4 region:1 procedure:1 almost:1 vi:17 vj:18 vk:16 thus:2 antiderivative:2 iv:1 vp:12 vq:4 vanish:1 fermion:1 recursion:5 belong:1 same:1 hierarchies:1 finite:1 independent:1 indicies:1 publ:1 v0:10 v1:8 v2:1 v3:1 sattinger:1 identity:2 recent:2 model:2 usual:1 obtain:4 immediately:1 differentiation:6 scattering:1 adv:1 adding:1 density:1 appeared:1 gave:1 showing:2 cruz:1 know:1 press:1 integer:1 mod:1 appearing:2 helpful:1 follows:3 either:2 polymers:1 become:1 right:7 neumann:1 some:1 deduce:3 examples:1 kdv:1 proofs:1 scale:1 affects:1 shall:2 integration:1 comments:1 expressing:1 schwarz:1 kyoto:1 equivalent:2 pp:1 santa:1 integers:1 impenetrable:1 rederived:1 commun:2 range:1 fredholm:7 cambridge:1 into:1 obtaining:1 references:2 operator:9 log:7 u4:1 there:2 u1:15 u0:53 u3:2 u2:10 inner:4 ed:1 was:4 asymptotics:1 function:6 complete:1 form:3 denoting:1 but:2 pj:3 removed:1 adler:1 applying:2 places:1 leclair:1 wish:1 uq:4 up:13 us:1 below:1 dms:2 ui:28 uk:23 uj:17 b432:1 mechanics:1 later:1 proved:2 defined:1 certain:1 abstract:1 general:4 consulted:1 proves:1 physica:1 transcendents:1 physical:1 functions:11 no:1 when:1 vanishes:2 field:1 other:2 b13:1 department:2 mathematics:2 izergin:2 nice:1 models:2 polynomials:1 deriving:1 commutator:1 important:1 ising:2 variable:2 barouch:1 sides:2 independently:1 using:3 factors:2 together:1 time:3 4d:1 having:1
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solv-int9507001.txt |@word represent:1 consider:8 leads:1 mild:1 commute:1 edu:1 perturbations:3 cases:1 issues:1 analiz:1 increase:1 tz:2 calculate:1 charge:9 contours:1 elliptic:17 under:3 mrst:1 must:2 encircle:1 belonging:1 deforming:1 very:2 keeping:1 every:2 associated:1 exact:1 categories:1 dim:6 riemann:6 presented:1 list:1 solution:2 ri:3 try:2 feigin:1 vector:2 small:1 mn:2 speci:1 discover:1 integrability:1 pass:3 rigorous:1 cft:3 odd:1 eigenspaces:3 even:1 what:3 trivial:1 section:2 brief:1 expressed:1 current:1 sheeted:1 above:6 new:7 increasing:3 method:2 3e:1 satisfy:1 polyakov:1 degree:3 respectively:2 here:4 understanding:2 ranges:1 growing:1 address:2 represented:1 along:4 sine:1 z1:6 change:1 obtained:2 institute:1 studied:1 vbs:4 spheres:8 usually:1 fateev:2 studies:2 reg:4 projection:1 explained:1 should:1 linearly:1 use:1 takes:1 usa:1 bukhvostov:1 contains:1 next:1 handles:1 going:1 call:1 therefore:2 survive:2 doubling:1 theoretical:1 more:2 knows:1 sotkov:1 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solv-int9507002.txt |@word partial:2 gp:1 vasiliev:1 trigonometric:2 invent:1 leads:1 remarkably:1 inverse:1 providence:1 switched:1 divergent:2 g0:13 very:1 rise:1 wave:1 jack:1 difference:15 condition:1 hamiltonian:8 turns:1 discrete:1 annihilates:1 eigenvalues:2 anal:2 zn:6 zero:4 dordrecht:1 substitute:1 even:4 appear:1 