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solv-int9803013.txt |@word partial:1 remarkable:1 similarity:1 eaires:2 results:2 l11:7 four:12 eds:5 scalar:18 consists:1 expressions:1 contributions:1 whose:3 preserves:1 c0:3 paris:4 tu:6 γt:3 γj:1 aus:1 tj:8 present:2 elliptic:2 under:2 tc:5 norm:1 case:10 g2:1 advantage:2 far:1 pages:3 springer:4 choice:1 entries:1 ρe:3 difference:3 matrices:2 deformations:3 condition:1 riemann:1 roy:1 p5:12 list:3 solution:1 t1:1 deals:1 discrete:29 ml:1 βcd:1 optics:1 der:1 programme:1 unexpected:1 neighborhood:1 subproblems:1 direct:2 painleve:1 design:1 quelques:1 implemented:1 4x2:1 theory:5 residue:1 established:2 nonlinear:5 advantageous:1 d2:6 section:6 expressed:1 tσ1:1 current:1 poles:3 sur:7 goes:1 sup:1 new:3 method:4 filled:1 satisfy:1 full:3 degree:6 4s:2 component:2 here:1 diagonal:1 l21:5 desired:1 inverse:1 possibility:2 address:1 alone:2 sine:1 equations:36 change:1 obtained:8 convert:2 study:1 garnier:21 allows:1 h2:3 later:2 resulting:3 advantages:2 makes:2 quotient:1 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solv-int9803014.txt |@word partial:2 consider:3 global:3 results:4 produce:1 four:5 eds:2 scalar:4 consists:2 perturbations:1 whose:4 inverse:5 depend:1 system:3 paris:7 disposal:1 equivalence:1 nonlocal:1 good:2 recurrence:1 finally:6 does:2 those:1 elliptic:9 under:7 fronti:1 analogous:1 spec:1 norm:1 started:1 p2:16 conjecture:3 g3:8 g2:23 g1:10 orthogonal:2 very:1 bulletin:1 account:2 choice:6 every:4 lecture:1 discretizations:6 difference:11 exact:8 condition:11 school:2 p4:5 gf:1 notes:1 p5:3 t2:6 solution:10 enforce:2 discrete:112 vector:1 recall:1 small:1 joshi:2 noted:1 monomial:1 correct:1 work:1 neighborhood:2 zk:2 isolate:1 direct:7 zb:1 painleve:1 irreducibility:1 gn:9 iσ2:4 odd:1 ode:1 canonical:3 even:3 established:1 what:1 nonlinear:3 adds:1 appear:1 g21:1 diag:1 section:12 brief:1 tσ1:1 birkhoff:1 3h:1 en:1 sur:3 above:5 conduct:1 new:5 method:30 satisfy:1 2h2:5 simultaneously:1 degree:23 excludes:1 deduces:1 respectively:3 never:1 component:1 here:6 diagonal:1 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solv-int9803015.txt |@word concept:1 partial:11 consider:4 trisecant:2 results:4 integration:3 leads:2 ψ1i:1 proposition:11 maffei:1 alv:1 follow:1 equivalences:1 devoted:1 whose:1 terms:15 lki:1 paris:1 tn:3 charge:7 tm:1 tj:5 spain:3 th:13 ti:24 sapienza:1 te:1 worth:1 norm:1 applied:2 fay:7 amplitudes:1 string:4 orthogonal:2 very:1 erale:1 conditions:3 induce:1 geometrical:6 vertex:18 witten:3 interpreting:1 rm:2 resonant:1 elena:1 difference:2 matrices:1 deformations:3 condition:1 common:1 school:1 dubrovin:1 riemann:5 hamiltonian:2 turns:2 notes:1 pacs:1 list:1 solution:6 t1:3 used:3 evy:28 εkl:1 εkj:10 εki:11 section:2 indices:1 brezin:1 warszawa:1 peterson:1 zm:2 zn:7 unexpected:1 t2:1 truncated:1 za:1 literature:1 painlev:1 omez:1 reine:1 substitute:1 theory:23 bilinear:12 established:1 what:1 nonlinear:3 plays:1 stands:4 diag:2 sum:2 shares:1 paying:1 en:1 sur:1 above:3 sup:2 new:9 net:18 row:4 hˆopital:1 satisfy:6 edited:5 agreement:1 lec:1 notions:1 αij:3 respectively:4 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solv-int9804003.txt |@word secondly:1 func:1 similarity:1 four:12 ginzburg:7 consists:6 