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solv-int9601004.txt |@word consider:2 chain:1 out:1 sca:4 results:3 scb:2 four:4 gf:1 rˆ:1 generalize:1 expressions:4 λabcd:2 devoted:1 inverse:1 depend:2 paris:2 gab:1 finally:1 those:1 tf:1 analogous:4 me:1 straightforward:2 than:1 choice:1 redefinition:2 difference:4 condition:3 entire:1 diverging:1 list:1 leave:1 discrete:12 indices:3 upr:1 13a:2 second:5 further:3 zw:2 odd:10 theory:1 bilinear:6 trick:1 what:1 abc:3 abd:1 appear:3 iterating:1 section:7 expressed:3 version:1 above:3 sixth:2 3b:1 3a:1 ever:1 method:3 satisfy:3 full:3 component:1 here:2 papageorgiou:1 ansatz:2 others:1 ratio:2 strong:1 equations:14 appears:2 change:1 obtained:10 cλ:1 remark:4 property:1 dividing:1 study:1 allows:2 contradiction:1 suggests:2 periodic:4 resulting:1 tilded:3 changes:2 involves:1 although:1 aps:1 vii:1 brs:1 replace:1 names:1 generality:2 apc:1 brc:1 readily:1 use:5 proceed:2 would:3 contains:1 miura:11 next:2 therefore:1 simpler:1 type:2 more:2 introducing:2 formally:1 ecole:1 becomes:4 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solv-int9601005.txt |@word consider:7 springer:1 induces:1 datum:4 results:8 leads:4 scalar:1 disc:1 computation:3 consists:4 oevel:1 disk:1 forget:1 devoted:1 inverse:9 depend:1 referring:1 technique:1 tr:3 uniqueness:1 according:1 th:1 under:3 ivanov:1 analogous:2 worth:2 applied:1 evolves:2 very:1 conditions:1 dokl:2 wave:3 summarized:2 difference:5 matrices:3 plemelj:2 four:1 riemann:8 solves:2 level:1 transmission:7 solution:25 large:3 discrete:26 small:2 a123:1 eiϑ:1 zh:1 evaluating:1 direct:3 pulse:1 second:4 evaluated:2 further:1 canonical:1 spectral:64 calogero:1 nonlinear:19 developed:1 section:1 expressed:1 version:5 poles:4 fuchssteiner:1 above:19 subtracting:1 method:11 coefficient:10 discontinuity:3 chose:1 ibid:1 respectively:1 here:11 diagonal:2 them:2 address:2 consideration:1 standard:1 equations:20 change:4 knowledge:1 obtained:6 remark:1 involved:1 study:2 studied:3 allows:3 amount:1 resulting:2 poisson:1 identity:1 conveniently:1 fourier:4 changes:1 involves:1 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solv-int9601006.txt |@word partial:1 consider:1 ron:1 results:1 fluids:1 proposition:3 gc:1 parameterization:1 sci:1 denotes:1 gj:2 localized:9 whose:1 γs:1 γt:5 finally:1 program:1 preserved:1 include:1 ingredient:1 ginn:1 orthogonal:5 continues:1 conditions:1 choice:1 drexel:1 commute:1 condition:7 centerline:1 hamiltonian:1 turns:1 notes:1 tanh:1 list:1 t0:2 t1:11 involution:1 vector:24 recall:1 anal:1 zn:3 century:1 zi:1 zj:2 zk:1 miller:1 cosh:5 zero:1 perspective:1 dynamics:1 odd:2 theory:4 even:2 nonlinear:3 annals:1 reconstruction:2 new:3 t2:14 method:3 evolving:3 mel:2 realizations:1 component:1 equals:1 κb:3 tangent:3 geometer:1 κt:2 along:14 quite:1 equations:9 z1:1 κs:2 separation:1 great:1 thirty:1 technical:1 studied:1 allows:1 spheres:1 resulting:4 bob:2 makes:1 york:2 via:5 useful:1 family:1 pinkall:2 cylinder:1 private:1 brought:1 ai:8 unit:2 derivatives:1 feb:1 asymptotic:1 prove:2 give:2 negative:1 ψt:1 next:1 few:1 linear:5 melko:2 associated:9 compactly:1 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solv-int9602001.txt |@word represent:1 concept:1 partial:3 consider:2 funct:1 varying:1 ds:3 leads:1 eds:1 scalar:7 disc:3 edu:1 consists:4 gk:69 row:1 compact:4 whose:3 inverse:1 analytic:6 equivalence:1 acting:1 tn:2 tl:36 dressing:3 analogous:2 include:1 norm:9 applied:1 conjecture:1 deforming:1 string:2 orthogonal:1 very:4 nonselfadjoint:1 pek:2 springer:2 choice:1 additional:1 entries:13 difference:1 lefthand:1 condition:6 subsets:1 solves:2 bn:22 nucl:1 solution:18 t1:1 discrete:7 commute:1 science:1 indices:2 anal:1 upper:6 neighborhood:3 zk:11 estimates:2 go:1 second:7 substituting:1 linear:2 even:2 what:1 nonlinear:4 appear:3 invertible:13 sum:1 expressed:3 version:2 fuchssteiner:1 above:7 kyoto:1 replaced:3 method:4 funtion:1 satisfy:4 justification:1 simultaneously:2 respectively:4 component:1 equals:2 here:8 cylindrical:5 free:1 sinh:2 address:1 path:8 bk:4 equations:31 change:1 extreme:1 obtained:6 convert:1 property:1 shift:1 ignoring:2 periodic:10 products:4 correct:1 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solv-int9603002.txt |@word unavoidable:1 results:9 existing:1 leads:4 gf:1 ǫa1:3 broader:1 consists:2 expressions:5 paris:2 mutatis:1 finally:1 dz2:2 those:1 under:2 mutandis:1 analogous:1 multilinear:2 γf:1 case:9 advantage:1 very:3 exception:1 splitting:1 putting:1 difference:1 vast:1 four:1 presented:4 discrete:21 differential:1 upr:1 zm:1 work:4 10b:1 10c:1 zf:12 10a:2 direct:1 10d:1 go:2 painleve:1 zx:1 canonical:1 bilinear:30 established:1 what:1 nonlinear:1 version:1 goes:1 kyoto:1 new:5 method:1 here:6 consideration:1 equations:24 appears:1 obtained:12 search:1 study:3 studied:1 suggests:2 resulting:2 symmetrical:8 departement:1 shorthand:1 4a1:1 vii:1 plenum:1 highly:1 8c1:1 hindsight:1 des:1 use:3 proceed:1 would:1 france:3 program:1 a56:1 scope:1 more:7 ecole:1 becomes:2 award:1 vm:1 2w3:1 particular:2 known:1 cases:3 eζ:3 me:1 equation:17 mn:13 ere:1 hiroshima:2 dζ2:11 f2:2 division:1 process:2 india:1 something:3 sense:1 counting:1 straightforward:1 rather:2 six:2 feature:2 till:1 instead:1 3w2:1 obeys:1 mar:1 ζf:2 may:3 after:1 singularities:2 higashi:1 xzz:3 ff:3 fg:35 choice:2 parallel:1 transposed:1 trilinear:2 so:5 acknowledges:2 indeed:1 over:1 paper:1 through:10 japan:3 satisfies:2 its:6 acknowledge:1 kagamiyama:1 interesting:4 forms:11 resort:1 systems:1 ours:2 main:1 easier:1 non:2 uhk:1 introduce:2 yy:1 asymmetrical:1 they:2 singularity:12 now:5 b278:1 2w:2 2p:1 materialized:1 university:2 zdz:1 2x:1 2v1:1 2z:3 establishing:1 2f:4 2a:2 done:1 universit:1 constraints:1 24e:1 24d:1 24f:1 24a:1 another:2 24c:1 expectedly:1 reduce:1 related:2 2hk:2 expect:1 our:6 mapping:1 avoided:1 out:4 shown:1 jimbo:3 since:4 unknown:1 fellowship:1 math:1 linear:1 standard:4 whereupon:1 york:1 put:1 asi:1 degeneracies:1 derivation:2 ministry:1 could:3 counterpart:1 u21:1 4p0:1 hence:1 first:2 already:1 ζw:1 number:6 xz:2 instances:1 xx:5 simplified:1 directly:2 2a1:3 little:1 needed:2 introduction:1 leading:4 behaves:1 system:1 relations:1 their:4 structures:1 final:1 gives:1 2af:2 profited:1 4b1:1 17f:2 17e:2 exactly:1 17c:1 17b:2 17a:1 authors:2 x2:3 x3:2 convinced:1 than:1 18b:3 18c:1 18a:1 18f:2 18d:1 18e:2 sections:1 piii:5 painlev:17 preparation:1 matter:1 were:5 etage:1 turned:1 argument:2 recover:1 convenient:1 latter:4 able:2 note:1 majority:1 transcribed:1 take:1 analogy:1 explanation:1 schlesinger:1 cnrs:1 continuous:43 though:1 collaboration:1 who:1 most:3 involving:4 acknowledgements:1 why:1 observation:1 considered:1 clear:1 coincides:1 lpn:1 ohta:2 8a1:1 hietarinta:5 fact:6 precise:1 zhk:1 v12:1 ǫv1:1 trivial:1 find:6 d0:5 based:3 knowledge:1 only:5 transcendental:1 factor:1 notation:1 df:2 between:5 24b:1 ones:5 dz:4 arxiv:1 wz2:1 qf:3 view:1 2p0:1 mandatory:1 exists:3 ǫc1:2 result:7 eliminating:1 existence:1 pvi:11 close:1 analog:2 eres:1 pattern:1 symmetric:1 written:1 simplest:2 progress:1 approach:6 αn:1 terms:1 missing:1 however:2 implementing:2 solv:1 wz:1 suggested:2 c21:3 reverse:1 limits:1 many:3 contract:1 foreign:1 tour:1 became:1 expression:3 cm:1 point:4 simple:1 corresponds:2 cd:2 analyzed:1 sakai:3 moreover:1 pq:10 pv:3 equivalent:1 three:1 ramani:4 much:1 pf:3 pi:11 25b:1 25c:1 sufficient:1 25a:1 25f:1 remark:1 25d:2 25e:2 systematic:1 remedied:1 c2:2 c1:3 c0:5 spirit:1 present:4 wzz:1 applied:2 p0:2 novel:1 appearance:1 ǫu1:1 will:1 while:5 ǫw:1 property:1 a21:2 thus:5 them:2 ii:2 reads:1 examined:1 worry:1 different:5 education:1 suggest:1 make:1 same:4 check:1 palaiseau:1 accumulating:1 several:1 higher:2 status:1 used:1 dgf:1 faculty:1 satsuma:1 upon:1 counterparts:1 v1:3 2u1:1 recent:2 well:1 analysis:2 patterns:2 left:1 exceeding:1 just:2 grammaticos:4 obtain:5 transforms:1 useful:1 yet:1 previous:1 nǫ:1 preprint:2 alternate:1 had:3 nato:1 easy:1 5e:1 transformation:1 identical:1 2c1:2 possible:4 cf:3 necessary:1 systematically:1 follows:2 reduces:1 translates:1 indication:1 polytechnique:1 2a2:1 multiplicative:1 conclusion:1 minist:1 right:1 old:1 some:6 play:1 okamoto:1 b0:4 b1:2 b2:5 lead:1 shall:2 integration:1 dz3:2 does:1 eliminate:1 provides:1 proc:1 sixth:1 kruskal:5 although:2 substitution:1 relating:1 ǫb1:1 properties:1 bz:4 simpler:1 about:1 constraint:2 freedom:1 17d:1 introduces:1 compatible:1 addition:1 a2:4 greatly:2 introduced:1 slightly:1 into:1 obtaining:1 appropriate:2 acad:1 references:1 financial:1 coalescences:1 log:8 support:2 there:3 u1:3 specifically:1 start:2 way:2 2m:1 translate:1 was:13 function:2 form:23 but:2 back:1 hk:54 true:1 treats:1 made:2 wish:1 up:1 us:1 below:1 limit:19 problem:1 called:1 pii:4 ab:2 af:2 int:1 certain:1 abstract:1 engineering:1 exist:1 dζ:14 az:4 proceeds:1 piv:5 derivative:1 again:5 functions:16 no:3 amounts:1 when:3 setting:2 role:1 department:1 mathematics:2 you:1 nice:1 hirota:1 a1:2 a0:4 important:1 variable:2 structure:9 cpt:1 time:1 starting:4 once:1
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solv-int9603003.txt |@word consider:1 remarkable:2 results:5 existing:1 leads:2 go:1 particularly:1 localized:1 terms:1 analytic:1 paris:2 program:1 those:1 excluded:1 under:3 pay:1 analogous:2 must:3 case:16 stud:2 straightforward:1 very:2 putting:1 αλn:6 cellular:15 condition:2 impressive:1 presented:3 list:2 solution:13 large:2 discrete:51 anal:1 upr:1 noted:1 jump:2 fold:1 painleve:1 value:3 further:1 dynamics:2 canonical:5 gunn:1 established:1 what:4 nonlinear:2 appear:4 sum:1 3k:1 version:1 above:2 retrieved:1 new:1 method:2 satisfy:1 full:1 led:1 meth:1 degree:2 respectively:1 component:1 papageorgiou:1 focused:1 8d:5 19d:1 equations:35 appears:2 change:1 box:1 convert:1 property:5 study:2 studied:3 allows:3 subcase:1 example:1 periodic:3 resulting:2 σxn:3 automaton:9 studies:1 departement:1 appropriately:1 captions:1 br:1 family:1 9a:1 merely:1 vii:1 replace:1 addressed:1 santini:1 hindsight:1 apply:2 establish:1 plot:1 use:1 takes:1 would:2 commun:1 positive:2 negative:2 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solv-int9603004.txt |@word sci:1 consider:3 splitting:6 leads:1 proposition:2 grateful:1 inverse:1 paris:1 elliptic:11 te:1 case:8 supported:1 translations:1 geometrical:1 matrices:6 condition:1 four:1 riemann:2 hamiltonian:4 list:1 solution:1 enon:7 convenience:1 vector:1 der:1 direct:2 past:1 second:3 dynamics:6 canonical:3 even:1 nonlinear:1 giving:1 abels:1 expressed:3 uniform:1 sheeted:3 fifth:2 above:5 new:2 method:1 body:1 weikard:3 degree:2 respectively:1 here:2 magnetism:1 q13:1 sawada:1 concluding:1 quite:1 equations:8 logarithmic:1 ukraine:2 remark:3 institute:2 involved:1 studied:1 periodic:1 permit:1 action:1 heiles:7 apply:1 univ:1 unit:1 readily:2 use:2 takes:1 working:1 prove:1 positive:1 hudson:1 theoretical:2 2y1:1 separated:1 nauka:1 th:1 operators:1 odinger:1 berlin:1 rigid:1 known:6 cases:8 iii:3 ramani:1 springer:1 quartic:4 equation:7 det:1 ms:1 novikov:2 following:4 making:1 closing:1 example:2 curves:2 high:1 sn2:2 normalize:1 end:1 s2:5 s1:6 means:2 write:2 how:2 pair:1 belongs:1 product:1 mar:1 algebro:1 after:1 derived:2 applications:1 lax:19 representations:5 λ2k:1 natural:1 third:1 si:1 so:1 sn:7 representation:12 order:3 hierarchy:2 eqs:1 years:1 paper:5 through:1 y1:2 existence:1 still:1 its:1 chosen:2 2e3:2 tori:11 coordinates:4 degrees:1 systems:9 jacobi:6 derivative:1 main:2 them:1 ye:1 introduce:1 they:1 rotation:1 2u:1 inversion:2 finite:1 university:2 zdz:2 possibilities:1 2e:12 theory:4 2a:2 each:1 higher:1 baronissi:1 ed:1 reduce:2 idea:1 inverted:2 used:2 quantum:1 eq:2 shown:1 superscripts:1 kiev:1 kummer:2 kotera:1 rev:1 particles:1 attracted:1 hill:1 linearising:1 istituto:1 formula:1 induced:1 ref:2 math:3 linear:1 fisica:1 gesztesy:3 standard:3 completely:1 york:1 e1:1 e3:3 e2:3 fixed:1 motion:4 manakov:1 allied:1 buchstaber:1 u22:1 isf:1 