hansson:1 brink:1 version:5 goes:4 consisting:1 pioneering:1 simultaneously:1 mem:1 here:2 obtained:3 sending:3 shift:1 study:1 studied:1 amount:1 permutation:2 domains:1 projection:1 hermite:1 univ:1 commun:1 positive:1 ψn:12 associated:4 type:21 more:1 lowering:1 hahn:8 formally:1 becomes:2 operators:4 normalized:2 particular:1 cases:1 tokyo:2 science:1 mn:16 cal:10 arrive:1 root:7 proof:1 give:1 relativistic:2 states:1 dxn:3 numbers:1 rather:1 orthogonal:3 nontrivial:1 product:3 algebra:2 may:2 reps:1 after:4 dx1:3 applications:1 types:1 realized:1 joint:1 onto:1 explicit:1 st:1 bunkyo:1 so:1 sn:1 order:5 over:4 years:1 course:1 paper:1 london:1 japan:2 its:2 before:1 parts:1 systems:5 constitutes:1 non:1 practice:1 introduce:1 they:2 now:4 eigenvalue:2 university:1 iff:1 l2:2 each:1 found:1 monomials:1 square:2 ei:3 weight:5 ed:2 energy:1 hypergeometric:1 ea:3 related:1 eb:2 society:1 obtains:1 quantum:3 our:3 special:1 out:1 matrix:1 space:1 since:1 denotes:3 particles:2 re:1 rational:3 diagonalized:1 rn:3 math:13 theory:1 diagonal:1 quite:2 van:3 asi:1 ruijsenaars:5 definition:1 transition:3 βg:2 promotion:1 generalizations:1 xj:49 xk:26 xn:3 laguerre:1 sutherland:1 size:3 given:5 degenerations:1 introduction:1 leading:1 adjoint:1 system:14 their:1 statement:1 siam:2 continuous:9 x2:12 x1:4 coefficients:2 suslov:1 second:1 limiting:1 determined:4 minus:1 lowest:1 spectrum:5 generalization:3 manner:1 recover:2 clearly:1 lie:1 wilson:13 self:1 sciences:1 potential:1 generalized:1 olshanetsky:2 jul:1 letter:2 multiply:1 interacting:1 ecal:4 considered:1 coincides:1 exp:4 fact:1 supported:1 find:1 ground:2 dividing:2 analytic:1 factor:2 integrable:2 hamiltonians:4 dn:1 above:1 viewpoint:1 means:1 de:1 overall:1 famous:1 boils:1 interpreted:1 gen:3 differential:2 hcal:11 set:1 exists:1 j2:2 see:1 recently:2 theoretic:1 eigenfunctions:13 positivity:1 symmetric:11 state:2 simplest:1 invariant:1 reading:1 conditions:4 terms:1 attention:1 solv:1 multivariable:10 amer:2 askey:5 both:2 essentially:1 diejen:3 2n:2 x2j:1 families:1 cn:4 nonrelativistic:1 simple:2 corresponds:2 dimensional:1 polynomial:6 respect:2 ensures:1 basis:5 addition:1 due:1 int:1 much:1 richards:1 nato:1 algebras:2 pn:15 koornwinder:3 2iz:2 arxiv:1 confinement:1 external:4 case:3 being:1 pacs:1 value:1 will:3 contemp:1 replaced:6 iz:14 vol:1 thus:1 reads:2 same:2 noninteracting:1 split:1 several:1 numerical:2 functions:8 counterparts:1 jsps:1 off:1 well:2 without:1 solve:1 model:5 calogero:10 monomial:3 hongo:1 preprint:1 kluwer:1 conclude:1 except:1 macdonald:3 transformed:3 lett:1 excited:1 eigenfunction:2 showing:1 iβ:2 harmonic:4 follows:2 integrals:1 become:1 mathematical:1 classical:1 some:1 remarking:1 atakishiyev:1 lead:1 everything:1 assuming:1 bessel:1 bn:1 pp:2 expansion:1 step:3 substitution:1 