analiz:1 relationships:1 whose:7 fronts:4 collisions:1 paris:9 pantano:1 characterises:1 z1l:1 under:10 lord:2 characterised:1 conjecture:2 rational:5 etriques:1 every:8 school:1 z12:1 solution:62 indices:18 c01:2 c02:2 wronskian:1 sturm:2 specially:1 direct:3 pulse:4 painleve:1 chen:2 circolo:1 2aλ:1 established:1 dr2:1 above:4 new:14 ever:1 shocks:2 coefficient:5 med:1 ichikawa:1 never:1 here:3 represented:1 logarithmic:3 obtained:21 property:16 study:2 changed:1 physiological:1 fourier:1 tu:1 classification:7 convecting:2 explained:5 plenum:1 total:1 derivatives:12 would:1 negative:1 e0:1 choosen:1 call:1 therefore:3 type:11 successful:1 solitons:9 couette:1 odinger:16 berlin:4 aux:1 hole:1 must:11 springer:8 ma:1 dodd:6 work:2 reads:2 ere:1 concepts:1 mx:2 give:3 generically:1 indicates:1 degenerate:5 advancing:1 guarantee:1 boussinesq:9 provide:3 feature:2 iiii:1 how:2 nontrivial:2 ordinary:4 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solv-int9804009.txt |@word consider:11 alh:15 rev:1 results:1 commute:1 types:1 expressions:1 sch:1 devoted:1 inverse:2 sogo:1 remarkable:1 tr:1 nonlocal:1 tl:1 tk:4 under:1 applied:1 r11:3 rise:1 difference:1 t2:6 solution:1 t1:5 discrete:1 vector:1 relation:2 wronskian:1 sign:3 second:3 chen:3 theory:1 subscripts:1 established:3 nonlinear:8 ˆt:1 stands:1 invertible:1 ˆx:1 cnls:2 section:7 expressed:3 find:1 version:4 above:2 new:15 scr:1 satisfy:2 lee:3 exchange:1 respectively:2 component:5 here:4 concluding:2 sine:1 equations:48 implicit:1 change:1 obtained:2 remarks:2 suggests:1 action:1 chain:1 spatially:1 apr:1 santini:1 establish:1 use:1 proceed:1 contains:1 next:1 ψj:2 few:1 call:1 ψa:3 type:10 jpn:6 duality:3 solitons:1 operators:3 odinger:6 site:1 bogdanov:1 particular:1 known:2 cases:1 tokyo:2 equation:17 det:2 modified:1 mt:8 ms:3 following:4 example:1 give:1 dnls:15 organized:1 significances:1 r23:5 r22:2 information:1 darboux:1 means:1 nontrivial:1 pure:1 instead:1 sato:1 simplicity:1 de:1 ρ2q:2 mapping:3 lax:11 summarize:1 constants:1 realized:1 dynamical:1 explicit:1 martina:1 allow:1 representation:4 order:1 davey:6 multidimensions:1 dx:1 hierarchy:17 pointed:1 abstract:1 paper:4 through:1 during:1 japan:1 its:5 cll:3 ln:6 conjugation:4 lr:1 systems:3 derivative:5 them:3 combination:3 universality:1 acklund:7 introduce:4 fokas:1 they:1 now:1 discuss:1 february:1 φk:1 2p:1 hereafter:3 university:1 2d:3 2a:4 each:2 found:1 tˆ1:2 constraints:2 mikhailov:1 differential:5 ef:4 t3:4 isospectral:1 toda:2 decays:1 tˆ:1 out:1 space:1 u2n:1 crucial:1 iizuka:1 mα:2 math:1 linear:3 kaup:3 standard:2 york:1 pairs:1 times:2 manakov:2 exponentially:1 first:5 initial:2 symmetry:4 miura:2 variables:10 linking:1 xx:2 aratyn:2 degenerations:1 introduction:1 adjoint:2 system:53 construct:3 1d:3 gives:4 commutativity:1 2an:1 newell:3 part:2 x2:11 double:14 were:1 symmetries:3 rewrite:3 already:1 conjugate:2 need:1 any:5 viewed:1 petviashvili:3 efs:4 note:6 liu:3 take:1 indexed:1 calculus:1 bilinear:1 play:1 shall:1 simplify:1 connected:1 successive:1 nothing:4 r32:5 r33:2 yamilov:1 considered:1 flow:2 kn:2 kp:28 ku:1 vries:1 fact:2 nls:5 akhiezer:1 multicomponent:1 purely:2 bright:2 gauge:4 solutions:3 d2:3 d3:3 decade:1 d1:3 q1:5 analytic:1 only:2 qx:5 integrable:9 do:4 get:5 