first:4 separable:2 xi:1 researches:1 variables:1 symbolic:1 number:1 clear:2 open:1 illustrate:1 given:4 cartesian:1 publication:1 introduction:1 top:1 system:12 construct:3 their:2 calculations:1 hyperelliptic:6 gives:1 holomorphic:1 statement:1 academy:1 moscow:2 vanhaecke:1 part:1 2aq:2 x2:30 x3:12 x0:8 x1:23 separability:2 x4:1 acknowledgement:1 str:1 were:2 result:2 generalization:2 any:1 angle:1 convenient:1 nonseparable:1 k2:1 potential:2 take:2 jacobian:2 finding:1 spectral:1 who:1 simplify:1 satisfying:1 formulae:1 remarks:1 pages:1 soliton:1 considered:1 calculated:1 later:1 cover:2 physica:1 humbert:1 points:1 verdier:1 physics:3 bateman:1 show:2 authors:1 d2:5 find:1 chaplygin:2 d1:5 q1:16 q3:2 q2:15 just:1 freedoms:1 only:1 explicitly:1 transcendental:1 integrable:11 enolskii:3 dn:5 di:2 dependent:1 ones:1 dz:8 during:1 du:1 covering:3 arxiv:1 including:1 cycles:2 pitaevskii:1 moduli:4 set:1 national:1 differentials:1 see:6 computer:1 w2:1 equip:1 bobenko:1 y2:3 symmetric:1 written:2 between:1 theta:1 approach:3 matveev:1 terms:8 attention:1 however:1 solv:1 both:1 according:1 quantization:1 etc:1 picard:2 passing:1 genus:3 among:1 ci:1 cn:5 point:2 q12:2 corresponds:1 dimensional:1 simply:1 respect:1 described:1 transformations:1 discriminant:1 addition:1 three:1 been:1 reduction:2 much:1 6b:1 corresponding:1 gap:2 external:1 c3:1 c2:5 c1:4 weierstrass:2 present:1 p2:3 p1:4 aim:1 frameworks:1 while:1 intas:1 revisited:1 della:1 surface:4 ii:1 ij:2 italy:1 grant:2 perform:1 make:1 linked:1 gavrilov:1 arguments:1 several:1 erdelyi:1 difficult:1 investigated:1 published:1 materia:1 flows:1 potentials:5 infinite:1 expand:1 schr:1 kleinian:5 largely:1 well:2 analysis:1 s22:1 s21:1 solve:1 aproach:1 usual:1 proposed:1 obtain:1 integer:1 differentiation:1 λi:1 scattering:1 sciences:1 zakharov:1 characterization:1 other:1 transformed:2 lett:1 theorem:2 transformation:5 generalized:1 leipzig:1 around:1 represents:2 indexed:1 press:3 using:2 ams:1 particle:3 follows:1 integrals:2 arbitrary:4 mcgraw:1 stationary:4 terminology:1 acad:1 some:1 algebraically:1 q22:2 q23:1 examples:1 b2:3 diff:1 kdv:5 lead:1 equivalent:1 substitution:1 fordy:1 would:2 freedom:1 basis:2 discussed:2 leykin:2 ubner:1 cambridge:4 kuznetsov:1 into:1 integral:1 isomorphic:2 multiply:1 references:1 additional:1 u1:5 u2:8 ci1:1 way:2 salerno:3 lnσ:1 function:3 form:10 extended:1 volume:1 construction:1 hn:2 dvi:1 level:1 applying:1 uq:1 us:4 ui:4 uj:1 problem:6 more:3 similar:1 called:2 b1:3 associated:2 int:2 flow:2 abstract:1 describe:1 lehrbuch:1 covers:2 denote:1 dξ:1 exist:1 nazionale:1 constructed:2 functions:14 no:2 field:2 valid:1 details:1 department:2 dv1:4 dv2:4 briefly:1 elements:1 polynomials:1 includes:1 a1:3 a2:4 matrix:4 xk1:1 4z:1 coulomb:1 baker:1 curve:8 xk2:1 4e:1
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solv-int9603005.txt |@word gt:1 partial:2 consider:14 remarkable:2 equalities:3 global:1 results:3 gg:20 kxs:1 proposition:2 grateful:2 zˆl:1 consists:1 sci:2 research:2 gk:8 gi:17 skeleton:1 compact:1 depend:3 xtr:1 paris:1 show:1 tr:1 send:1 coincide:1 reductions:1 swap:1 elliptic:12 under:1 exposition:1 analogous:1 te:1 xtk:4 worth:1 hill:2 division:1 yr:3 fay:1 g3:4 g2:8 g1:1 very:2 pages:2 connects:1 corollaries:1 corollary:10 4p2:1 putting:4 rationality:1 entries:4 difference:2 matrices:11 condition:3 leads:2 dubrovin:3 riemann:23 immediately:1 presented:6 evaluation:1 notes:1 t2:1 solution:10 zds:2 t1:1 involution:4 vector:16 min:1 science:1 small:1 radio:1 der:5 zl:1 upper:1 zn:4 periodic:4 says:2 periodicity:3 zk:2 farkas:1 det:24 wirtinger:1 zg:5 direct:3 literature:1 sign:1 ggk:14 yk2:1 second:14 pres:1 zt:4 further:4 4x5:1 odd:4 4x2:1 canonical:5 spectral:4 will:6 nonlinear:3 plays:1 stands:1 invertible:2 diag:2 section:8 celebrated:1 contributed:1 while:2 sheeted:2 kum:5 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solv-int9603006.txt |@word partial:1 gr:1 chain:2 alg:2 trigonometric:5 leads:2 computation:2 consists:1 follow:1 remarkably:1 denotes:1 whose:3 inverse:2 depend:1 calculate:1 skii:1 b262:1 disposal:1 tr:2 answered:1 quasi:1 petersburg:4 elliptic:31 under:1 insights:1 applied:2 far:7 results:4 entries:1 difference:4 exact:2 condition:2 entire:1 presented:3 turns:1 presumably:1 sklyanin:5 enol:1 solution:1 leave:2 discrete:11 independence:1 relation:3 noted:1 freidel:1 grateful:1 direct:2 elegant:1 integrability:6 further:1 dynamics:1 odd:1 canonical:4 even:4 established:1 brackets:4 giving:1 sln:1 expressed:1 maillet:2 version:4 poles:1 3c:1 3b:1 3a:1 3d:1 body:4 full:3 respectively:1 neveu:2 here:5 understanding:1 objects:1 leeds:3 separation:5 along:2 quite:1 equations:6 wait:1 obtained:5 great:1 eij:14 remarks:1 institute:4 shift:1 allows:1 periodic:2 poisson:8 permutation:1 hospitality:1 makes:1 via:1 shorthand:1 search:1 namely:3 talon:1 establish:1 use:5 proceed:1 would:3 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solv-int9603007.txt |@word scalapino:1 consider:2 chain:1 results:3 leads:1 ge:1 follow:2 cases:1 row:2 referring:2 graph:3 tu:1 young:5 under:5 fermionic:1 worth:2 resources:1 conjecture:4 advantage:1 orthogonal:1 supercomputer:1 dongen:1 ortolani:2 difference:1 exact:3 partitions:1 four:2 hamiltonian:4 t6:1 t2:5 solution:1 large:1 discrete:2 eigenvalues:1 degeneracy:2 direct:1 further:1 implemented:1 odd:2 eigenspaces:1 even:3 appear:2 giving:1 sum:1 3t:1 3n:1 above:5 new:1 increasing:1 method:3 filled:6 satisfy:1 condensed:1 respectively:1 understanding:1 reported:1 objects:1 ansatz:1 appears:1 obtained:4 remark:4 technical:1 involved:1 study:1 vectors:2 allows:2 simultaneous:2 products:1 permutation:5 action:1 makes:2 useful:1 family:2 translational:1 total:5 readily:1 use:1 would:1 9t2:1 hilbert:3 noting:1 m1:3 therefore:1 m2:3 type:5 theoretical:1 more:2 introducing:1 remarkable:1 operators:2 constructs:1 particular:2 known:2 hole:1 iii:1 must:3 mf:3 mi:4 values:2 following:2 making:1 example:2 lanczos:1 f2:2 figure:1 organized:1 states:20 performed:1 end:1 di:2 tableau:5 how:1 wolfram:1 mar:1 blocks:1 may:1 after:1 derived:1 coming:1 minimizes:1 sz:12 diagonal:2 natural:1 computations:2 acknowledged:1 su:4 complexity:1 cannot:2 so:1 automatically:1 allow:1 keeps:1 representation:2 sf:8 produces:1 hierarchy:1 expects:1 paper:1 scott:1 captions:1 its:2 derive:2 group:5 la:1 lm:1 systems:5 clusters:3 arrange:1 hirsh:1 non:1 good:1 fig:4 introduce:1 rank:1 they:1 half:4 yu:1 easily:4 february:1 several:2 2s:1 always:3 university:2 level:3 filling:8 each:5 found:1 difficult:1 characterized:1 financial:1 weight:1 ed:1 energy:5 obtains:1 entering:1 quantum:2 our:2 eq:5 matrix:5 space:3 furthermore:2 since:4 rev:6 particles:1 istituto:2 linear:1 fisica:2 standard:2 york:1 van:1 e0:6 could:1 times:1 generalizations:1 symmetry:9 omitted:1 symbolic:1 number:7 tableaux:14 restrict:1 done:2 directly:1 given:5 system:9 construct:3 indicate:1 listed:1 bosons:1 continuous:1 part:1 authors:1 than:2 annihilation:1 matter:1 doubly:3 were:2 decompose:1 result:1 symmetries:2 spectrum:1 occupied:4 permutational:2 depending:1 convenient:1 lin:1 note:2 liu:1 take:2 unconstrained:3 heisenberg:1 lectures:1 singlet:1 2tu:1 most:1 partition:1 physica:1 bipartite:2 electrons:3 principle:1 subgroup:1 physics:2 show:1 solutions:1 ground:17 computability:1 just:5 spite:1 implementation:1 only:3 integrable:2 local:1 get:2 ones:4 combinations:1 lattices:3 denmark:1 arxiv:1 acknowledgments:1 analytical:6 fixed:1 set:1 unpublished:1 up:4 see:1 computer:1 projections:1 techniques:1 eigenfunctions:2 ways:1 sites:3 fano:2 symmetric:2 state:22 between:1 invariant:2 approach:1 email:1 triplet:1 terms:2 however:1 reproduces:1 solv:1 configuration:1 both:1 σi:1 limits:1 according:1 unisa:1 expression:2 characterization:2 2nd:1 dimensional:1 respect:2 singlets:1 basis:4 addition:1 simplification:1 three:1 been:1 ai:1 empty:1 define:1 box:1 direction:1 corresponding:6 commutes:1 denote:1 spin:9 present:1 case:3 pacs:1 value:4 rectangular:1 will:2 while:3 error:1 property:2 characterizing:3 della:2 changed:1 thus:2 site:1 equal:2 ii:1 characterize:1 limit:1 different:1 hubbard:10 italy:1 same:2 parts:1 diagonalize:1 constructed:1 higher:1 used:3 numerical:4 materia:2 hand:1 levels:1 moving:2 invariance:3 hopping:3 programs:1 studies:1 well:2 obviously:1 solve:1 model:11 dimension:4 left:2 eilbeck:2 diagonalizations:2 less:1 being:2 cjσ:2 identify:1 integer:1 seems:1 lattice:5 other:2 iσ:2 eigenstate:1 identical:1 references:1 lacking:1 represents:2 rules:5 possible:2 department:1 boxes:2 vacuum:1 using:2 like:2 particle:1 sizes:2 follows:1 specific:2 sezione:1 arbitrary:7 right:2 methods:1 creation:1 moreover:1 proper:1 diagonalizing:3 dimensions:1 lead:1 per:1 minimal:1 wesley:1 although:1 properties:2 about:1 fillings:2 mario:3 column:2 compatible:1 introduced:1 block:4 functions:6 into:4 rotations:1 down:4 rising:1 operator:3 span:1 support:1 there:2 start:1 conservation:3 quanta:9 salerno:8 complete:3 form:1 irreps:3 denoting:2 but:1 construction:1 highest:3 true:1 infm:1 made:1 compute:1 flip:3 us:1 bethe:1 fermi:2 strongly:2 associated:7 addison:1 int:1 abstract:1 general:1 single:2 ar:2 exist:1 nazionale:2 check:2 fill:1 ni:3 nj:2 compared:1 no:1 mathematica:3 when:2 nf:1 application:1 valid:1 test:1 elements:1 problems:1 a1:2 a2:1 correlated:2 4f:1 n1:1 n2:1 parola:1 once:2
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solv-int9603008.txt |@word partial:1 consider:2 remarkable:1 results:1 four:1 commute:1 expressions:2 row:2 referring:2 graph:4 young:4 charge:3 tj:7 under:5 must:4 conjecture:7 far:1 dongen:1 electron:1 putting:1 exact:3 condition:1 partitions:1 annihilated:2 hamiltonian:4 irreducible:1 t0:3 t1:2 solved:1 vector:2 direct:1 sign:1 fold:1 second:1 cost:1 odd:3 even:4 aim:1 appear:2 giving:1 3t:1 above:7 acknowledgments:1 filled:9 satisfy:1 respectively:2 here:3 understanding:1 reported:1 magnetism:1 them:1 groups:1 others:1 woynarovich:1 strong:1 transformation:3 obtained:4 remark:1 antisymmetric:2 antisymmetrizer:1 vectors:7 leaving:1 permutation:1 action:1 studies:1 useful:1 lanczos:1 total:3 select:1 readily:1 use:3 prove:1 tasaki:1 finally:1 next:1 comparing:1 ψi:3 m1:2 m2:2 means:1 type:5 theoretical:1 more:2 becomes:1 operators:1 validity:1 excellent:1 known:1 hole:3 iii:1 fermionic:1 pseudospin:1 keeping:1 mf:2 recall:3 equation:1 work:1 mi:4 mj:2 following:4 bipartite:1 example:1 figure:1 give:1 calculation:1 states:41 performed:2 degenerate:11 s1:1 s0:1 tableau:2 how:2 criterion:1 mar:1 algebra:4 may:1 after:1 derived:2 coming:1 representations:1 sz:2 resemble:2 acknowledged:1 su:13 sj:3 complexity:1 cannot:2 so:3 keeps:1 representation:2 order:2 saturated:2 flips:1 feature:1 symbols:1 whilst:1 paper:2 existence:2 kinetic:1 still:1 perfect:1 derive:3 group:3 exclusion:2 maps:1 energies:2 interesting:1 systems:1 clusters:4 hidden:2 main:1 non:2 rotations:1 introduce:1 flipping:1 they:7 half:6 2u:1 february:1 finite:2 always:4 university:1 2e:1 2f:4 each:2 found:1 2j:2 financial:1 weight:9 energy:6 ferromagnetism:3 related:1 interplay:1 quantum:1 our:4 eq:5 special:1 shown:3 since:1 rev:3 denotes:2 increase:1 istituto:2 mielke:1 ref:5 occurs:1 shows:2 theory:3 fisica:2 standard:3 clarify:1 completely:1 formation:1 van:1 could:1 consequence:1 generalizations:1 first:2 symmetry:9 symbolic:1 number:6 tableaux:14 illustrate:1 given:7 checked:1 similarly:1 leading:1 top:1 system:2 construct:2 confirming:1 statement:1 1f:2 gives:2 than:3 double:4 programs:1 annihilation:1 doubly:2 symmetries:1 manner:1 seen:1 occupied:10 depending:2 ideas:1 mechanism:2 note:4 potential:1 take:1 unconstrained:2 shall:1 decreasing:1 rearrange:1 extending:2 nagaoka:1 partition:1 sf:7 graphs:1 electrons:5 principle:2 usual:1 physics:1 fact:2 show:2 find:2 ground:35 knowledge:1 spite:2 itinerant:1 kagome:1 state:17 only:1 generators:1 local:1 hope:1 goes:1 di:3 ones:1 invariant:2 report:1 lattices:1 arxiv:1 analytical:5 requirement:1 up:8 observed:1 see:4 computer:2 result:1 captions:1 satisfying:1 jz:3 definite:1 sites:3 symmetric:1 written:1 between:1 limit:1 approach:2 email:1 extend:2 implementing:1 solv:1 come:1 equal:1 unisa:1 expression:2 among:1 ci:6 simply:1 respect:5 singlets:1 basis:1 simplification:1 empty:2 fig:10 corresponding:4 maximally:5 spin:27 present:3 case:5 diagonalizations:3 eigenstate:1 will:2 while:1 intas:1 couplings:1 della:2 site:2 according:4 ii:1 hubbard:8 italy:1 grant:1 parts:1 pauli:2 several:2 higher:3 numerical:2 functions:1 doublets:1 moving:2 changing:1 invariance:2 subgroups:1 hopping:2 fully:1 changes:1 well:1 analysis:2 concrete:1 model:11 left:2 just:5 being:2 cjσ:2 obtain:1 aspect:1 eigenstates:1 previous:1 adding:1 lattice:3 belongs:1 lett:2 iσ:2 solvable:1 remaining:2 eigenvalue:1 rules:4 showing:1 possible:1 boxes:2 makes:1 vacuum:1 press:2 using:2 unique:1 necessary:1 like:1 particle:2 sizes:4 follows:1 arbitrary:6 rearrangement:2 spins:1 right:2 creation:1 examples:1 moreover:1 filling:11 does:2 agreement:3 shifting:1 references:1 accompanied:1 properties:2 conducting:2 fillings:6 ferromagnetic:17 mario:1 column:4 compatible:1 automatically:1 into:6 obtaining:1 down:8 rising:1 operator:2 span:1 removing:1 support:1 there:1 quanta:8 way:1 salerno:7 analyze:1 was:1 function:1 complete:4 form:1 but:3 highest:10 applying:1 flip:1 us:5 below:1 fermi:1 similar:1 jz2:1 strongly:1 associated:2 int:1 holes:1 abstract:1 describe:1 singly:2 denote:1 single:2 exist:2 nazionale:2 proceeds:1 fill:1 ni:2 materia:2 thermodynamical:1 no:1 when:2 application:1 details:1 spatial:1 department:1 accidental:1 correlated:1 implies:5 coupling:2 pseudo:5 together:1 once:2