hilbert:1 stand:1 introduced:3 xnn:1 perelomov:2 soc:2 within:1 compos:1 down:1 pair:1 operator:8 ixj:8 span:1 there:1 specifically:1 jeu:1 restricts:1 inner:1 series:1 exceptional:1 was:1 naturally:1 function:6 complete:1 form:5 reduce:2 triangular:1 but:1 construction:1 hb:7 ha:13 raising:1 factorized:1 versions:1 up:2 us:1 placed:1 limit:3 problem:1 similar:3 constant:3 computing:1 defined:1 certain:1 denote:1 corresponding:2 commuting:2 again:1 nj:7 nn:6 no:2 amounts:1 whereas:1 field:4 setting:1 department:1 elements:3 ku:1 models:2 polynomials:24 jastrow:1 nevai:1 structure:1 ago:1 bcn:2 implies:1 longer:1 monic:2 assume:1 time:1 n1:6 n2:6 original:1
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solv-int9507003.txt |@word concept:1 partial:2 consider:8 pointing:1 equalities:5 particular:2 results:1 four:2 commute:1 ga:1 dϕ0:6 dϕ1:4 dϕ2:5 hold:1 depend:4 ıt:1 ıw:6 tu:1 dp:1 ıa:3 ıb:3 c5:4 elliptic:1 under:9 analogous:3 p2:1 belonging:1 g2:1 g1:1 returning:2 very:3 pages:1 rise:1 splitting:4 emphasized:1 condition:2 leads:1 level:2 notes:1 list:7 solution:21 leave:1 solved:1 convenience:1 vector:1 math:6 eigenvalues:2 anal:1 βx2:1 ıu:1 possibility:1 force:2 specially:1 foundation:1 miller:2 sin2:1 b22:5 b21:5 cosh:21 imply:2 further:1 expressions:6 substitute:1 canonical:1 index:1 what:4 nonlinear:10 d3:5 above:22 new:13 acknowledgments:1 publications:1 clausthal:2 full:1 component:1 here:8 ansatz:9 separation:17 const:3 shapovalov:1 equations:18 z1:4 b2a:1 ukraine:4 remark:9 dividing:1 division:1 institute:4 involved:2 study:1 studied:3 ourself:1 hospitality:1 makes:2 sci:1 zhdanov:5 equivalence:4 classification:3 namely:2 summation:1 apply:1 establish:1 readily:2 derivatives:4 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solv-int9507004.txt |@word proposition:11 represent:1 gu:1 since:4 evidence:1 consider:11 funct:1 results:4 r1x:1 chaos:1 four:2 p02:3 p01:1 gd:18 2r2:2 2r1:1 depend:2 tu:6 reductions:1 finally:1 tj:1 under:1 introduce:1 case:13 r14:2 r15:1 r12:4 r13:1 p0k:4 p0j:1 rise:3 connects:1 choice:1 putting:1 remarks:1 rn:1 nijenhuis:3 entire:1 hamiltonian:86 turns:1 who:1 solution:9 enon:42 try:1 solved:1 differential:2 math:7 anal:1 mn:17 zi:10 zk:2 literature:1 sign:1 integrability:34 cost:1 choices:2 odd:1 ode:2 canonical:17 bilinear:1 index:1 plays:1 invertible:2 diag:1 section:2 associate:1 analogously:1 expressed:2 d3:1 δq1:1 above:3 new:13 increasing:1 method:7 coefficient:3 fiz:1 respectively:11 here:3 2kg:1 tangent:4 q13:2 q12:1 directions:1 along:3 equations:17 z1:8 knowledge:1 obtained:12 scienze:2 algebra:1 suitably:1 leaves:1 garnier:35 allows:4 8x:2 marsden:1 δqk:1 p2:18 periodic:1 poisson:57 action:4 studi:2 suitable:1 makes:1 quotient:1 heiles:42 subsect:3 followed:1 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