dependent:3 between:8 db:3 straightforwardly:1 ones:1 ϕi:1 words:1 dy:4 report:1 meguro:1 ds:38 evolution:1 kadomtsev:3 approach:2 arxiv:1 contain:1 qi:1 2p1:2 set:14 exists:1 see:1 w2:2 w1:2 2pu:1 eigenfunctions:2 bureau:1 ladik:6 simplest:1 conditions:1 terms:4 wn:28 attention:1 wk:8 key:1 solv:2 jetp:1 come:1 both:1 pempinelli:1 last:3 according:1 embedding:1 hierarchies:8 among:3 conclude:1 corresponds:1 leon:1 dimensional:2 coordinates:1 sequences:1 respect:2 masato:1 transformations:8 been:2 int:3 reduction:1 pi:1 pn:11 komaba:1 define:5 determinant:1 relations:5 received:1 pacheva:1 present:1 case:9 multi:1 p1:4 consultant:1 will:1 while:1 p2:1 property:1 ix:2 coupled:37 iq:2 boiti:1 vk:1 thus:2 non:1 vn:89 ii:1 ij:1 dual:1 different:1 φs:1 same:2 φa:3 complex:5 auto:1 φj:1 several:1 higher:4 independent:1 flows:9 hand:4 infinite:3 ablowitz:6 schr:6 well:2 obviously:1 solve:1 sets:1 proposed:1 3p1:2 3p2:2 obtain:21 stewartson:6 previous:2 nissimov:2 sciences:1 zakharov:1 lattice:2 transformed:2 lett:3 adj:7 transformation:4 generalized:2 eigenfunction:2 iα:2 couple:2 dark:1 background:1 using:5 2q:1 follows:5 reduces:2 korteweg:1 arbitrary:1 become:2 qxx:1 works:1 reduced:1 2qu:1 sequence:1 2iδ:1 some:2 recently:1 dimensions:1 investigations:1 2q1:4 problems:2 equivalent:6 aj:3 bk:1 bt:18 about:3 constraint:1 novikov:1 wadati:4 compatible:3 konopelchenko:1 soc:6 functional:1 pair:1 references:1 sov:1 operator:8 ψk:1 there:4 quadratic:1 way:2 was:2 function:1 form:4 tally:4 but:4 construction:1 2d1:3 considerable:1 ux:1 iqt:1 uv:2 us:3 un:80 those:1 uk:1 called:1 defined:4 certain:1 ak:1 describe:1 denote:2 proves:1 formalism:1 commuting:1 defines:1 satsuma:1 functions:1 no:1 pitaevsky:1 field:1 other:12 role:1 spatial:1 department:1 exp:1 asterisk:3 generated:1 structure:1 ghost:11 implies:1 dψ:1 dφ:2 baker:1 pseudo:3 orbit:2 sasa:1 time:1 original:2
solv-int9804010.txt |@word r00:2 now:1 acts:1 words:1 chain:1 integro:1 sklyanin:3 delta:1 σnz:3 obtain:3 σnx:2 brief:1 σ0x:4 scalar:5 paper:4 relation:5 using:3 λk:2 japan:2 satisfies:2 yamamoto:2 scattering:5 eigenstates:5 λm:1 λl:12 whose:1 inverse:5 group:1 calculate:2 bogoliubov:1 ln:8 interesting:2 ll:12 dynamical:1 lj:1 preprint:2 wall:4 explicitly:1 coth:2 th:3 theorem:1 integrable:3 eigenstate:2 mjn:1 r12:8 references:1 frahm:2 bm:1 p0n:2 rapidities:1 σ1z:1 they:1 zm:2 meguro:1 respectively:3 σny:3 matrices:1 gen:3 condition:2 r0n:1 down:1 annihilated:1 detm:1 particle:1 hamiltonian:2 university:1 arxiv:1 solution:2 derive:1 spaces:2 l2:1 math:5 l1:4 2l:4 2m:1 essential:1 spins:4 depend:2 baxter:3 tensor:1 domain:4 weyl:1 hte:1 sinh2:1 2iη:46 creation:2 some:1 related:5 cosh:1 each:2 inhomogeneous:3 see:1 elements:2 λj:12 quantum:9 rapidity:1 mat:1 spectral:1 lemmas:1 tsuchiya:3 impurity:1 space:4 review:1 extensively:1 denotes:1 boundaries:3 µl:3 state:2 lattice:6 above:4 between:2 formula:7 boundary:21 conditions:17 method:5 o1:4 ωl:25 satisfy:2 commutation:4 folowing:1 linear:1 degree:1 simultaneous:1 bl:2 vertex:14 bn:1 reflection:5 jp:1 diagonal:1 here:2 its:1 concentrate:1 comm:1 ansatz:4 sinh:91 address:1 solv:1 bose:2 along:1 equations:1 generate:1 regular:1 commutative:1 obtained:1 last:1 σn:2 impenetrable:1 institute:1 similar:1 studied:3 o:2 2λl:2 