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solv-int9603009.txt |@word consider:1 chain:8 global:1 splitting:5 four:3 ge:1 follow:1 gi:1 poorly:1 devoted:1 certainly:1 referring:2 graph:1 young:7 languages:1 finally:1 those:2 th:2 under:7 include:1 tc:1 alternating:1 presently:1 advantage:1 zhang:1 translations:1 results:2 matrices:3 partitions:1 severely:1 annihilated:1 hamiltonian:8 irreducible:1 t2:1 solution:1 discrete:1 science:1 small:1 eigenvalues:3 degeneracy:2 direct:1 sign:4 past:1 zero:2 pass:1 further:1 odd:3 10t:1 linear:1 even:6 aim:1 adds:1 appear:5 giving:1 sum:2 expressed:1 3t:10 above:5 row:6 method:3 filled:6 full:2 respectively:2 component:1 here:4 diagonal:6 reported:6 objects:1 them:1 others:1 along:2 table:23 appears:1 change:2 box:3 great:1 shift:2 study:1 vectors:9 allows:1 simultaneous:2 4t:1 permutation:2 usually:1 implement:1 studies:1 projection:1 f2:1 translational:2 apply:1 total:7 select:3 readily:3 tn:2 use:4 would:2 contains:2 negative:1 hilbert:4 call:1 m2:2 taken:3 theoretical:1 more:3 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solv-int9603010.txt |@word sci:1 consider:8 results:4 skii:1 partial:2 compact:1 whose:1 tv:9 equivalence:3 γj:9 norm:1 applied:1 g2:3 g1:3 g0:3 kω:8 springer:2 corollary:4 cook:1 difference:2 matrices:1 condition:13 solution:9 t1:25 large:1 vector:3 independence:1 small:2 eigenvalues:4 α2j:1 zero:1 further:1 theory:2 bilinear:1 d2:1 hereditary:1 current:1 above:5 new:3 journal:1 xθ:1 represented:2 equations:10 obtained:3 vectors:2 contradiction:2 periodic:2 via:2 saunders:1 apr:1 limv:1 limj:1 limi:1 establish:2 linearly:2 use:2 prove:4 remains:1 positive:3 negative:1 next:1 therefore:5 israel:1 operators:1 validity:3 berlin:2 correspondingly:1 virtue:2 particular:3 known:5 cases:1 hold:9 iii:2 balakrishnan:1 account:1 equation:23 values:1 henry:1 following:8 example:5 proof:5 control:19 process:1 bellman:1 contradicts:3 numbers:5 verlag:2 provide:1 holds:7 write:2 criterion:1 instead:2 ordinary:1 sin:7 max:4 after:1 plane:2 natural:3 third:1 element:1 so:5 fundamental:1 decreasing:1 order:1 superscript:1 ϕjk:4 soc:1 london:2 banach:1 y0:5 satisfies:1 controllable:8 complex:2 systems:11 main:1 bu0:11 non:4 greater:1 evolution:1 jα:4 hale:1 optimal:1 now:2 eigenvalue:4 equality:1 university:1 2x:1 sufficiently:2 inequality:9 l2:10 each:9 2h:4 constraints:8 homogeneous:2 xǫ:1 domain:3 differential:12 series:1 measure:2 shown:1 matrix:3 space:5 since:2 denotes:2 re:1 contained:1 at0:3 at1:5 formula:5 math:2 shows:2 lag:1 linear:10 york:3 definition:5 βp:1 v2:2 hence:10 βi:2 βj:10 βk:1 origin:2 formulas:1 initial:3 number:5 rank:1 approximate:6 lectures:1 approximately:8 impossible:1 illustrate:1 necessarily:1 adjoint:9 system:9 relations:1 assumption:1 statement:1 autonomous:2 lot:1 continuous:2 α1j:1 x0:9 x1:2 completes:1 toronto:1 accordance:1 imply:7 classes:1 argument:1 manner:1 apparently:1 any:11 min:1 general:1 lim:1 self:7 phillips:1 generalized:2 sufficiency:4 calculus:1 inequalities:1 allow:1 arguing:1 gλ:5 tl1:6 segment:1 class:2 eigenfunctions:3 considered:3 into:1 points:1 exp:30 show:2 notations:1 purely:1 spaces:1 solutions:2 substituting:1 trivial:2 parameters:4 implementation:1 delays:2 distributed:2 state:2 than:1 lemma:3 only:7 various:1 irn:6 means:2 cannot:1 ϕk:1 ϕj:4 dt:1 closure:1 lloc:1 bar:1 transposition:1 arxiv:1 nα:4 ψjk:3 set:10 exists:14 respect:2 j1:8 j2:8 result:3 tl3:3 tl2:2 hilbert:3 said:2 αt:8 µt:1 irr:4 written:2 enumerated:1 closed:5 between:3 αi:2 boundary:1 αj:1 conditions:12 comp:1 weak:3 however:2 ln2:4 solv:1 amer:1 ker:2 lu0:1 restrictions:1 cos:3 c21:1 last:1 ir2:2 assure:1 col:1 point:2 simple:1 dimensional:3 bα:1 lagrange:1 moreover:1 cu:1 pp:4 described:3 been:1 korobov:1 int:1 b0t:5 empty:1 define:1 c22:1 generating:1 corresponding:9 easy:1 sufficient:4 spectrum:2 gan:1 proven:1 c0:3 c11:3 case:5 expanded:1 evaluated:1 will:6 dept:1 suppose:1 almost:2 ir:10 thus:2 iv:4 ii:2 ij:2 im:1 cone:6 dual:1 containing:1 same:1 parts:2 finite:4 independent:2 i1:3 i3:4 i2:3 i5:4 i4:4 v0:3 v1:4 moment:2 necessity:2 infinite:2 eigenvectors:3 well:5 analysis:2 obviously:4 academic:1 usual:2 unified:1 λt:2 obtain:13 λk:1 λj:11 λi:7 λh:1 δpj:1 hille:1 ψkl:1 theorem:21 c12:1 semigroup:4 heidelberg:2 euler:1 real:11 easily:1 evaluate:1 posed:2 press:1 using:5 bir:2 necessary:4 follows:12 δp:1 steps:1 either:2 arbitrary:5 because:2 sequence:5 absolutely:1 some:2 b0:6 b1:3 b2:3 convex:5 dense:2 integration:1 providence:1 does:1 provides:1 δj:2 philadelphia:1 δk:1 equivalent:8 l1:2 continuing:1 bj:1 bu:15 properties:4 injective:5 ϕij:1 o:14 range:1 mean:1 jξ:4 convergent:1 unbounded:1 h0:1 functional:6 appropriate:1 references:1 operator:30 support:2 there:19 u1:3 u0:8 u2:3 way:1 δlk:1 function:4 complete:2 form:1 sequel:1 buv:1 buk:1 heat:1 attainable:1 ramat:1 true:3 hg:15 multiplicity:2 variations:1 us:1 limit:1 uk:1 problem:7 similar:1 eigenvector:6 examples:2 strongly:1 controllability:14 a1v:1 constant:3 defined:3 abstract:4 doesn:2 denote:3 dξ:4 proves:1 exist:2 dθ:1 ax:2 nh:1 functions:3 no:9 na:2 yang:1 company:1 conclusion:1 elements:1 generates:2 ilan:1 uniformly:2 variation:1 a1:6 a0:7 bounded:1 implies:1 assume:6 dτ:7 required:2 together:1 time:1
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solv-int9603011.txt |@word remarkable:3 alg:2 results:2 abelian:1 generalize:1 expressions:3 certainly:1 lkm:11 const:2 chain:1 uniqueness:1 encyclopaedia:1 elliptic:17 semenov:1 enjoying:1 wjm:1 r12:2 wjk:3 straightforward:2 very:1 geometrical:1 matrices:11 discovered:1 trl:1 hamiltonian:9 turns:2 sklyanin:3 list:1 solution:1 discrete:1 relation:1 anal:2 shansky:1 freidel:1 findings:1 direct:1 second:2 further:4 canonical:2 spectral:1 aim:1 stands:1 brackets:4 sum:1 analogously:1 supplied:1 maillet:1 current:1 above:4 new:1 satisfy:3 here:6 reported:1 objects:3 ansatz:3 directions:1 depend:1 sine:2 equations:3 obtained:1 sending:1 ekm:5 eij:5 ekk:11 ekj:4 theoretic:1 poisson:9 usually:1 lrel:1 formulated:2 useful:2 apr:1 wim:1 vii:1 wik:1 talon:2 reyman:1 use:1 yangian:1 prove:1 visit:2 linear:3 arutyunov:1 type:6 kostant:1 more:3 th:4 billey:1 solitons:3 appendix:2 particular:2 known:1 cases:2 springer:1 rights:1 equation:1 work:1 theories:1 following:3 my:2 example:1 proof:2 give:4 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solv-int9603012.txt |@word concept:1 gs:5 consider:16 funct:1 parallelogram:5 equalities:4 global:3 rod:1 1g2:3 illustrated:1 continual:1 commute:2 gb:6 ga:7 go:1 denotes:3 causes:1 whose:9 preserves:4 bannai:1 const:1 paris:2 alamos:2 byrd:1 finally:2 program:3 present:8 elliptic:14 under:4 spec:4 ℜh:2 applied:1 g2:28 g1:46 orthogonal:1 far:2 geometrical:1 got:1 hirosawa:1 difference:2 matrices:20 condition:12 groups:2 riemann:1 hamiltonian:36 irreducible:1 t4:1 t2:10 solution:13 enon:2 t1:14 solved:2 pˆ2:1 science:1 small:1 eigenvalues:27 anal:1 concluded:1 sin2:6 sin1:1 integrability:49 tangential:2 nonhomogeneous:3 dynamics:1 odd:8 canonical:1 even:3 dissertation:2 what:1 nonlinear:39 appear:1 representative:1 completely:1 giving:2 trivial:1 section:12 bc:3 brief:1 cell:3 poles:1 3n:2 above:2 scientists:1 international:1 consisting:1 satisfy:2 edited:1 degree:24 respectively:4 never:1 here:12 les:1 them:3 cos2:2 q13:1 represented:1 along:7 standard:1 equations:34 obtained:6 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solv-int9604001.txt |@word consider:1 ceases:2 illustrates:1 rev:1 abramovici:1 tensile:3 consists:1 whose:1 inverse:1 chain:1 concerned:1 charge:1 critical:8 th:10 under:1 case:2 sitting:2 very:1 continues:2 prof:1 encounter:1 entire:1 riemann:1 level:8 positions:1 notes:1 large:2 solved:1 phase:14 nucleated:2 configurations:5 smaller:4 force:3 periodicity:1 second:1 further:1 even:3 sub:1 section:4 expressed:1 unpinned:1 new:4 increasing:2 acknowledgments:1 condensed:1 dictates:1 lee:3 zuckerman:1 respectively:2 aubry:6 learn:1 equals:1 china:1 respect:1 change:2 publisher:1 institute:1 study:1 larger:2 meiss:1 existent:1 resonance:1 chang:1 changes:1 taipei:1 composed:3 griffiths:2 apr:1 merely:1 vii:1 mackay:1 kontorova:3 use:2 would:2 remains:1 positive:4 negative:1 vol:2 call:1 type:5 until:2 andr:1 fractions:7 introducing:2 israel:1 solitons:7 berlin:2 correspondingly:1 everywhere:1 hilger:1 particular:2 known:1 effort:1 evolves:1 springer:2 locked:1 indicates:2 science:2 equation:2 work:2 values:6 starts:1 following:2 making:1 example:3 proof:1 f1:3 f2:3 νq:1 council:1 process:1 sense:2 pq1:1 pq2:1 minimum:5 numbers:1 degenerate:1 allowed:1 tan:3 νn:6 occur:2 varied:1 rather:1 breaking:2 csc:1 how:2 pure:1 instead:1 frenkel:3 map:2 express:1 irrational:2 staircase:2 may:1 max:1 wiley:1 diagram:1 applications:1 plane:2 fk:8 types:3 realized:1 dynamical:1 schneider:1 so:1 fundamental:1 increase:1 order:6 indeed:1 stability:1 paper:1 statistical:1 satisfies:1 its:2 before:1 derive:1 located:1 interesting:1 solving:1 convexity:1 non:1 break:1 now:2 possess:1 term:1 2q:5 accompanying:1 concave:1 filling:1 turns:1 fω:14 d47:1 side:2 characterized:2 domain:1 chung:1 ed:4 energy:4 related:1 obtains:1 our:1 transitions:6 eq:7 shown:3 shallow:1 induces:2 denotes:2 particles:14 rational:3 lecture:1 occurs:5 theory:1 hull:4 quite:1 york:2 8q:1 irreducible:4 language:1 sinica:1 could:2 transition:10 turn:1 arccos:1 hence:2 first:9 there:6 number:14 reaches:2 tricritical:2 defects:1 carry:1 size:6 jer:1 given:9 introduction:2 eqs:1 system:3 pinned:2 their:1 john:1 gives:3 fraction:5 continuous:1 proving:1 part:1 authors:2 than:2 distance:1 kind:1 tree:14 zero:3 matter:1 determined:2 lowest:1 shrinks:1 ann:1 locations:1 winding:9 say:1 manner:2 seen:2 hsien:1 any:1 strength:1 min:1 thoroughly:1 montgomery:1 note:1 sciences:1 cantor:1 exactly:4 multiple:1 though:2 denominator:1 kao:3 systems:1 wells:8 coordinate:1 letter:1 pair:2 soliton:1 χq:12 considered:1 average:3 calling:1 physica:3 typeset:1 points:1 physics:4 nω:9 particularly:1 show:1 supported:1 dissociate:2 minimizing:1 solutions:1 d8:1 d7:1 find:1 ground:12 q1:23 q0:1 q2:21 proportion:1 completes:1 only:2 explicitly:1 molecules:11 circle:4 local:4 equilibrium:1 do:1 mixture:1 fractional:1 beijeren:1 ones:2 consecutive:7 commensurate:4 arxiv:1 summary:1 qc:10 fixed:1 discussing:1 set:1 exists:4 uq:1 national:1 see:4 