periodic:2 products:4 permutation:1 consequence:1 consequently:1 assign:1 essler:3 trigonometrical:1 zl:7 soc:1 plays:1 osamu:1 upper:1 apr:1 fig:1 number:1 dimensional:2 nothing:1 pol:2 right:1 choose:1 construct:1 determine:2 operator:4 proved:1 open:13 coker:1 given:6 rewritten:1 start:1 addition:1 transfer:1 u1:4 three:1 relations:6 z1:2 choosen:1 calculation:1 difference:1 noting:1 call:1 opposed:1 tr0:1 type:3 komaba:2 1n:2 function:16 determinant:8 corresponding:1 kojima:1 form:1 xxz:9 operators:6 pseudovacuum:3 gas:2 but:1 σ0z:3 reflecting:10 mail:1 line:2 spin:1 present:1 auxiliary:5 commun:1 applying:1 tokyo:3 holds:1 ut:1 equation:9 up:1 us:1 bethe:4 matter:1 ωj:6 values:1 monodromy:3 were:2 following:1 p2l:2 matrix:6 example:1 ac:1 constant:1 dual:2 find:1 int:1 abstract:1 thus:2 argument:2 uniquely:1 denote:1 states:3 conserved:2 cond:1 dλ:1 σlz:1 any:1 constructed:1 functions:4 end:9 lemma:4 locality:1 recursion:2 ωm:3 six:13 same:2 note:1 k1:4 other:4 role:2 0n:6 quantities:2 parameter:1 izergin:4 conclusion:1 heisenberg:1 product:2 used:2 fundamental:3 models:2 λn:24 act:2 problems:1 hand:1 algebraic:3 important:1 infinite:1 representations:1 luttinger:1 reference:1 interacting:1 lower:1 especially:1 liquid:1 ωn:14 kj:1 calculated:1 partition:11 korepin:5 together:1 yang:3 ku:1 correlation:7 model:31 physics:2 section:1 polynomial:1 left:1
solv-int9804011.txt |@word consider:2 crucial:1 results:1 gx:3 four:1 parametrisation:1 go:4 expressions:2 excluded:1 issues:1 γy:1 γx:1 calculate:1 paris:5 containing:1 βxx:1 finally:5 those:1 elliptic:1 under:4 analogous:1 division:1 g5:3 g1:1 choice:2 putting:1 condition:11 leads:5 presented:1 did:1 cause:1 list:4 solution:2 discrete:19 convenience:1 relation:3 upr:1 programme:1 direct:1 sign:1 integrability:7 pass:1 rigorous:2 further:2 ode:4 canonical:12 even:2 established:1 what:6 incompatible:2 section:3 goes:1 new:3 upward:1 ever:1 consisting:1 coefficient:3 27a:1 27b:1 full:3 simultaneously:1 degree:3 never:3 here:5 papageorgiou:1 ǫxy:3 possibility:3 others:2 alone:1 quite:2 equations:17 appears:3 obtained:12 remark:7 ǫx:2 2aσ:1 study:2 studied:4 allows:3 experience:1 periodic:4 resulting:2 situations:1 usually:1 resonance:3 suitable:1 makes:2 divide:1 classification:2 apr:1 vii:2 prefer:1 brought:3 addressed:1 hindsight:1 apply:2 linearly:1 derivatives:3 use:2 additive:1 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solv-int9804012.txt |@word roberts:1 consider:4 rev:1 focus:1 leads:12 quadrature:1 generalize:1 computation:1 devoted:1 γy:1 γx:13 depend:1 paris:5 γq:2 γp:1 βxx:6 finally:6 investigation:2 elliptic:1 under:3 mutandis:1 include:1 division:3 straightforward:1 far:1 account:1 choice:1 putting:1 decide:1 linearizability:2 condition:7 four:1 presented:3 diverging:1 turns:2 list:2 solution:4 occurs:1 discrete:13 upr:1 programme:1 direct:1 translating:2 integrability:9 rigorous:1 further:6 substitute:1 linear:9 even:1 what:2 nonlinear:2 appear:1 section:4 m33:2 m32:2 m31:2 above:4 obvious:1 method:1 full:4 led:2 notions:1 degree:5 component:1 here:5 papageorgiou:1 ǫxy:1 focused:1 xν:2 equations:12 appears:1 obtained:23 remark:2 dividing:1 study:5 studied:4 allows:1 subcase:1 periodic:1 resulting:3 data:1 m3i:1 usually:1 complicated:1 explain:1 