phases:1 convex:1 state:14 between:1 invariant:1 approach:1 nature:1 however:2 incommensurate:3 le:1 solv:1 configuration:17 cos:1 cot:6 contract:1 figures:1 context:1 minima:1 co:4 point:5 corresponds:2 insist:1 height:1 dimensional:1 grants:1 anti:2 associated:2 throughout:1 gratitude:1 devil:2 described:5 equations:1 create:1 three:3 been:2 describes:1 fig:2 corresponding:4 defect:2 maps:1 observe:1 present:1 p2:15 p1:14 pacs:1 solid:1 schellnhuber:1 value:3 enthalpy:4 will:3 while:1 characterizing:1 studied:1 2un:1 almost:2 ip:1 them:2 elsevier:1 chudnovsky:1 recurrent:2 bishop:1 widely:1 largest:1 several:1 higher:1 investigated:1 bristol:1 hand:2 domains:1 moving:1 infinite:1 kept:1 studies:1 depending:1 well:5 academia:1 uq1:3 position:1 model:12 usual:2 λv:1 just:1 being:2 when:11 obtain:2 λc:1 underlying:1 integer:5 touch:1 taiwan:2 yet:1 adding:2 preprint:1 dissociation:1 regarded:1 had:1 wen:1 farey:17 potential:13 lett:1 versa:1 occurring:1 solvable:3 transformation:1 period:4 increases:3 background:1 using:1 unique:2 moreover:1 mod:1 like:2 particle:7 sizes:5 follows:2 reprints:1 steps:1 arbitrary:1 become:1 stationary:4 therein:1 right:3 truncated:1 creation:1 some:2 understood:2 niven:1 specified:1 happens:1 dimensions:1 bottom:4 shall:1 per:3 does:1 unstable:1 molecule:5 each:2 step:2 revtex:1 dictated:2 about:1 o:1 soc:1 into:10 nsc:1 lies:1 references:2 van:1 removing:1 sequence:1 u0:2 way:2 notices:1 sections:9 function:10 complete:3 form:1 regard:1 but:2 hu:1 instructive:1 whether:1 smooth:2 up:3 differentiable:1 un:8 limit:1 demonstrate:1 problem:1 similar:1 mechanics:1 shih:1 constant:1 int:12 certain:1 abstract:1 describe:3 general:2 chap:1 exist:5 hamiltonian:1 internal:1 constructed:1 integrability:1 no:3 generally:1 vanishes:2 field:1 other:1 republic:1 mathematics:1 conclusion:1 models:3 problems:1 important:1 qχ:2 structure:2 tzeng:3 implies:1 longer:2 vice:1 interval:1 curve:1 orbit:1 adam:1 starting:1 having:1
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solv-int9604002.txt |@word concept:1 partial:4 results:2 fluids:1 four:2 ginzburg:13 whose:2 depend:1 calculate:1 subjected:1 intensive:1 investigation:3 th:1 tc:15 case:4 none:1 uwo:1 continued:1 condition:1 arrange:1 leads:3 riemann:2 list:2 solution:2 vector:2 3b:2 anal:1 direct:5 painlev:17 further:2 ode:2 theory:1 spectral:1 what:1 nonlinear:2 sheeted:2 3i:1 poles:1 above:3 new:2 method:3 seeks:1 coefficient:1 never:1 component:1 groups:1 address:1 equations:10 implicit:1 obtained:3 resonance:1 chang:1 indeterminacies:1 heiles:1 9k:1 formulated:1 apr:1 derivatives:3 ψx:6 ψy:9 working:1 generators:1 themselves:1 more:4 odinger:1 berlin:1 virtue:1 integrable:1 must:3 account:1 valued:2 integrating:1 equation:25 values:8 codimension:1 learn:1 following:4 making:1 compare:1 give:1 calculation:1 sense:2 arise:1 lacks:1 verlag:1 information:1 φx:2 rather:1 write:1 criterion:1 fourth:1 ordinary:5 parameter:4 tension:1 algebra:2 thermodynamic:1 wiley:1 singularities:1 movable:1 applications:1 plane:3 φ2y:1 φ2x:1 natural:2 dynamical:1 third:1 henon:1 perform:1 ones:1 so:4 allow:1 φy:2 every:2 order:10 over:1 despite:1 paper:1 london:1 2v:1 motions:1 hypersurface:1 still:1 its:3 group:9 singular:1 fractal:1 temporal:1 solving:1 systems:1 mail:1 formulæ:2 eventually:1 non:1 greater:1 landau:13 they:1 identically:1 now:2 possess:7 2t:1 represents:1 february:1 several:2 fully:1 university:1 2b:4 each:2 found:1 2k:3 domain:1 arxiv:1 successively:2 series:3 reduce:1 our:2 beyond:1 living:1 shown:2 space:1 since:2 chaos:1 looking:1 re:1 daniel:1 cause:1 math:3 ψ2x:9 seventh:1 orbits:1 formation:2 york:1 definition:2 could:1 transition:1 place:1 hence:3 first:8 xi:1 symmetry:7 variables:9 symbolic:1 number:1 another:1 ψxy:2 ψxx:2 equating:1 temperature:2 introduction:1 carnevale:1 system:3 relations:1 their:2 listed:1 calculations:1 siam:1 behaved:1 final:2 continuous:1 western:1 requisite:1 than:1 coefficients:2 wide:1 fuchs:1 second:4 symmetries:1 stubbs:1 say:1 manner:2 concentration:1 seek:1 any:3 lie:2 computationally:1 self:1 instance:1 potential:1 generalized:2 5b7:1 fundamental:1 simplify:1 regular:1 definitions:3 phase:1 analytically:1 extremely:1 laurent:3 calculated:1 physics:1 precise:2 particularly:3 solutions:3 d2:3 find:1 fifth:1 knowledge:2 parameters:7 should:3 analytic:4 only:8 2bk:1 employed:1 mixture:1 means:2 dependent:1 there:4 fluid:5 cannot:2 competing:1 singularites:1 ds:1 fields:2 differential:11 multi:1 yield:1 investigate:1 contain:1 through:1 reveals:1 set:2 undergoes:1 see:1 result:2 fail:1 inequivalent:1 theoretic:1 surfaces:1 fails:1 various:1 between:1 boundary:2 meromorphic:1 terms:1 solv:1 packages:1 relying:1 restrictions:2 pde:6 expression:1 ci:1 relevant:1 ca:1 dimensional:2 distinguish:1 exploit:1 table:1 described:1 transformations:1 basis:1 odes:2 int:1 reduction:4 arises:1 corresponding:1 indeterminacy:1 both:2 understand:1 olver:2 c2:2 c1:2 those:1 applied:1 bφ:3 contexts:1 will:3 euclidean:1 property:16 procedure:2 seven:1 vi:3 thus:1 surface:2 regularity:1 itself:2 vt:1 vanish:2 binary:1 different:1 φt:3 generic:1 recursion:2 make:3 complex:7 φi:1 φj:4 finite:1 independent:7 comprehensive:1 numerical:1 upon:1 possible:1 v0:4 ψyy:4 expand:1 subgroups:1 relies:1 schr:1 no:1 well:2 analysis:1 does:3 components:1 position:1 possesses:2 being:1 keefe:1 obtain:1 valuable:1 detail:1 character:1 weiss:2 valid:1 spirals:1 theorem:2 transformation:1 real:1 term:1 using:2 vague:1 like:1 δl:1 yields:6 either:2 always:1 become:2 because:1 methods:2 some:1 springer:1 n6a:1 respect:1 indirect:4 mcleod:1 dimensions:2 integration:1 critical:1 eliminate:2 tabor:3 sixth:1 arbitrary:4 use:2 expansion:5 substitution:1 about:1 would:1 discussed:2 2x2:1 other:1 presence:1 into:1 references:1 determine:2 often:2 ontario:1 log:1 area:1 twodimensional:1 specifically:1 was:1 function:2 complete:1 but:4 failure:1 illuminating:1 pdes:1 consist:1 us:1 below:1 similar:1 called:1 defined:2 abstract:1 general:2 single:2 exist:1 dη:11 check:1 functions:4 integrability:1 variety:2 when:6 vanishes:1 interested:1 spatial:3 department:1 mathematics:1 allowing:1 variable:2 structure:3 dφ:7 required:1 4b:1 original:1
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solv-int9604003.txt |@word partial:1 consider:3 scalar:1 hyperboloid:1 homomorphism:1 expressions:1 gk:2 gj:1 compact:4 whose:5 inverse:8 depend:1 tx:1 equivalence:2 noncompact:4 γt:1 tj:1 tk:1 th:1 under:2 applied:4 far:2 dell:1 choice:1 resonant:1 exact:1 condition:4 turns:1 t2:11 prolonged:1 t1:9 vector:8 math:4 dealing:1 direct:3 consists:2 integrability:2 subscripts:1 index:1 what:2 nonlinear:7 stands:1 diag:1 expressed:2 version:1 above:1 3c:1 3b:2 3a:2 method:10 satisfy:1 respectively:4 never:1 here:3 leo:3 consideration:2 sine:1 equations:19 κs:6 obtained:1 sjx:15 study:2 vectors:3 soliani:2 products:1 procedure:3 studies:2 quotient:1 via:3 dϑ1:1 family:3 apr:1 requiring:2 9c:1 9b:1 gordon:1 apply:1 should:1 linearly:1 derivatives:1 ψx:1 handled:1 prove:1 ψt:1 few:1 ψi:3 m1:8 therefore:1 m2:5 type:4 minor:1 more:1 introducing:1 becomes:1 operators:2 ti:6 y1t:1 virtue:1 particular:1 known:2 cases:1 keeping:1 recall:1 equation:6 mi:1 reproduce:2 following:2 arrive:2 example:1 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solv-int9604004.txt |@word gt:4 lakshmanan:2 consider:5 funct:1 rev:4 equalities:3 varying:1 results:3 four:1 commute:1 expressions:1 jˆ1:1 scr:1 devoted:1 preserves:2 inverse:4 depend:1 calculate:1 shanghai:2 tn:4 γj:2 γi:1 tj:2 γn:4 th:18 under:6 analogous:2 include:2 fax:1 rise:3 recursively:1 wave:2 ηit:3 σxt:1 matrices:1 common:2 leads:1 hamiltonian:47 bn:2 suffices:1 δh2:4 δh1:5 leave:1 convenience:1 vector:23 science:3 small:3 anal:1 optics:1 application:2 dealing:1 variables:3 direct:1 burger:1 zero:9 dordrecht:1 korteweg:5 chen:1 further:4 dynamics:1 linear:7 spectral:4 established:3 what:1 nonlinear:10 stands:1 invertible:2 diag:2 section:5 mechanics:1 kamran:1 expressed:1 hereditary:23 current:1 3i:4 fuchssteiner:6 above:12 new:10 ˆj:1 method:4 ˆn:22 edited:1 ξi:2 full:1 degree:2 respectively:3 equals:1 here:4 water:3 china:4 concluding:2 consideration:1 equations:40 revisited:1 differential:5 remark:1 institute:1 vectors:6 amount:1 resulting:5 poisson:3 usually:1 t20:2 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solv-int9604005.txt |@word consider:4 chain:2 similarity:1 rev:6 magnetic:13 results:2 four:1 commute:3 grateful:1 go:1 follow:1 expressions:1 contributions:3 inverse:1 concerned:1 funct:1 tn:1 finally:2 does:1 petersburg:1 th:1 under:3 analogous:2 must:1 string:1 very:1 springer:1 novel:1 putting:1 lecture:1 difference:1 matrices:1 condition:1 leads:2 riemann:1 hamiltonian:1 notes:1 solution:5 large:6 solved:1 convenience:1 small:4 zm:4 dealing:1 painlev:13 correlator:1 further:2 linear:2 spectral:1 established:3 what:2 nonlinear:1 sum:2 expressed:1 agrees:1 above:3 capital:1 new:2 method:2 filled:1 here:4 xλ:1 objects:1 cos2:1 sinh:20 invented:1 equations:5 appears:1 obtained:4 great:1 arrive:2 orbach:1 institute:3 chalmers:1 leaves:1 larger:1 allows:1 identity:1 digamma:1 via:3 shorthand:1 mobility:1 apr:1 explained:1 summation:2 apply:1 orderings:1 derivatives:2 use:5 asymptotic:1 would:1 commun:1 perk:1 positive:1 contains:1 direction:1 next:1 nucl:2 mori:1 therefore:1 m2:1 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solv-int9605001.txt |@word represent:1 remarkable:1 trigonometric:2 leads:2 eds:1 scalar:1 abelian:1 expressions:1 gl:1 whose:1 weierstrass:1 chain:1 tr:2 finally:1 those:1 elliptic:11 γl:1 tf:2 takes:1 very:2 results:6 entries:2 discretizations:8 difference:3 matrices:6 condition:3 level:1 positions:1 sklyanin:2 solution:8 discrete:14 interpolating:4 small:2 eigenvalues:3 direct:1 approximation:2 integrability:4 rigorous:1 further:3 theory:1 even:2 what:3 nonlinear:1 appear:1 diag:2 analogously:1 version:2 above:1 new:4 satisfy:1 bi:1 respectively:3 neveu:1 here:7 diagonal:7 bogoyavlensky:1 ansatz:10 sinh:14 directions:1 along:5 sine:1 equations:21 implicit:2 change:1 obtained:2 generalizing:1 shift:2 studied:3 allows:4 mx:4 resulting:1 action:2 suitable:1 makes:1 via:1 followed:1 namely:5 prefer:2 talon:1 proceed:1 would:1 commun:3 covariant:2 contains:1 visit:1 uniqueness:1 gibbons:1 opposed:1 taken:1 means:1 type:4 kostant:1 more:5 th:6 billey:3 started:1 solitons:4 under:2 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solv-int9605002.txt |@word gu:6 consider:1 rev:1 equalities:1 leads:1 roy:1 ahler:1 gj:2 gi:6 gh:1 whose:5 inverse:7 calculate:1 shanghai:2 λn2:2 nonlocal:1 γj:2 γi:7 investigation:1 γn:1 under:2 include:1 applied:1 conjecture:1 kent:1 g1:2 very:1 rise:1 choice:1 matrices:9 condition:6 riemann:1 presented:1 list:1 solution:9 solved:1 ndimensional:1 relation:2 venus:1 takhtajan:1 direct:1 zero:11 cosq:1 further:5 mason:1 1n1:1 spectral:15 established:2 what:3 nonlinear:5 developed:1 appear:1 invertible:1 diag:4 section:6 interactions:1 expressed:1 version:1 fuchssteiner:1 above:6 new:9 connected:1 consisting:1 satisfy:4 hasn:2 respectively:2 here:2 sinq:1 china:2 consideration:3 along:1 equations:39 obtained:2 great:1 property:1 deriving:1 hλl:3 institute:2 involved:1 study:1 vectors:1 p2:5 resulting:2 usually:1 hospitality:1 suitable:1 makes:1 useful:1 establish:1 unit:1 would:3 prove:1 covariant:1 positive:1 contains:3 negative:3 hilbert:1 few:2 noting:2 therefore:7 more:9 µi:7 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solv-int9605003.txt |@word spherical:3 comment:1 since:1 manifold:2 u0:3 show:1 v6:1 restored:1 summarized:1 grammaticos:1 satisfied:1 course:1 hietarinta:1 through:1 solutions:2 reductions:1 integer:1 mentioned:2 japan:1 scattering:1 its:1 u1x:1 relationships:1 current:1 inverse:1 system:1 true:1 fix:1 original:1 weiss:1 should:1 lattice:1 only:4 12t2:2 systems:3 integrable:10 variables:2 divided:1 ramani:3 non:2 sub:1 around:1 fukuyama:2 dependent:2 assuming:1 suffice:1 assumed:1 introduce:1 obtain:4 department:1 cannot:1 every:2 know:2 dx:2 identically:2 resonant:1 using:3 singularity:2 kusatsu:1 yu:1 ordinary:1 condition:1 2t:11 term:3 appearing:1 conclusion:1 did:1 follows:4 university:1 arxiv:1 solution:4 2z:1 t1:1 2d:1 ai:2 differential:3 yields:2 nakamura:3 arbitrary:1 become:3 repeating:1 probably:1 side:1 2j:1 mean:1 concluded:1 ars:3 another:2 arbitrariness:1 exhaust:1 direct:1 challenges:1 painlev:10 result:1 zz:2 substituting:2 chen:1 further:1 kdv:11 eq:17 substitute:2 zzz:1 bilinear:2 3z:1 nonlinear:3 dimensions:1 nonintegrable:2 space:2 trivial:1 furthermore:2 bkc:2 definite:1 find:1 u2t:1 does:4 tests:1 respectively:1 prog:1 new:2 get:3 previous:1 u2x:2 method:2 compliment:1 shiga:1 satisfy:1 dx4:2 terms:1 linear:1 extend:1 tabor:1 gkdv:13 ju:1 complement:1 jp:4 however:3 expansion:1 quite:1 step:1 test:11 here:3 substitution:3 ask:1 degasperis:3 equations:8 between:1 logarithmic:2 undetermined:1 both:2 constants:1 extension:2 could:1 put:1 suggests:1 math:2 cylindrical:5 extensions:1 u4:3 solitons:1 argue:2 ritsumeikan:1 dz:1 soc:2 rev:1 φxx:4 point:2 requiring:1 into:10 corresponds:1 coincidence:1 dimensional:9 solv:1 xx:1 references:1 least:1 determine:1 operator:1 apply:1 rep:1 consider:2 ct:1 passes:2 given:1 zψ:1 log:2 leading:1 eqs:6 u6:5 question:2 three:1 u3:9 u2:6 comparing:1 reduction:1 therefore:3 u0x:1 expected:1 airy:1 u0t:1 instead:1 topics:1 partial:2 gives:1 function:2 obtained:3 divergence:1 statement:1 form:1 becomes:3 concerning:1 converse:1 but:2 calogero:3 maxon:1 segur:2 authors:1 known:1 separated:1 cases:1 irrelevant:1 present:1 case:16 springer:1 made:1 coefficients:1 whether:1 ut:1 equation:20 6uux:1 toda:2 verlag:1 transformation:1 reviews:1 ul:4 remain:1 determined:1 takeshi:1 following:1 situation:1 define:1 u1t:1 procedure:1 strongly:1 mails:1 ac:2 constant:1 nuovo:3 int:1 allows:1 abstract:1 pass:2 thus:2 conjecture:4 generalization:3 ii:2 say:1 his:1 z0:2 performed:1 sense:1 uxxx:1 βt:2 fractional:1 ψzz:1 different:1 classified:2 φt:3 integrability:3 φx:13 φz:3 song:1 when:1 lett:4 same:2 power:2 parts:1 dt:2 generalized:3 branch:1 spatial:1 answer:2 so:3 vanished:1 theor:1 φl:2 higher:3 independent:1 used:1 suppl:1 singular:1 may:2 preceding:1 consistency:1 miscellaneous:1 movable:3 hand:1 most:1 important:2 uses:1 purpose:1 letter:1 bountis:1 variable:2 grateful:1 φ2x:4 ablowitz:2 sides:1 expand:2 αt:3 exact:1 soliton:1 x4:2 natural:1 special:2 imply:1 u1:6 assume:2 clear:1 well:1 correspond:1 order:5 λ2z:1 6u2:5 place:1 exp:1 hirota:3 five:1 physics:3 dimension:1 fact:1 subgroup:2
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solv-int9605004.txt |@word partial:2 consider:2 results:2 four:1 c2:6 whose:1 inverse:2 tr:1 nonlocal:1 finally:1 present:1 under:1 ankara:1 condition:5 potentiation:2 list:1 solution:2 integro:1 c00:3 βx2:1 consistent:1 integrability:3 bilkent:1 further:2 canonical:1 subscripts:1 will:12 what:2 nonlinear:3 trivial:3 section:1 fifth:1 u31:11 new:2 method:2 satisfy:2 edited:2 respectively:3 groups:2 address:1 equations:45 appears:1 change:1 box:1 study:1 studied:1 leaving:1 resulting:1 involves:1 via:2 classification:18 rσ:1 apply:1 total:1 linearly:1 derivatives:1 use:7 would:2 substitutions:5 therefore:1 taken:1 type:1 until:1 possible:1 subcases:1 fokas:3 operators:1 berlin:3 virtue:1 known:2 cases:3 hold:2 springer:3 ρi:4 recall:1 equation:49 work:2 ρt:1 following:10 give:8 sokolov:2 generically:1 council:1 allowed:1 verlag:3 e2u:2 e2v:2 s2:4 s1:1 write:1 nontrivial:1 fourth:1 instead:1 allowable:2 u21:20 may:1 applications:1 φ2u:3 faculty:1 φ2x:1 mam:1 compatibility:1 outline:1 imply:1 whenever:1 author:1 explicit:2 st:1 so:1 sm:3 suggest:1 order:8 se:1 a02:39 a03:15 a01:26 a04:16 course:1 paper:1 existence:4 satisfies:4 sciences:1 thank:1 ln:4 solving:1 actually:1 forms:2 permanent:1 mail:1 non:2 integral:1 introduce:1 easily:1 term:4 university:2 2x:1 2d:2 2a:1 done:1 higher:1 mikhailov:3 differential:15 related:2 1d:1 eu:1 eq:1 rt:2 shown:2 solved:1 furthermore:1 crucial:2 research:2 investigation:1 gov:1 occurs:1 math:1 linear:7 8b:1 8c:1 8a:2 seventh:1 put:1 e3:1 βt:1 βx:5 linearized:3 turn:1 derivations:1 u22:12 hence:12 first:16 symmetry:11 miura:3 xx:1 simplified:2 given:9 checked:2 similarly:1 introduction:1 leading:1 system:3 1a:1 needed:1 1c:1 1b:1 vxx:1 dfg:1 gives:7 recursively:1 eliminates:1 part:1 eliminated:4 coefficients:2 dynamical:2 third:2 zero:1 powers:2 symmetries:6 considerably:1 linearizable:6 need:2 seen:2 their:2 lie:3 depending:2 k2:2 k1:1 potential:2 take:3 3z:1 4u3:1 sequence:1 class:10 inconsistency:1 αt:1 soliton:1 surprising:1 5u:1 considered:2 later:2 dηi:2 vries:1 fact:1 oevel:1 show:8 v13:4 supported:1 solutions:3 d2:1 d3:1 d0:1 d1:1 based:1 should:1 only:2 candidates:1 vxxx:1 integrate:1 integrable:11 local:9 fuchssteiner:1 do:1 dependent:2 de:1 solvability:1 cannot:1 dx:3 evolution:11 densities:3 approach:1 arxiv:1 uu:2 coefficient:4 set:11 uu1:1 observed:1 b202:1 result:5 discussions:1 frechet:1 interacting:1 olver:1 closed:1 invariant:1 conditions:14 terms:2 shabat:2 uuu:6 however:1 solv:1 both:1 essentially:1 c21:1 last:1 chosen:1 otherwise:1 point:4 mkdv:6 cx:1 polynomial:3 respect:1 turkey:3 described:1 transformations:17 second:1 three:1 been:7 a212:1 int:1 3u4:1 3u2:3 3u1:1 obtained:3 6b:1 xxx:1 c20:1 derivative:5 c3:5 mu1:1 c1:4 general:2 those:1 case:15 classifications:1 expanded:1 single:1 b01:4 b00:2 b02:7 situation:1 thus:5 uxx:7 ii:1 itself:1 vt:8 vx:2 c0:2 uxxx:6 φt:2 φu:7 grant:1 φx:2 recursion:8 make:3 orders:1 parts:1 degasperis:2 independent:9 used:1 hand:1 v1:4 v3:7 center:1 paderborn:1 no:1 well:1 s22:1 without:1 solve:1 coordinate:13 σt:1 proposed:1 being:1 obtain:22 valuable:1 karasu:1 differentiation:1 previous:1 density:18 zakharov:2 tubitak:2 had:1 except:2 transformed:10 c12:1 c11:1 c10:11 5a:1 transformation:17 5b:1 2u:1 2v:2 admitting:2 department:2 using:13 formal:8 like:1 follows:1 reduces:1 korteweg:1 either:2 truncated:1 sends:1 b0:8 b1:5 choosing:4 kdv:5 nonzero:1 possibilities:1 dense:1 dimensions:1 lead:1 shall:4 subclass:1 eliminate:2 scientific:1 equivalent:1 expansion:1 step:1 substitution:1 stage:1 introduces:1 dependence:7 o:2 ensure:1 obtaining:1 appropriate:1 references:1 operator:10 u4:1 there:2 u1:71 u3:34 u2:31 a211:2 sections:2 function:4 transformable:7 form:17 branching:4 but:5 elimination:2 highest:2 partially:1 compute:1 ux:9 consist:1 whether:1 ut:38 up:2 um:5 below:3 stages:1 constant:5 6a:1 defined:2 certain:1 abstract:1 denote:1 conserved:21 ay:1 functions:1 completeness:2 locality:1 when:3 application:1 other:2 test:1 mathematics:2 conclusion:1 a11:23 a13:5 a12:9 a1:5 a0:4 a3:1 a2:7 variable:3 implies:2 assume:2 time:3 requires:1
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solv-int9605005.txt |@word represent:1 consider:2 remarkable:1 rev:1 particular:1 focus:1 fxxx:1 l11:1 leads:2 4pi:2 consists:8 expressions:3 contributions:6 localized:3 inverse:12 depend:1 technique:4 finally:1 those:1 stable:7 dramatically:2 ta:1 case:26 confirmation:1 amplitudes:1 very:1 frequencies:1 continues:1 results:5 lyapunov:2 putting:2 difference:2 condition:13 illustrated:2 presented:1 transmission:1 turns:3 upe:5 solution:96 large:11 solved:9 math:1 small:18 nine:1 concluded:3 upper:6 smaller:1 force:1 coordinate:2 consistent:1 second:8 7th:1 further:3 situated:2 theory:1 spectral:11 nonlinear:6 stands:2 witnessed:1 sum:6 brief:2 expressed:1 kun:3 experiment:3 poles:27 vetterling:1 3b:2 3a:3 method:2 contrast:2 coefficient:26 chose:1 degree:1 component:1 amplification:1 focused:1 eikx:5 represented:1 marchenko:2 equations:9 p3i:3 box:1 great:1 property:1 algebra:1 technical:1 study:1 studied:1 through:1 amount:1 fourier:2 changes:2 plotted:6 formulated:1 scales:2 ipj:1 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solv-int9605006.txt |@word allowed:1 consider:4 crucial:2 results:2 leads:2 proposition:14 consists:2 follow:2 expressions:12 row:1 devoted:1 whose:1 depend:6 calculate:1 concerned:1 tr:4 recurrence:1 finally:2 under:7 applied:1 straightforward:1 very:2 updates:2 advised:1 discretizations:6 difference:11 matrices:8 four:1 obvious:1 hamiltonian:9 turns:2 list:1 solution:2 large:1 discrete:15 small:2 says:1 specially:1 findings:1 approximation:5 second:6 further:2 canonical:5 subscripts:1 established:1 what:1 const:4 stands:1 brackets:9 d2:2 section:2 analogously:2 above:3 new:7 satisfy:4 respectively:3 even:2 here:6 canonically:10 identifications:1 situation:1 represented:1 consideration:1 equations:51 change:1 obtained:4 remark:1 ekk:8 studied:1 allows:3 periodic:8 resulting:2 poisson:14 usually:1 changes:1 uniquely:2 highly:1 wit:2 asymptotic:2 uniqueness:2 comparing:2 call:1 taken:1 means:2 more:5 fractions:6 correspondingly:2 particular:1 known:3 cases:1 must:2 account:1 recall:1 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solv-int9605007.txt |@word supersymmetrical:1 partial:1 consider:2 four:3 eds:1 spiridonov:1 φ1n:8 expressions:1 excluded:1 depend:1 company:1 petersburg:2 th:7 p2:7 g1:28 rise:2 translations:1 wave:1 georgia:1 polytechnic:1 redefinition:1 dim:1 hamiltonian:8 turns:1 list:2 solution:1 leave:1 solved:2 eigenvalues:1 degeneracy:1 upper:1 specially:1 miller:1 sign:2 integrability:3 dedonder:1 even:1 established:1 what:2 nonlinear:1 g22:1 appear:1 g21:5 diag:3 section:1 version:1 new:5 3g:2 method:3 satisfy:3 full:1 fiz:2 respectively:4 here:3 superhamiltonian:2 separation:6 represented:3 const:2 enveloping:1 equations:5 appears:1 z2:2 deduced:1 obtained:4 search:1 glk:1 shift:1 study:1 studied:1 poisson:1 published:2 suitable:1 formulated:1 useful:1 f2:20 replace:1 planck:1 p41:2 derivatives:12 conventional:3 eψ:1 would:1 contains:2 next:2 m4:3 nucl:1 m1:7 therefore:3 m3:3 memory:1 type:2 theoretical:1 more:1 nauka:1 elliptic:2 becomes:1 operators:13 corrected:1 odinger:2 borisov:2 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solv-int9605008.txt |@word sci:3 consider:1 similarity:1 results:1 eds:1 consists:1 gn:22 expressions:3 polinomials:3 inverse:1 const:1 paris:2 tl:1 those:1 th:2 p2:9 conjecture:1 straightforward:1 very:4 implicitly:1 account:1 wave:4 notations:1 hamiltonian:1 t2:5 solution:19 large:1 math:4 permutability:1 wronskian:4 cosh:6 second:1 dynamics:1 theory:1 bilinear:1 index:1 nonlinear:6 section:2 expressed:1 poles:1 above:1 new:1 method:6 body:1 condensed:1 degree:1 nimmo:2 here:3 sinh:10 directions:1 equations:5 z1:7 z2:7 obtained:10 institute:1 study:2 studied:2 complicated:1 useful:1 ratios:1 apply:1 univ:1 ando:1 distinct:1 suppl:3 next:1 ψi:2 taken:1 mckean:1 type:1 more:5 introducing:1 becomes:1 operators:1 known:4 mg:1 equation:13 paragraph:1 following:5 nonsingular:1 numbers:2 verlag:2 boussinesq:6 verify:2 means:1 foreseen:1 pure:1 significance:1 types:2 singular:1 may:1 variant:1 dx2:1 diagram:1 summarize:1 choice:2 fn:62 schneider:1 explicit:2 st:2 zakopane:1 order:7 developed:1 move:1 satisfied:1 paper:2 through:1 mentioned:1 its:2 derive:1 ln:1 adimensional:1 conjugation:1 complex:8 systems:4 mail:2 main:2 them:2 yn:23 mention:1 they:12 identically:1 nov:1 now:1 2t:1 easily:2 term:1 finite:1 presented:1 ifa:2 found:12 higher:4 en:13 ei:1 series:2 displacement:1 used:3 toda:19 extended:2 obtains:1 our:1 shown:2 gibbon:2 rev:1 rational:42 conjectured:2 formula:4 ro:2 interchanging:1 sinh2:1 linear:1 little:1 possibility:1 completely:1 advantages:1 ask:1 hand:1 e1:12 generate:1 e2:6 pairs:1 first:2 romania:1 there:3 neccesary:1 symmetry:4 number:1 philadelphia:1 enlarged:1 smaller:1 simplified:1 relations:3 given:4 introduction:2 least:1 their:2 appl:1 constants:2 calculations:5 dt2:2 siam:1 gives:1 segur:1 x2:2 than:1 dtj:2 dtn:4 see:2 dtd:2 matter:1 determined:2 were:5 already:1 seen:1 recover:1 any:3 depending:5 convenient:2 coresponding:1 take:1 shall:4 algebraic:1 multisoliton:1 phase:3 class:14 soliton:23 clear:1 later:1 exp:50 velocity:1 physics:2 fact:3 discovered:1 iǫ:20 relation:3 solutions:48 d2:1 find:3 spite:1 only:3 integrable:2 moser:2 perturbations:1 equilibrium:1 dn:12 his:1 dj:2 get:2 dependent:1 soon:1 ones:1 dt:7 coth:1 determinants:1 continuum:2 arxiv:1 investigate:1 common:2 satisfy:3 set:2 observed:1 namely:4 limiting:3 satisfying:2 αt:1 written:4 conditions:1 checks:1 cancelling:1 terms:10 extend:1 vanishing:2 comm:2 solv:1 both:3 last:2 limits:1 taking:5 equal:1 propagation:3 connection:1 expression:2 point:1 simple:3 cancel:1 cr:1 considering:1 transformations:3 been:1 dropping:1 pi:13 pn:3 2ǫt:5 direction:7 present:2 case:1 p1:9 tanh:1 solid:2 ǫj:2 ǫi:9 expanded:1 ǫn:1 aim:1 ǫt:24 procedure:4 larger:4 chaotic:1 vi:1 thus:1 yk:2 conf:1 different:3 perhaps:1 recursion:1 same:6 beside:1 shifts:2 unity:1 verifies:1 φi:1 constructed:1 difficult:1 investigated:3 satsuma:10 possible:1 moving:3 ablowitz:12 expand:1 keeping:1 poland:1 well:1 lim:2 firstly:2 position:1 model:1 being:1 obtain:1 atomic:1 scattering:1 yet:1 previous:2 preprint:1 δpi:1 lattice:13 lett:2 transformation:1 identical:1 february:1 using:8 particle:1 become:2 bucharest:1 acad:1 methods:1 successfully:1 some:1 somehow:1 choosing:1 kdv:5 ourselves:1 happens:1 polinomial:1 affects:1 opposite:2 does:1 assuming:1 prog:3 power:2 equivalent:2 use:1 bt:9 although:2 properties:1 most:1 o:12 nonvanishing:1 mixed:8 introduced:1 previously:1 into:1 ηi:3 down:1 appropriate:2 references:1 springer:2 initial:1 transform:1 long:4 bianchi:1 way:3 was:6 form:10 2ηi:1 but:3 line:1 adler:1 us:1 ωi:2 limit:8 backlund:4 similar:1 popularity:1 b2:2 int:2 certain:2 abstract:1 determinant:2 general:1 exist:1 ax:1 formalism:2 bishop:1 physical:1 tedious:1 again:1 functions:1 no:1 when:1 other:4 solitons:5 theor:3 nice:1 superposition:4 a12:5 a1:3 wadati:1 a2:5 hirota:7 n2:3 starting:8 4c:2