york:1 departement:1 cν:2 family:3 apr:1 vii:2 engineering:1 brought:1 put:7 apply:2 should:1 readily:4 use:6 distinct:2 contains:2 next:7 going:1 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solv-int9804013.txt |@word consider:1 priori:3 eqn:1 varying:1 edn:2 results:26 2c1:1 leads:1 scalar:1 proposition:65 latter:1 2e:2 grateful:2 consists:1 follow:4 expressions:13 involved:1 reasoning:1 issues:1 whose:4 inverse:8 graph:2 tu:4 tr:1 acting:1 tp:15 recurrence:12 γj:2 summarised:2 petersburg:1 th:2 under:2 tg:1 analogous:2 mcp:2 spec:1 norm:2 2γl:2 applied:1 rational:4 straightforward:3 very:1 rc:40 springer:1 dokl:1 corollary:8 p1:53 li:1 matrices:7 deformations:1 condition:12 four:1 blaschke:1 riemann:7 solves:9 presented:8 transmission:1 t7:2 notes:3 p5:4 solution:31 t0:1 large:1 integro:3 differential:3 math:15 ml:1 small:6 relation:3 anal:3 optics:2 manipulations:1 onerous:3 upper:5 abbreviated:1 employing:1 zj:1 zk:1 zd:14 takhtajan:1 estimates:2 direct:5 pulse:4 zc:2 feasibility:1 iu1:5 zero:3 8i:4 design:1 evaluated:3 equal:2 further:1 fibres:3 ode:1 canonical:4 even:5 nonlinear:5 appear:3 diag:2 section:7 transforms:1 analogously:8 expressed:1 3i:4 version:2 poles:3 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solv-int9804018.txt |@word consider:3 remarkable:1 crucial:2 results:5 four:3 scalar:2 compact:1 whose:1 γx:1 depend:1 stable:5 conjecture:3 orthogonal:1 far:1 wave:1 lyapunov:7 difference:1 condition:17 generalised:1 presented:1 solution:3 small:2 noted:5 estimates:1 sign:1 second:1 odd:1 linear:7 even:5 what:1 nonlinear:24 plays:1 appear:1 while:1 find:2 suspect:2 above:6 new:1 net:1 avinash:1 method:5 contrast:1 patt:1 respectively:1 here:2 reported:2 others:1 concluding:1 equations:30 change:1 bhubaneswar:1 obtained:6 derivable:1 weinstein:2 institute:1 study:2 studied:2 usually:1 formation:3 boundedness:1 apr:1 marked:1 use:1 would:3 prove:1 sake:1 positive:1 negative:1 therefore:2 criteria:2 type:2 solitons:5 under:1 pairs:1 validity:1 particular:1 known:1 dey:2 ulx:1 equation:8 values:8 drops:1 example:1 sense:1 india:2 lψ:4 minimum:9 allowed:10 sharp:1 provide:1 get:6 write:1 very:2 instead:1 parameter:14 product:2 may:4 max:3 after:1 derived:2 applications:1 waves:2 law:1 constants:1 dynamical:1 third:1 hmin:3 so:4 realizes:2 sb:1 order:17 restriction:2 satisfied:4 stability:38 experiments:1 through:1 its:8 before:2 solitary:2 la:1 interesting:1 lv:2 systems:2 derivative:1 travelling:1 thereby:1 collide:2 scaling:3 mention:1 they:1 now:7 discuss:1 mystery:1 easily:1 term:4 2p:5 always:1 university:1 hamiltonian:10 inequality:1 2b:2 inherent:1 higher:15 side:1 series:1 our:3 out:1 shown:7 hyman:2 since:4 lagrangian:4 ry:1 increase:1 collisions:2 u2x:4 math:1 i2:1 theory:2 seventh:1 completely:1 khare:4 put:1 pune:2 βx:2 a223:1 hence:3 another:1 dispersive:1 given:10 perturbation:2 checked:1 width:5 leading:1 system:2 relations:1 their:2 perturbations:1 too:1 calculations:1 eqn:28 variational:1 structures:1 gives:1 collapse:1 holder:1 relative:1 liquid:1 integrability:1 determined:1 amplitude:4 any:3 zero:1 min:1 responsible:1 mechanism:1 note:2 effectiveness:1 play:1 elastically:1 most:1 said:1 connected:1 compactons:13 why:1 soliton:12 kf:1 nonlinearity:10 considered:7 compacton:33 