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solv-int9605009.txt |@word φ1j:2 sci:1 consider:1 results:1 leads:1 ψ1j:2 grateful:1 gm:1 research:1 gh:2 inverse:1 depend:1 technique:4 tr:8 tn:10 δhn:2 th:4 under:2 p2:6 g0:2 very:1 rise:1 every:1 condition:1 common:1 gg:1 solves:1 hamiltonian:21 solution:4 δh0:1 leave:1 discrete:1 vector:3 eigenvalues:1 anal:1 noted:1 trv:1 integrability:3 chen:1 further:3 linear:2 spectral:5 will:1 nonlinear:4 appear:1 diag:1 section:1 expressed:2 hereditary:1 fuchssteiner:3 new:2 technology:1 d1:1 connected:1 method:2 satisfy:1 simultaneously:1 lee:1 respectively:1 here:2 china:4 separation:2 concluding:1 along:1 equations:14 remark:1 remarks:1 institute:1 involved:1 drs:1 vectors:1 suggests:1 resulting:2 poisson:2 dickey:1 geng:2 involves:2 control:4 shanghai:2 useful:1 tools:1 manipulate:1 derivatives:1 ψx:1 would:2 commun:1 distinct:1 ψs:1 jpn:1 ψj:4 few:1 therefore:1 ψl:1 taken:1 associated:1 more:2 separated:1 fellow:1 successful:1 ap3:1 operators:1 ap1:1 award:1 ma:6 science:2 equation:7 cao:1 following:5 example:2 stimulating:1 proof:2 f0:1 f1:1 give:1 accept:2 involve:1 vx:4 dm:6 sense:2 mel:1 fn:2 bargmann:9 get:2 write:1 how:1 ψij:2 parameter:2 ψin:1 konopelchenko:1 product:1 algebra:1 fx:1 φ2j:2 use:1 φi1:1 lax:22 waves:1 fm:3 constants:1 ψi1:1 natural:1 explicit:5 their:2 verify:1 representation:2 ghn:2 order:3 hierarchy:14 over:1 through:2 still:1 thank:1 interesting:1 temporal:5 solving:1 exhibits:2 late:1 absence:1 systems:18 derivative:1 main:3 fim:1 them:1 combination:1 noticing:1 introduce:2 they:2 now:1 discuss:1 possess:1 represents:2 fi1:1 2q:2 2r:2 always:1 university:1 applied:1 2a:2 2b:2 2c:2 higher:1 constraints:11 differential:3 financial:1 ej:5 series:1 energy:1 idea:3 related:1 constitute:1 isospectral:1 toda:1 extended:1 our:1 meth:1 out:2 shown:2 matrix:4 space:1 nuovo:1 since:1 denotes:1 may:13 investigation:1 math:8 ftn:1 foundation:2 theory:2 standard:1 york:1 besides:1 ψ2j:2 finite:8 publication:1 pairs:17 motion:5 int:1 hence:1 first:2 xh:1 there:1 humboldt:1 symmetry:19 variables:3 xf:1 xg:1 engenders:1 directly:1 open:1 given:2 rewritten:3 similarly:1 introduction:1 adjoint:9 system:12 compatibility:3 needed:1 too:1 variational:2 structures:1 gives:2 2an:1 φsj:1 exactly:2 2ai:2 debnath:1 somewhat:1 authors:1 kind:4 cimento:1 second:1 determined:1 symmetries:4 need:1 any:1 lin:1 note:2 k0:2 play:1 germany:1 pair:1 why:1 soliton:23 considered:1 sometimes:1 flow:1 kn:7 km:1 bracket:2 oevel:3 show:2 solutions:4 carefully:1 d2:1 find:1 d0:1 universitaet:1 q1:8 q3:8 q2:6 ψsj:1 should:1 2bn:1 only:1 2bi:2 integrable:8 constant:1 narrows:1 dh:1 di:2 dependent:2 dx:3 gen:1 alexander:1 arxiv:1 acknowledgments:1 involutive:6 qi:14 including:1 discussing:1 dpi:1 reveals:1 set:1 national:1 differentials:1 result:3 discussions:1 irn:1 between:1 sorts:1 conditions:2 terms:1 however:2 jl:1 solv:1 informatik:1 mono:3 deduction:1 symplectic:1 pitn:1 expression:2 point:1 dimensional:7 analyzed:1 mkdv:1 polynomial:1 moreover:2 λtn:1 zimmermann:1 commutative:1 puts:1 source:1 addition:1 δλj:4 three:4 been:1 defined:3 basic:3 pi:11 fudan:1 choose:2 generating:1 corresponding:6 nikov:1 gap:3 general:1 case:6 p3:7 intriguing:1 p1:7 value:1 wojciechowski:2 intimately:1 suppose:1 property:1 procedure:4 coupled:1 vol:1 vi:2 von:1 thus:1 non:1 ii:1 ij:2 im:2 φij:2 φin:1 binary:9 different:3 φs:1 φt:1 φx:3 recursion:1 make:1 same:1 φj:4 φk:1 difficult:1 independent:1 used:1 i1:2 upon:1 potentials:1 infinite:1 covariants:1 eigenvectors:2 paderborn:2 well:2 burgers:1 without:1 solve:1 possesses:1 proposed:2 being:1 generally:1 λj:14 λn:4 fokas:1 previous:1 field:1 quadratures:1 lattice:1 potential:8 transformed:1 lett:3 pitman:1 dqi:1 read:1 advances:1 spatial:8 prominent:1 like:2 δu:8 specific:2 integrals:5 arbitrary:1 become:1 stationary:1 because:4 neumann:1 successfully:1 some:2 examples:1 respect:2 jln:1 provides:1 prog:1 bc:1 elucidate:1 nonlinearization:14 ragnisco:1 akns:8 carried:1 constraint:9 o:1 covariant:1 2cn:1 important:2 2ci:2 idh:1 idf:1 idg:1 soc:1 into:4 phase:2 references:1 determine:1 operator:3 often:1 ixh:1 additional:1 commission:1 support:1 initial:1 anderson:1 appl:1 inner:1 ed:1 function:4 but:2 hn:7 themselves:1 illustrative:2 he:1 whether:1 utn:8 liouville:3 problem:4 similar:2 called:3 sort:3 proved:1 ai:4 physica:2 am:6 zeng:1 denote:2 pix:1 conserved:1 exist:1 qix:1 functions:5 mathematik:1 when:2 ny:1 kp:1 role:1 becomes:1 mathematics:1 theor:3 problems:3 polynomials:1 helpful:1 generated:3 a2:1 variable:1 structure:1 starting:1 time:2 requires:1 once:2
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solv-int9605010.txt |@word partial:1 consider:1 remarkable:2 lagrangian:12 results:4 leads:2 proposition:8 expressions:4 row:1 whose:1 preserves:1 calculate:2 concerned:2 tr:2 finally:2 under:3 analogous:1 dramatically:1 orthogonal:1 very:2 updates:3 entries:1 discretizations:16 difference:9 matrices:4 obvious:1 presented:2 turns:2 large:1 discrete:13 small:1 consistent:1 direct:1 second:9 further:2 remarkably:1 canonical:3 subscripts:1 established:1 nonlinear:2 stands:1 brackets:10 section:4 analogously:2 expressed:1 above:3 new:8 hb1:3 bn:1 hb2:1 satisfy:1 respectively:2 here:3 papageorgiou:1 canonically:9 consideration:1 along:1 equations:24 implicit:4 obtained:2 remark:1 hbn:3 ekk:5 hbk:5 elaborate:1 allows:2 periodic:6 resulting:1 poisson:17 changes:1 uniquely:1 turning:2 readily:2 asymptotic:1 would:1 prove:1 remains:1 ψk:1 noting:1 taken:1 more:2 fractions:4 introducing:1 pairs:1 uhler:1 particular:2 known:1 iv:1 must:1 ramani:1 account:2 recall:4 equation:21 values:1 resembles:1 following:7 my:1 proof:6 relativistic:6 preserving:1 share:1 dxk:2 want:1 arise:2 simple:1 practical:1 end:4 rather:1 get:3 how:1 nontrivial:1 parameter:2 map:21 de:1 beauty:1 may:9 after:1 applications:1 lax:13 representations:2 types:1 physical:1 dynamical:1 imply:6 explicit:6 spectral:3 so:3 representation:2 βk:21 order:1 recurrent:3 interpretation:1 help:1 hierarchy:5 essence:1 suris:5 satisfied:1 course:1 paper:1 japan:2 still:1 its:3 continued:4 temporal:1 coordinates:6 writing:1 lu:2 systems:3 mail:1 defining:1 renaming:2 them:2 combination:3 acklund:5 introduce:1 they:7 now:8 yu:3 discuss:1 several:1 equality:1 invariants:3 university:1 hamiltonian:14 each:3 found:1 soc:2 2h:2 differential:1 another:4 ek:6 r2n:2 related:5 toda:22 our:3 out:5 reminding:1 matrix:15 ejk:1 induces:1 induced:1 math:2 shows:1 reformulation:2 linear:8 circumstance:1 possibility:1 standard:5 admits:6 yuri:1 put:1 e1:1 generate:1 log:8 unique:1 motion:14 turn:6 hence:11 βn:1 first:14 xk:266 xn:3 variables:19 thereof:1 directly:1 precisely:2 open:4 given:11 checked:1 introduction:1 system:11 relations:2 their:9 realization:1 recovered:1 gives:1 exactly:3 serve:2 x0:2 x1:1 observed:1 approximations:1 see:7 kth:1 supposed:1 str:1 were:2 hz:1 sees:2 rewrite:2 apparently:3 newtonian:3 depending:2 note:4 generalized:2 formulas:5 continuous:6 shall:3 algebraic:5 germany:1 definitions:1 phase:3 φk:1 appear:2 observation:2 considered:3 kh:1 flow:14 bracket:10 exp:136 physics:4 fact:4 show:1 converge:1 relation:5 find:3 knowledge:1 written:3 only:4 factor:1 integrable:10 dk:33 notation:1 means:1 simplest:3 ones:5 closely:2 despite:1 lattices:6 dt:1 evolution:1 approach:1 arxiv:1 qd:2 dpk:2 require:1 view:1 hλ:3 set:4 connections:1 namely:3 alternative:1 analog:1 satisfying:1 ways:2 consequence:2 enough:1 jth:1 between:6 boundary:3 conditions:2 notice:2 terms:4 however:1 vanishing:1 extent:1 solv:1 holds:1 both:6 last:1 equal:3 admit:3 symplectic:6 uni:1 expression:1 ck:40 relevant:2 conclude:1 appeared:1 lagrange:5 polynomial:1 moreover:1 transformations:2 due:1 int:1 much:1 certain:1 pk:33 prototype:1 abstract:1 define:1 generating:2 corresponding:4 case:11 value:2 while:2 property:1 procedure:1 non:1 according:6 ii:1 reads:1 flaschka:2 different:10 author:1 perform:1 formulations:1 same:6 complex:1 finite:3 literature:1 parametrized:5 infinite:3 well:4 obviously:3 solve:1 sets:3 1ck:2 entry:1 usual:1 just:5 being:4 grammaticos:1 obtain:2 underlying:1 momenta:5 previous:4 visualization:1 hak:2 point:1 parametrization:4 lattice:16 conjugated:9 easy:11 transformation:4 read:2 evaluate:1 possible:1 resolves:1 immediately:7 intersection:1 mod:1 imposed:1 like:4 identifying:1 follows:11 either:2 integrals:2 arbitrary:1 reduced:2 old:1 parametrizations:1 some:1 b1:1 respect:14 nonzero:1 2xk:2 centre:1 chains:1 equivalent:12 bi:4 bk:30 properties:1 takes:4 column:1 introduces:1 o:1 mixes:1 compatible:2 connected:2 introduced:5 consequently:1 considerations:1 discretization:4 letters:5 h2:45 into:2 three:5 down:1 lies:1 en:5 references:1 leningrad:1 additional:2 comparing:2 initial:2 start:1 quadratic:2 way:2 was:1 function:10 complete:1 form:12 jun:1 but:2 true:2 up:1 us:2 below:1 demonstrate:3 problem:1 similar:1 called:1 sort:1 proved:2 defined:9 coincides:3 ak:47 general:1 proves:2 formulation:11 dη:4 check:1 defines:1 again:1 functions:5 integrability:1 when:1 bremen:3 hpk:16 other:4 spatial:1 conclusion:1 generates:1 models:5 time:17 problems:1 a1:2 a0:3 generated:1 important:2 structure:7 independently:2 implies:6 algorithm:2 space:3 together:2 equivalently:1 hirota:4