typeset:1 principle:1 αx:1 physics:3 fact:5 laws:5 iopb:1 show:7 discovered:2 relation:1 solutions:27 substituting:1 agrees:1 fifth:2 q1:1 q3:1 q2:1 based:2 q4:1 parameters:1 should:3 only:6 integrable:2 hamiltonians:1 extremum:1 his:2 means:1 dd:2 cannot:1 dx:8 report:1 dt:2 dp:9 approach:1 arxiv:1 paper:1 dpc:4 fixed:1 set:2 j2:5 up:7 observed:2 depends:3 result:5 recently:2 αp:1 uξ:1 pattern:1 definite:1 unable:1 between:1 probably:1 conditions:1 terms:2 nature:2 however:6 comm:1 extent:2 clues:1 solv:1 both:2 cos:3 a101:1 many:1 fulfilled:1 etc:1 admit:1 context:2 expression:1 otherwise:1 point:5 had:1 j2p:1 corresponds:1 cd:1 respect:2 considering:2 marg:1 puts:2 due:1 been:6 pc:4 a210:1 interest:1 direction:1 corresponding:3 quantities:1 sufficient:7 coherence:1 subspace:1 evidence:1 present:2 case:7 unlike:5 pacs:1 will:5 near:1 property:2 karpman:4 ve:1 shepard:1 almost:1 ip:4 thus:5 ernet:1 different:1 generic:2 suggest:1 same:3 beside:1 proved:1 finite:2 difficult:1 independent:6 see:9 trivially:1 numerical:1 effect:2 hand:3 edges:1 uses:1 infinite:1 invariance:1 weakly:1 3x:1 rosenau:5 well:4 analysis:11 obviously:1 patterns:1 usual:1 λx:1 obtain:1 immediately:1 speed:5 preprint:1 5x:1 conclude:1 seems:1 except:1 valid:2 transformed:1 lett:6 transformation:4 momentum:3 march:1 rev:4 eigenvalue:1 possible:1 using:8 αj2:4 height:1 like:6 follows:3 reduces:1 steps:1 δh:1 arbitrary:8 become:1 soft:1 therein:1 because:1 creation:1 phenomena:1 kdv:1 cooper:5 does:3 assuming:2 limitations:1 run:1 power:2 equivalent:1 revtex:1 cξ:1 although:1 earlier:1 comparison:1 constraint:1 stationary:2 eqns:6 pξ:1 remains:1 range:6 perturbed:1 localised:1 kuznetsov:1 communication:1 within:2 sol:1 three:1 right:1 references:2 operator:5 schrodinger:1 additional:1 elastic:1 support:2 there:3 question:1 u2:3 dispersion:16 start:1 conservation:6 low:1 stabilises:1 function:1 elsewhere:1 form:3 some:3 regard:1 analyse:1 but:2 hc:7 true:4 ux:2 ut:2 robustness:1 maximum:1 us:1 kumar:1 um:3 ul:2 below:4 un:3 problem:4 similar:2 uc:9 taylor:1 associated:1 ad:2 int:1 certain:1 abstract:1 general:2 dξ:1 conserved:2 proves:1 exist:1 whereas:3 other:3 role:2 details:1 department:1 nice:1 calculating:1 γup:1 sodano:1 variation:1 meaning:1 important:2 bounded:3 linearization:4 assume:1 stabilizes:1 4p:1 weights:1
solv-int9804019.txt |@word lieb:2 consider:3 allows:1 show:1 indeed:2 particular:2 results:1 seen:1 eε:1 paper:2 relation:1 looks:1 existence:2 satisfies:1 steklov:1 scattering:12 roots:1 ground:1 accepted:1 based:2 thank:1 ln:2 except:1 should:1 thermodynamics:1 finally:2 valid:3 specify:1 easy:2 under:1 integrable:5 main:2 solvable:3 possessing:1 formulæ:1 real:1 do:1 supported:1 provides:1 combination:1 replaced:1 express:1 obtain:1 define:1 corollary:2 putting:1 listed:1 words:1 press:1 bogoliubov:1 difference:3 yu:1 differentiating:1 heaviside:1 term:1 finite:2 necessary:1 qt:5 particle:3 did:1 turns:2 university:1 arxiv:1 unsuspected:1 solution:3 math:2 2c:1 found:3 mathematical:1 kernel:6 set:1 weight:5 energy:1 some:1 related:1 see:3 bare:4 us:2 respect:1 quantum:4 our:2 defining:1 dµ:1 eq:2 substitute:1 spectral:4 ru:1 given:1 nonlinear:6 describing:2 matrix:2 since:1 rev:2 boundaries:1 state:1 cambridge:1 goes:1 between:1 