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solv-int9606001.txt |@word partial:2 consider:1 chain:2 edk:1 moutard:9 quadrature:2 proposition:11 inverse:1 depend:4 paris:1 answered:1 infinit:1 elliptic:1 analogous:2 far:1 erale:1 choice:3 every:1 2rx:11 solution:9 wronskian:1 neighborhood:1 zero:1 further:1 nonlinear:1 appear:3 sur:1 above:1 congruences:1 method:1 etriques:1 coefficient:2 nimmo:2 desired:1 les:1 others:1 equations:9 obtained:1 uniquely:2 appropriately:2 via:3 rϑ:2 uzz:1 des:1 establish:1 derivatives:21 use:1 ψy:1 links:1 prove:4 century:1 pedagogical:1 m1:13 therefore:2 m2:2 th:2 solitons:1 px1:3 odinger:1 validity:2 everywhere:1 uxx:1 known:1 hold:3 springer:1 equation:6 mn:1 mk:11 krasnoyarsk:3 values:7 mp:17 ms:1 following:2 example:3 proof:1 indicated:1 give:1 numbers:2 sense:1 verlag:1 darboux:4 holds:1 how:1 imbedded:2 ryy:1 de:1 may:4 earlier:1 applications:4 data:3 clarkson:1 su:1 so:2 fundamental:1 order:2 quasiperiodic:1 over:5 paper:1 still:2 nets:1 its:3 le:1 la:1 ln:3 actually:1 systems:1 mail:1 main:7 yn0:12 correspondence:1 yk:6 ym:14 yn:5 inductively:1 framework:1 they:2 half:1 yq:1 now:3 easily:2 equality:1 university:1 found:6 2k:2 arxiv:1 ed:2 comprises:1 our:1 rs:1 since:4 rx:16 ry:14 research:1 formula:2 induction:9 after:1 theory:5 possibility:2 asi:1 inductive:12 r1:2 r2:3 geometry:2 βy:2 bologna:1 hence:1 origin:3 xk:9 already:4 xn:2 xm:8 number:2 xy:4 another:2 xr:3 xs:3 xp:1 open:1 given:12 checked:1 obtainable:1 unknown:1 construct:1 their:3 xix:1 dfg:1 gives:2 part:1 x2:1 eliminated:1 x1:1 positively:1 wide:1 second:1 determined:2 russia:1 alongside:1 multivalued:1 conjugate:1 any:4 petviashvili:1 note:1 potential:10 build:1 coincide:2 salle:1 formulas:1 uyy:1 class:2 soliton:1 rogers:1 considered:1 vries:1 oevel:1 show:2 supported:1 gauge:1 solutions:8 find:5 principal:12 apriori:1 jan:1 analytic:1 only:13 uxy:1 coefficients:1 indeed:2 integrable:5 get:2 express:1 ones:1 dx:1 dy:1 during:1 du:1 differentiating:2 kadomtsev:1 differential:5 fixed:3 set:5 arw:1 depends:4 surfaces:1 definite:1 state:1 between:1 geometria:1 geometric:1 numerous:1 terms:2 initially:1 matveev:1 analogues:1 veselov:1 2αx:1 key:1 solv:1 parentheses:1 equal:6 chosen:3 contribution:1 arbitrarily:1 among:1 conclude:1 appeared:1 dimensional:5 indefinite:1 described:1 transformations:8 addition:1 px:7 py:5 due:3 been:1 int:1 bianchi:1 collected:1 nato:2 choose:3 modern:1 corresponding:5 quantities:5 gap:1 finished:1 derivative:9 present:2 case:5 reciprocal:1 value:1 will:11 dept:1 calcul:1 suppose:3 di:1 cons:1 played:1 almost:1 them:2 surface:1 according:4 rfbr:1 different:1 grant:1 perform:1 make:3 same:1 orders:5 epoch:1 finite:1 isometries:1 higher:5 independent:1 used:1 see:5 upon:4 steps:1 potentials:2 changing:1 lower:1 schr:1 undefined:1 nevertheless:1 well:2 just:1 obtain:4 rest:1 rn0:1 eorie:1 previous:1 kluwer:1 density:1 except:3 instrument:1 k0:9 transformed:1 theorem:3 transformation:4 rev:1 possible:1 using:2 mod:1 performing:1 yields:1 arbitrary:2 mathematical:1 methods:1 classical:2 some:2 choosing:1 provided:3 dense:1 dimensions:2 esimal:1 does:1 korteweg:1 proc:1 problems:2 step:4 central:1 novikov:1 dependence:1 yk0:4 mixed:1 consequently:1 other:3 locally:2 variable:3 appropriate:1 en:1 references:1 determine:1 operator:1 consecutively:1 additional:3 initial:5 question:2 way:3 series:1 call:1 was:5 m0:17 function:1 complete:1 form:1 applying:1 smooth:2 us:5 below:1 utt:1 mk0:35 problem:1 detailed:1 proved:6 defined:3 general:2 proves:2 families:1 check:1 constructed:1 again:2 functions:5 completeness:1 no:1 pfaffian:1 lezioni:1 valid:1 role:2 mathematics:1 calculating:1 xn0:10 june:1 included:1 goursat:1 implies:1 auxiliary:4 physics:1 space:2 eom:1 rxx:3 n0:71
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solv-int9606002.txt |@word partial:1 consider:3 remarkable:1 edk:1 equalities:2 moutard:6 roy:1 quadrature:2 proposition:11 generalize:1 sci:2 inverse:1 const:1 chain:2 paris:2 answered:1 infinit:1 tk:1 th:2 ti:1 analogous:2 x00:1 norm:2 cm0:1 conjecture:1 orthogonal:7 far:2 erale:1 wave:1 resonant:1 pt1:1 xyz:2 wm0:5 solution:5 differential:3 inversions:1 definable:1 wronskian:1 neighborhood:3 zi:1 zk:1 coordonn:1 conjugu:1 sign:1 second:2 linear:1 established:1 nonlinear:2 euclidean:2 calcul:1 expressed:1 3k:1 sur:6 3m:1 sup:2 new:1 congruences:1 etriques:1 coefficient:4 simultaneously:1 respectively:2 desired:1 les:8 depend:8 equations:9 obtained:2 remark:2 mations:1 studied:1 resulting:1 conveniently:2 cth:1 uniquely:3 via:4 pxs:4 pxp:7 marked:1 pxk:6 pxm:2 apply:1 des:1 establish:1 linearly:3 derivatives:33 use:1 prove:1 monographs:1 pedagogical:1 call:3 m0:66 m2:1 type:1 more:1 formally:1 ecole:2 initial:10 px1:1 px0:2 validity:3 particular:1 known:5 hold:1 springer:1 include:2 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solv-int9606003.txt |@word diss:1 partial:3 skeleton:1 edk:1 moutard:12 four:2 quadrature:3 proposition:1 generalize:1 computation:1 consists:1 sci:1 row:1 whose:1 inverse:1 const:1 analytic:1 γs:6 γq:1 γk:2 γi:6 th:1 exposition:1 analogous:1 conjecture:1 2γi:2 orthogonal:10 erale:1 wave:2 figs:2 2rx:1 resonant:1 deformations:2 2γs:1 notations:1 gov:2 presented:1 did:1 forth:1 notes:1 vertex:1 solution:17 indices:1 permutability:2 noted:1 coordonn:1 direct:1 second:1 aγi:1 ode:1 nonlinear:11 dept:1 trivial:2 expressed:1 sur:3 intersect:1 new:2 construction:1 congruences:3 method:4 etriques:1 satisfy:1 nimmo:2 here:1 diagonal:1 les:3 tangent:2 others:2 sine:3 equations:7 interpret:1 obtained:7 studied:2 circumferences:4 spheres:1 resulting:2 usually:2 u3x:1 uniquely:2 via:5 projection:3 family:1 summation:1 apply:2 establish:1 use:1 additive:1 links:1 intensively:1 sake:1 give:2 pedagogical:1 explicitly:1 m1:8 m0:12 m3:1 m2:5 taken:1 type:3 triply:5 diagrams:2 more:1 becomes:1 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solv-int9606006.txt |@word secondly:1 casimirs:3 partial:4 consider:10 represent:1 results:7 four:2 scalar:1 commute:1 edu:1 consists:5 expressions:14 gl:2 toric:1 row:2 compact:3 whose:17 preserves:2 inverse:2 depend:7 equivalence:1 tr:1 λid:4 finally:2 monotonically:1 weyl:4 preserved:1 th:1 under:48 exit:1 analogous:2 vli:1 applied:1 g1:1 far:1 continues:1 choice:3 every:2 entries:2 matrices:5 convexity:4 illustrated:3 conjugating:1 level:22 irreducible:8 solution:3 t0:2 deals:1 trx:5 proposition:16 eigenvalues:31 shows:2 barbara:1 proof:6 lˆ:1 upper:4 illustrating:1 consistent:1 discover:1 suffices:1 zero:24 chopping:1 represention:1 writing:1 oneto:1 λrk:4 what:1 diag:1 section:5 expressed:1 cell:2 en:3 subspaces:2 fractional:1 suppose:1 construction:1 method:2 contrast:1 satisfy:1 full:13 simultaneously:1 degree:1 respectively:10 component:4 here:3 strata:4 others:1 represented:1 along:1 standard:7 equations:4 extreme:4 obtained:4 remark:5 study:6 studied:3 allows:1 approaches:1 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solv-int9606007.txt |@word gd:8 partial:2 consider:8 springer:2 results:1 fxxx:2 leads:1 commute:1 grateful:1 φt:1 follow:1 disk:2 gi:1 compact:2 inverse:1 paris:1 technique:1 funk:1 th:1 dressing:4 kν:1 applied:1 belonging:1 g2:5 g1:5 very:2 rise:4 dell:2 seemingly:1 geometrical:1 matrices:1 iut:2 condition:2 riemann:1 solves:1 tokyo:1 solution:6 vector:1 anal:1 imply:1 dynamics:2 canonical:1 spectral:1 established:1 what:1 nonlinear:2 plays:2 near:1 expressed:1 sur:1 goes:1 new:1 method:4 full:3 simultaneously:1 respectively:2 even:1 component:1 here:8 les:2 tangent:1 xν:12 equations:43 appears:1 change:2 obtained:5 great:1 dividing:1 institute:3 lomi:1 study:1 allows:1 domains:1 hospitality:1 demonstrates:1 studies:1 exeter:1 via:4 tools:1 unit:4 readily:1 use:2 takes:1 would:1 remains:1 contains:2 call:2 type:10 theoretical:1 more:1 incorporates:1 solitons:1 operators:1 under:5 berlin:1 bogdanov:4 known:2 account:1 integrating:2 science:1 equation:59 det:2 modified:9 reviews:1 vy:7 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solv-int9606008.txt |@word gw:4 consider:4 remarkable:1 splitting:6 invent:1 extends:1 commute:4 consists:3 follow:2 gm:1 research:1 compact:8 whose:3 preserves:1 inverse:1 calculate:2 tr:1 trivial:5 tq:2 finally:2 weyl:4 manifolds:2 ti:2 semenov:3 analogous:4 norm:1 straightforward:2 sitting:1 rise:1 pressley:1 dokl:1 results:2 corollary:10 every:2 entries:3 tridiagonal:1 matrices:6 eit:8 solves:6 hamiltonian:9 irreducible:1 notes:1 solution:4 large:1 involution:5 vector:5 phase:38 math:5 reyman:2 degeneracy:2 upper:3 work:1 neighborhood:5 second:3 reine:1 expressions:1 dψ1:1 victor:1 bilinear:3 disk:4 invertible:2 sun:10 section:9 while:1 symes:6 ˆa:2 ˆb:1 version:1 above:4 new:3 increasing:2 r2ℓ:2 ˆn:1 satisfy:1 guillemin:1 respectively:2 ihα:1 component:2 here:3 desired:1 them:1 groups:4 address:1 along:1 equations:2 implicit:3 obtained:1 shansky:3 hamiltonians:1 technical:2 allows:1 reason:1 periodic:13 idγ:1 poisson:3 pick:2 action:17 makes:1 via:2 projection:3 family:11 claim:1 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solv-int9606009.txt |@word gw:1 minors:1 equalities:2 results:1 gf:1 proposition:10 generalize:1 broader:1 edu:1 go:1 gn:2 expressions:3 kassel:3 gj:3 gh:1 whose:1 depend:6 recurrence:5 uniqueness:1 program:1 tk:2 th:1 ti:1 p2:14 fay:9 g3:8 g2:16 g1:68 zhang:1 corollary:3 parameter:1 condition:3 obvious:3 presented:2 suffices:1 t2:5 t3:2 z10:1 t1:5 solved:2 independence:1 cmp:1 second:1 follow:1 3z2:2 further:2 bilinear:1 3z:1 what:3 plays:3 sum:3 3p:3 3w:6 expressed:2 above:3 3c:1 3b:1 3a:1 satisfy:3 degree:2 here:6 others:2 represented:1 equations:11 z1:93 z2:92 obtained:6 shift:2 larger:1 contradiction:1 schur:3 useful:1 claim:1 manage:1 replace:1 apply:2 circumvent:1 tn:1 use:2 asymptotic:2 would:2 prove:6 positive:1 contains:1 finally:3 next:2 few:1 call:3 therefore:2 memory:1 means:1 type:1 more:3 operators:5 z1i:1 2w1:1 holl:1 wi2:9 wi1:9 known:4 foundations:1 cases:2 hold:2 must:4 account:3 recall:3 equation:30 work:1 values:2 following:7 oberwolfach:1 proof:8 f0:10 f1:1 f2:1 f3:1 give:2 expanding:5 lψ:1 states:1 aratyn:1 conversely:1 guarantee:1 straightforward:2 discussion:1 holds:4 nontrivial:1 criterion:1 significance:1 3w1:2 instead:1 establishment:1 sato:3 fq:6 product:1 derived:1 abuse:1 lax:1 fj:6 imply:1 explicit:5 so:1 sect:3 fundamental:1 order:1 acts:2 help:2 hierarchy:19 over:1 paper:1 existence:1 satisfies:5 pj1:2 its:5 pj2:2 derive:1 ln:9 interesting:1 solving:1 lk:3 actually:1 systems:1 mail:2 main:1 them:3 was:1 introduce:1 2p:4 they:3 now:2 easily:4 term:6 2w:10 equality:3 always:2 university:1 2z:1 2z2:3 each:1 found:1 universit:1 difficult:1 2h:1 side:4 constraints:1 homogeneous:1 arxiv:1 simplicity:1 series:8 solution:4 used:1 obtains:3 our:1 eq:9 special:1 out:1 shown:3 rw:1 matrix:2 oklahoma:1 since:3 denoted:2 formula:3 induction:1 math:1 theory:2 contain:1 complicated:1 van:1 definition:1 language:1 turn:1 hence:2 think:1 first:8 symmetry:1 rank:1 multiplying:1 done:1 relations:3 another:1 given:1 zψ:1 1w:1 their:1 introduction:1 adjoint:1 construct:1 needed:2 assumption:1 calculations:3 resz1:7 gives:1 statement:8 exactly:2 proving:1 part:1 eliminated:1 than:1 coefficients:3 double:1 zero:3 limiting:1 kth:1 were:1 providing:1 powers:7 minus:1 eliminating:1 argument:1 generalization:2 need:1 cumbersome:2 constrained:14 any:3 instance:1 new:4 formulas:5 norman:1 kosmann:1 most:1 germany:1 jul:1 nothing:3 especially:1 coincides:1 kp:13 verdier:1 exp:7 section:1 fact:1 quantity:1 precise:1 dickey:1 reductions:1 recipe:1 notations:1 relation:3 solutions:1 decompositions:1 substituting:1 trivial:1 find:4 subtracting:1 q2:1 dividing:1 hrz:1 lemma:10 only:3 going:1 integrable:3 hope:1 do:3 cheng:1 get:2 de:1 words:1 supplies:1 runs:1 qr:5 conditions:2 differential:11 yield:1 accomplish:1 qg:1 qf:3 coefficient:3 2p3:2 set:1 exists:2 j1:3 j2:3 see:7 result:1 w1:100 w0:2 discussions:1 αs:4 qf0:1 symmetric:2 written:2 smallest:1 gw1:1 neither:1 approach:1 αl:2 terms:4 wk:1 however:1 wi:8 solv:1 article:1 2pj:1 informatik:1 parentheses:1 last:4 many:1 taking:4 etc:1 uni:1 passing:1 mean:1 expression:6 simple:1 forschungsinstitut:1 sequences:1 respect:2 schwarzbach:1 addition:1 skew:1 three:1 int:1 pj:18 pn:3 abstract:1 pl:1 walter:1 wants:1 determinant:2 enable:1 quantities:2 sufficient:2 denote:1 those:1 case:6 p3:5 multi:1 p1:5 expanded:1 value:1 will:6 while:1 suppose:1 aij:1 aid:1 property:1 thus:4 non:2 rip:1 helped:1 reads:1 itself:1 vanish:2 2g1:3 different:1 suggest:1 make:1 same:1 virtually:1 hierarchies:8 gets:4 higher:1 independent:3 arrives:1 eds:1 leonid:1 i1:3 sums:1 i2:3 nj:15 hand:5 louis:1 infinite:1 frequently:1 identity:13 least:1 acknowledgement:1 whole:1 well:2 without:1 deserve:1 firstly:1 jean:1 left:5 just:2 less:1 being:1 generally:1 3p2:1 3p3:1 obtain:3 transforms:1 world:1 letting:1 preprint:1 infinitely:1 belongs:5 corollaries:1 easy:3 showing:1 posed:1 possible:1 3pj:2 using:5 unique:1 string:1 formal:2 wˆ:110 necessary:2 follows:3 yields:2 arbitrary:3 become:1 terminology:2 namely:1 lectures:1 some:5 back:1 pαs:1 happens:1 fachbereich:1 does:5 eliminate:1 assuming:1 scientific:1 equivalent:3 expansion:3 pα1:1 step:1 shifting:1 properties:1 takes:2 pβ:1 pγ:1 about:2 ok:1 usa:1 constraint:6 compatible:1 cartier:1 introduced:1 slightly:1 moerbeke:1 into:4 thankful:1 references:1 operator:7 strasse:1 hep:1 additional:1 prepare:1 there:4 u1:1 u2:1 sections:1 function:13 form:9 but:3 true:3 absent:1 applying:1 us:4 below:1 limit:1 problem:2 similar:1 called:2 proved:1 defined:4 universal:8 pseudodifferential:1 proven:3 general:3 proves:1 numerators:2 identities:11 check:1 constructed:1 again:1 functions:4 nk:1 no:1 mathematik:1 when:2 rewriting:1 application:2 other:2 role:3 department:1 qz2:2 mathematisches:1 models:1 problems:1 polynomials:3 meaning:1 important:3 allowing:1 lemmata:1 implies:3 4w:1 baker:8 required:3 appendix:2 n1:2 n2:1 starting:1 having:2
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solv-int9606010.txt |@word proposition:13 represent:1 emile:1 partial:4 gr:2 funct:2 rev:1 comparatively:1 leads:3 eds:5 scalar:1 gd:6 latter:1 computation:5 sci:1 n32:1 gl:1 consider:19 devoted:1 whose:4 ihes:1 depend:3 zone:1 iii:3 concerned:1 show:4 canonical:1 tn:2 finally:4 tm:6 tj:24 those:1 th:1 connecting:1 analogous:1 akhiezer:1 case:19 conjecture:1 proved:1 presently:1 far:1 rise:4 geometrical:2 denoted:2 coprime:1 entries:1 redefinition:1 p0x:1 matrices:7 condition:8 3h1:6 dubrovin:2 3h4:1 solves:1 hamiltonian:12 ref:1 t5:11 t2:16 solution:7 t1:51 involution:2 vector:31 relation:10 path:1 zn:5 h13:1 h41:2 2k2:4 direct:2 literature:1 second:10 perspective:1 pass:1 further:3 zp:2 theory:31 even:1 aim:2 nonlinear:2 appear:1 iterating:1 brackets:4 sum:2 celebrated:1 brief:1 expressed:1 cell:1 birk:1 suspect:1 above:2 fractional:18 new:3 method:1 seeks:1 coefficient:1 compact:1 hkx:1 full:5 led:1 degree:2 exchange:1 component:1 discrete:1 here:3 2h4:8 tangent:5 possibility:1 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solv-int9607001.txt |@word chain:1 particular:1 abramovici:1 leads:1 go:1 whose:1 device:1 th:4 under:1 p2:1 global:1 straightforward:2 very:2 rise:1 fall:1 difference:1 exact:2 condition:6 riemann:1 positions:2 notes:1 pacs:1 solution:2 solved:1 convenience:1 vector:1 configurations:3 upper:1 force:1 periodicity:2 b21:2 zero:2 enclosed:1 even:1 what:1 nonlinear:1 sub:10 section:1 axel:1 above:7 new:1 increasing:2 acknowledgments:1 satisfy:4 condensed:2 lee:1 respectively:2 aubry:13 here:10 atoms:5 china:1 cos2:1 represented:2 equations:1 change:1 obtained:5 institute:1 studied:1 c18:1 periodic:3 resulting:1 domains:8 chang:1 suitable:2 changes:1 taipei:1 griffiths:4 slices:1 discontinuous:2 requiring:3 highly:1 modulated:2 unit:1 kontorova:4 derivatives:2 use:1 takes:2 distinct:1 negative:2 depicted:1 ip:1 diagrams:4 more:2 introducing:1 israel:1 mellon:1 δhi:1 becomes:2 berlin:2 mather:1 varying:1 known:1 iii:1 must:6 springer:2 locked:3 science:1 equation:4 work:2 obvious:2 cam:1 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solv-int9607002.txt |@word sci:1 consider:3 yasuhiro:1 similarity:4 rev:1 results:2 gf:2 scalar:3 proposition:12 grateful:1 research:1 devoted:1 whose:1 inverse:1 depend:1 paris:1 technique:1 young:3 finally:1 does:1 those:2 applied:1 stud:2 straightforward:1 far:1 putting:4 entries:5 difference:1 matrices:1 condition:2 solves:2 wronskians:2 solution:17 discrete:5 relation:1 equation:24 wronskian:3 direct:2 painlev:20 zz:1 odd:1 theory:1 bilinear:18 3z:1 what:1 nonlinear:2 deeply:1 section:7 brief:2 expressed:7 version:1 above:4 new:2 nakamura:1 satisfy:3 ibid:2 respectively:2 here:3 desired:1 concluding:2 standard:1 equations:33 appears:1 obtained:4 remark:1 deriving:1 dividing:1 clarify:1 shift:3 study:1 example:1 studies:1 york:2 beautiful:1 schur:4 useful:2 family:1 vii:2 apply:2 univ:1 readily:1 would:1 prove:3 give:8 next:2 call:1 therefore:2 taken:1 survive:1 means:1 type:11 more:2 separated:1 kinokuniya:1 solitons:1 operators:4 particular:2 known:5 iii:2 ramani:5 tokyo:1 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solv-int9607003.txt |@word secondly:1 gu:1 skeleton:1 equalities:1 eds:4 scalar:1 commute:1 computation:1 c1:1 gi:2 gh:1 inverse:2 shanghai:2 nonlocal:1 tn:1 tkn:1 tm:2 those:3 δhi:1 must:1 p2:1 conjecture:1 g2:2 advantage:1 g0:9 very:2 rise:1 p0:2 every:1 difference:1 matrices:1 condition:1 presented:1 notes:1 guo:1 solution:4 t1:2 solved:3 convenience:1 vector:3 math:8 eigenvalues:1 anal:1 lk0:1 zi:1 10b:1 10a:1 direct:1 second:1 further:1 approached:1 spectral:11 what:1 nonlinear:12 section:2 expressed:1 hereditary:4 current:1 fuchssteiner:4 above:2 3c:3 new:1 3a:3 method:3 full:1 simultaneously:1 ichikawa:1 component:3 here:3 focused:1 equations:10 search:1 institute:1 study:1 allows:1 resulting:3 permit:1 involves:1 φkm:1 santini:1 apply:1 vix:1 univ:1 readily:1 would:3 prove:1 sake:1 jpn:1 suppl:1 next:1 linear:2 therefore:4 characteristics:1 iteratively:1 boiti:2 more:1 introducing:1 successful:1 becomes:2 operators:1 hirota:1 berlin:2 potential:2 couldn:2 evolves:1 springer:1 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solv-int9607004.txt |@word gs:2 angles:2 mcgrawhill:1 truncated:1 results:3 invent:1 eds:3 commute:2 grateful:1 go:1 follow:2 consider:8 ihes:1 depend:3 young:1 recurrence:3 company:1 finally:1 according:1 manifolds:3 under:4 stochastic:1 analogous:2 norm:1 conjecture:2 straightforward:1 eiλx:1 desired:1 dokl:3 probability:2 sons:1 entries:1 difference:1 matrices:3 convexity:19 entire:5 solves:1 hamiltonian:4 transmission:1 turns:2 stuttgart:1 solution:12 prob:3 solved:1 vector:2 equation:20 solutions:7 upper:9 sturm:2 computation:5 estimates:1 direct:3 cosh:1 tex:1 zero:4 dordrecht:1 pass:1 iσ3:1 iσ2:1 odd:3 selfadjointness:1 zs:2 spectral:12 what:3 nonlinear:8 brackets:1 section:16 transforms:1 brief:1 expressed:5 uniform:1 en:1 establishes:1 sup:1 new:5 l1:1 method:1 bdz:2 coefficient:2 guillemin:1 even:3 discrete:2 here:5 following:4 inverse:3 represented:1 along:1 marchenko:4 equations:4 ordinary:1 sobolev:2 suitably:1 study:2 allows:1 sbornik:1 denominator:2 periodic:9 poisson:1 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solv-int9607007.txt |@word partial:2 consider:2 global:1 rod:1 results:3 polydisk:3 edu:1 dist:1 disk:2 compact:9 whose:1 careful:1 recurrence:1 finally:1 those:1 norm:2 far:1 choice:2 valued:1 every:1 exact:1 generalised:1 school:1 ref:2 solution:10 math:4 small:2 relation:2 work:1 10m:2 consistent:1 estimates:1 direct:1 literature:1 painlev:17 established:1 nonlinear:4 section:2 uniform:4 wxxx:1 3h:5 poles:1 above:2 sup:35 new:2 3a:5 method:6 satisfy:1 respectively:1 here:1 believed:1 inverse:1 2kb:1 equations:10 obtained:2 remark:1 involved:1 pick:1 domains:3 classification:1 unif:1 limj:1 addressed:1 rρ:1 apply:1 readily:1 derivatives:1 use:5 proceed:1 would:2 prove:10 remains:1 give:2 next:1 ψj:27 therefore:1 means:1 type:2 more:1 nkb:9 definition:2 initial:1 particular:1 known:1 must:1 ramani:2 ρb:1 recall:2 equation:13 mn:19 mi:2 london:1 mj:3 values:1 following:2 petersen:1 proof:16 claim:4 stated:1 suggestions:1 numbers:3 council:1 lemma:2 holds:1 srinivasan:1 how:1 varies:2 ordinary:2 singular:2 may:2 max:2 singularities:1 movable:2 consequence:1 cambridge:1 wave:1 data:19 suspected:1 varied:1 short:1 clarkson:1 imply:1 consequently:1 explicit:2 so:2 definitions:1 six:1 over:5 paper:5 through:1 satisfies:1 still:2 its:2 before:1 thank:1 lect:1 estimating:1 absence:1 choose:6 relate:1 wales:1 main:2 defining:2 them:1 combination:1 was:1 inductively:1 topologized:1 singularity:3 now:5 possess:1 easily:2 name:1 always:1 university:2 b3:2 2m:1 subset:2 domain:2 arxiv:1 series:7 used:5 our:4 neighbourhood:1 dominates:1 space:2 furthermore:1 since:8 research:2 mδ:5 contained:4 dominated:2 stud:1 denoted:1 formula:1 rn:24 induction:7 ri:5 rj:1 shows:3 linear:1 like:1 estimate:8 remainder:1 r4:1 r5:3 r1:8 r2:6 int:1 u4:23 hence:1 south:1 first:3 origin:3 major:1 u6:23 xb:2 question:1 nested:1 restrict:1 open:4 given:13 checked:1 introduction:2 carnevale:2 their:1 gives:2 holomorphic:6 continuous:2 proving:1 part:4 authors:1 norms:1 coefficients:1 double:2 iteration:2 painleve:1 were:1 b2ρ:1 nuovo:1 anm:5 7k:1 need:4 clearly:1 elsewhere:1 issue:1 jour:1 min:7 lim:5 latter:1 converges:3 note:7 emphasis:1 take:3 interior:1 modulus:2 regular:2 connected:3 but:1 an2:4 formulae:1 pair:1 acknowledgements:1 nonlinearity:1 later:1 kn:1 possesses:1 segur:2 principle:1 vries:3 precise:1 particularly:1 show:2 supported:1 converge:2 notations:1 radii:1 joshi:4 solutions:5 indicator:1 title:1 pdes:3 state:1 should:1 analytic:4 only:1 integrable:2 circle:1 continuity:2 notation:3 get:5 dependent:1 de:3 solvability:1 cannot:1 closure:2 evolution:3 differential:4 expansions:6 twice:1 common:1 including:1 set:6 ser:1 exists:5 cimento:1 j0:10 j2:1 bounds:1 see:2 radius:10 result:4 concentric:1 subject:1 surfaces:1 dn:4 away:1 supj:1 written:1 closed:2 between:1 limit:1 geometric:1 reading:1 meromorphic:4 notice:1 terms:4 extend:1 comp:1 attention:1 however:1 wj:2 wtc:12 solv:1 suggested:1 connection:1 wt:1 pde:1 whole:1 16m:1 ci:1 cn:1 bδ:12 pole:2 simply:1 moreover:1 described:1 second:2 locally:1 been:2 35q53:1 cauchy:6 oδ:15 define:4 6b:1 enable:1 finishes:2 25m:1 c2:4 c1:2 convergent:1 manifolds:1 noncharacteristic:1 case:2 subsets:4 will:3 suppose:1 applies:1 exist:1 property:6 refs:1 ii:2 supremum:2 containing:2 recursion:3 same:2 any:1 widely:2 subdomain:1 ball:1 ablowitz:3 centred:1 lower:5 suffices:1 well:7 posedness:6 analysis:1 sets:2 meanwhile:1 self:1 usual:1 manifold:4 obtain:1 facts:1 scattering:1 blow:1 lebesgue:1 except:1 weiss:2 improvement:1 lett:1 sydney:1 theorem:21 australia:1 around:2 lacking:1 press:1 using:2 formal:1 replacing:1 follows:6 collective:1 disks:3 ai:1 korteweg:3 arbitrary:10 become:1 because:3 methods:1 sequence:6 some:1 b1:2 b2:6 respect:2 kdv:9 describing:1 dimensions:1 majorant:3 power:1 tabor:2 kruskal:1 bi:1 expansion:7 unsw:1 substitution:1 completing:4 theorems:2 discussed:1 dependence:2 o:7 practical:1 slightly:1 converging:1 soc:1 contains:1 jδ:2 into:1 bound:4 references:1 determine:1 shrinking:1 nsw:1 u5:3 3ρb:3 there:6 u1:2 u0:1 u3:2 u2:3 appl:1 way:1 sections:1 referees:1 function:2 complete:1 form:3 enough:1 jul:1 construction:1 convergence:21 true:3 australian:1 commun:1 evident:1 maximum:3 us:1 below:2 un:45 ui:4 uj:8 continuously:1 problem:4 detailed:1 sometimes:1 associated:1 suprema:2 up:1 defined:6 abstract:1 describe:2 am:2 denote:1 single:1 referee:1 au:1 functions:6 nk:4 nm:1 integrability:1 no:1 other:1 special:1 solitons:1 test:1 mathematics:2 arithmetic:1 conclusion:1 uniformly:6 a1:1 meaning:1 a2:2 bounded:2 variable:2 implies:1 assume:3 required:1 4m:1 littman:1 n2:2 5kb:1
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solv-int9607008.txt |@word sci:1 consider:3 funct:1 global:1 trigonometric:2 four:2 p02:1 entropy:2 grateful:1 dϕ1:1 scr:1 compact:1 inverse:2 γp:4 presents:1 finally:1 program:1 lanford:2 elliptic:1 under:5 di1:1 ingredient:1 case:12 conjecture:2 dϕk:1 tends:1 translations:2 results:3 rotational:1 exact:1 deformations:1 condition:1 entire:2 school:1 symplectic:6 riemann:2 hamiltonian:7 positions:1 notes:1 try:1 defocusing:1 anal:2 configurations:1 prevent:1 force:2 jacobians:1 cosh:1 integrability:1 displays:1 pass:1 rigorous:1 dynamics:1 canonical:6 spectral:2 will:1 what:1 nonlinear:8 appear:2 section:6 3v:3 supplied:1 uniform:1 varadhan:1 version:1 international:1 increasing:1 equivalent:1 body:1 guillemin:1 mula:1 here:2 exceptions:1 objects:1 possibility:1 sinh:5 address:1 based:1 sine:1 equations:13 appears:1 change:1 obtained:3 almost:2 institute:1 study:1 studied:2 allows:3 periodic:5 usually:1 studies:1 via:1 useful:2 projection:2 family:3 namely:1 explained:2 gurevich:2 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