evidently:1 new:2 boundary:1 method:1 apr:1 choose:1 terms:2 linear:2 interactions:1 journal:1 arbitrary:1 weak:1 however:2 here:3 like:1 step:1 inverse:1 references:2 solv:2 bose:2 equations:5 properties:4 temperature:3 restrictions:1 property:6 last:2 would:1 institute:1 discussed:1 equal:1 solvability:1 russia:1 turn:1 connection:1 must:1 hence:2 discussions:1 special:1 expression:1 other:2 first:2 uniquely:2 therein:1 reduce:1 simplifies:1 useful:1 symmetry:1 simple:2 into:5 integral:6 dimensional:2 variable:1 simply:1 constant:1 theor:1 slavnov:2 substituting:1 transformations:1 second:1 due:1 comparing:1 therefore:1 resolvent:4 was:3 bethe:2 more:3 function:9 form:2 becomes:1 moscow:1 exactly:1 gas:2 observe:2 delta:2 known:1 c2:1 convergent:1 present:1 observation:1 case:1 wide:2 parts:2 2πif:1 integrating:1 type:1 equation:16 work:1 mi:1 depends:4 value:1 transformation:4 will:1 below:1 fermi:7 intas:1 following:2 arrive:2 example:3 proof:2 f0:13 proved:2 derivative:2 give:1 int:2 explicit:1 abstract:1 arise:1 thus:1 generalization:1 general:3 dξ:1 sphere:2 say:1 dν:10 ras:1 relates:1 limit:4 ic:2 identities:1 any:1 rfbr:1 functions:2 depending:1 rather:3 lim:2 image:3 check:1 chemical:1 potential:1 arguments:3 liniger:1 indentity:1 parameter:4 izergin:1 frolov:1 european:1 even:1 used:4 excitation:1 shall:1 models:6 use:3 hand:1 zinoviev:1 most:1 generated:1 important:1 phase:13 formal:1 class:2 identity:13 implies:1 coupling:1 third:1 considered:1 values:1 no:1 well:1 korepin:3 yang:4 exp:1 correlation:1 model:1 physics:1 order:3 fact:2
solv-int9805001.txt |@word limited:1 suny:2 consider:4 remarkable:4 represent:5 forbidden:1 global:1 results:7 projected:3 four:7 gf:4 σz:2 disc:1 gc:4 parameterization:1 follow:1 expressions:3 disk:5 displaying:1 causes:1 devoted:1 whose:5 inverse:23 depend:3 calculate:5 re:23 graph:4 concerned:1 deterministic:1 3b:1 recurrence:1 does:5 those:8 stable:4 c4:1 random:1 string:1 far:5 exception:1 choice:1 every:7 figs:3 stays:1 ims:2 experimentally:1 associated:4 difference:8 fractal:9 condition:9 school:1 meant:1 ref:1 solution:1 large:1 solved:1 recall:2 small:11 eigenvalues:8 inspection:1 ρk:11 degeneracy:1 zl:43 upper:1 zn:28 neighborhood:1 coordinate:1 zj:17 zk:8 lightest:1 past:3 discriminated:1 zero:4 evaluated:1 3a:1 further:2 dynamics:6 ρn:12 zp:11 approached:1 employ:1 what:4 nonlinear:4 appear:6 invertible:1 aν1:1 contributions:2 section:3 remain:3 uniform:2 cell:1 version:1 above:2 3c:1 new:4 experience:1 increasing:1 method:1 contrast:1 3d:1 satisfy:2 compact:3 full:3 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solv-int9805012.txt |@word inverse:1 εv:1 2u2:1 consider:1 4uv:1 show:3 reductions:2 grammaticos:1 results:2 notations:1 karasu:2 miwa:1 relation:2 solutions:1 uy:2 substituting:1 expressions:1 progress:1 its:5 make:1 εm:1 now:1 remarkable:1 parameters:4 kovalevskaya:1 aψ:1 original:1 had:1 weiss:3 should:5 only:3 εn:1 present:1 theorem:1 mail:1 possess:1 work:1 into:2 perturbations:1 details:1 conservation:1 ramani:1 non:2 belarus:1 dominant:1 ϕx:2 means:1 since:1 acklund:1 springer:1 satisfied:1 neither:1 answer:1 ϕi:2 get:2 they:3 identically:1 nor:1 applying:2 singularity:2 accepted:1 yu:3 discuss:1 condition:2 ux:2 2u:1 2v:1 bas:1 positions:2 differential:2 expansions:4 solution:1 admissible:1 either:1 characteristic:2 found:1 raised:1 uw:1 scattering:1 mathematical:1 satisfy:1 arxiv:1 transform:1 truncated:2 simplicity:1 bψ:1 national:1 revised:2 some:1 ωt:1 integrability:9 expect:1 choosing:1 pass:1 our:1 kdv:13 ur:1 acts:1 special:1 out:2 spectral:4 nonlinear:2 jimbo:1 appear:1 lead:1 remind:1 αy:2 resonances:3 rep:1 singular:2 artificial:1 find:4 fuchssteiner:3 assuming:1 new:2 net:1 conditions:5 kruskal:2 math:3 2αv:1 αt:4 2αu:1 recently:2 linear:2 tabor:1 wt:1 derived:2 journal:1 contain:1 choose:1 here:1 admits:1 how:1 objects:2 references:1 solv:1 equations:5 βt:1 received:1 copyright:1 dim:2 institute:1 could:1 aφ:3 βx:2 o:2 essential:1 compatible:1 april:1 minsk:1 rewrite:1 interesting:1 introduced:1 consequently:1 explicit:2 block:1 recursion:1 perturbed:5 there:2 groups:1 classification:4 follows:3 appeared:1 miura:1 variables:1 each:1 u0:2 dimensional:4 analyzed:2 simply:1 ψt:1 directly:2 apply:2 next:1 ψx:2 perturbation:5 transformations:1 remains:1 carnevale:1 arbitrary:1 question:3 system:15 relations:1 u2:1 reduction:1 cauchy:1 too:2 passed:2 αx:4 siam:1 scheme:1 exponents:1 systems:4 introducing:1 corresponding:2 way:3 form:2 academy:1 under:1 kupershmidt:1 jul:1 underlined:1 segur:1 qω:1 uxx:2 integrable:1 known:2 cases:1 vxxx:1 applied:2 ωx:1 bφ:3 ma:3 unfortunately:1 evident:1 whether:1 ut:3 equation:10 uv:2 6uux:1 painlev:9 us:3 hypersurfaces:2 will:1 easier:1 ui:2 behavior:1 following:2 olver:1 property:2 obtain:1 procedure:1 truncating:1 taylor:1 coupled:3 int:1 vi:2 abstract:1 thus:2 them:1 proven:1 general:1 vr:1 vt:2 governed:1 turns:1 vx:2 uxxx:1 check:2 lie:1 functions:1 φt:5 εx:1 turn:1 φx:5 studying:1 bulky:1 six:1 lett:3 same:1 note:1 sciences:1 other:2 take:2 branch:2 solitons:2 test:4 parameter:1 φy:2 exactly:1 sakovich:4 philadelphia:1 see:3 normal:1 may:1 june:1 substitute:1 v0:2 applications:1 generated:1 satisfying:1 lax:8 vxx:1 letter:2 bountis:1 pair:8 ablowitz:1 compatibility:3 constants:1 recent:2 possessing:1 branches:1 algorithm:1 no:1 well:5 berlin:1 analysis:2 dragon:1 automatically:1 verify:1 moreover:2 physics:2 possesses:2 came:1 laws:1
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solv-int9806001.txt |@word represent:5 linearly:1 partial:1 consider:13 remarkable:2 t2i:2 commun:2 results:4 nato:1 leads:5 eds:2 scalar:4 gd:7 consists:3 expressions:4 disk:7 gr:24 compact:1 inverse:5 const:1 technique:1 moskow:1 nonlocal:1 tn:15 v12:5 quasi:1 alvarez:1 manifolds:8 elliptic:1 dressing:11 semenov:1 grinevich:1 te:1 worth:2 ingredient:1 p2:2 r14:1 r12:1 string:2 straightforward:1 r11:1 rise:3 p0:4 wave:24 witten:1 every:1 chooses:1 allowed:2 ui:4 elena:1 exact:1 rn:4 condition:9 p7:2 bxy:3 dim:2 propagating:1 obvious:2 impressive:1 immediately:1 hamiltonian:1 bn:2 turns:1 t2:10 t3:5 t1:24 large:3 integro:1 sattinger:1 proposition:6 indices:2 anal:2 exhibits:1 optics:1 petersburg:1 illustrating:1 direct:1 sign:1 crete:1 painlev:2 plenum:1 j22:1 j21:1 further:1 odd:1 substitute:1 theory:10 spectral:3 index:46 what:3 nonlinear:16 stands:2 invertible:1 t2n:8 w5:1 d2:1 section:6 analogously:1 3u:2 cell:3 birkhoff:15 3i:1 u34:1 poles:5 3n:4 subspaces:4 3l:1 new:5 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