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solv-int9909023.txt |@word ck:1 world:1 internat:1 particularly:1 consider:4 proposed:1 hierarchy:21 over:3 supported:1 obtain:4 press:1 cambridge:1 3u:3 using:3 facts:1 japan:2 satisfies:2 research:1 d2:3 eη:1 decade:1 d1:3 relationships:1 whose:1 x1:2 cluster:1 yasuhiro:1 ma:1 instance:1 interesting:1 conclude:1 young:1 b265:1 tn:3 tm:3 systems:1 th:1 integrable:2 5a:1 setting:2 5c:1 5b:1 yk:3 dm:1 string:1 notation:1 orthogonal:5 rules:2 de:2 mironov:1 corresponds:1 kaku:1 preprint:2 pfaffians:3 dx:5 dy:2 report:1 meguro:1 j4:1 lett:1 matrices:2 φj:6 differentiating:1 widom:2 easily:1 2v:1 kadomtsev:1 determinants:1 continuum:2 solves:1 fields:1 university:2 arxiv:1 t2:6 identified:1 t1:16 specific:1 conformal:1 differential:2 2a:2 integrals:6 each:1 2n:8 river:1 reduces:1 solutions:3 mathematical:3 zn:24 set:1 directly:1 sep:1 clarified:1 fellowships:1 reduce:2 j1:4 j2:3 solution:4 past:1 understood:1 see:1 elements:4 examples:1 nekrasov:1 jpn:1 discussions:1 qk:2 j2n:6 attributable:1 eq:8 d4:1 yet:1 bilinear:8 shown:1 nonlinear:1 matrix:10 lead:1 bruijn:2 review:1 3v:1 expressed:3 d3:4 particles:1 models:1 defined:1 indian:1 dxdy:1 between:2 formula:1 utilized:1 proc:1 acknowledgments:1 demonstrated:1 satisfy:5 model:1 terms:4 theory:2 intimate:1 respectively:1 marshakov:1 spacing:1 given:2 here:2 however:1 gratefully:1 although:1 address:1 solv:2 article:1 equations:9 properties:3 random:1 topology:2 obtained:1 waseda:1 antisymmetric:1 kostov:1 extension:1 perspectives:1 geometry:1 aj1:1 aj3:1 hence:1 symplectic:4 context:1 t21:2 lax:1 fredholm:1 sci:1 first:2 xj:8 xk:12 soc:2 xi:3 xn:2 publishing:1 qkl:1 notes:1 ykj:1 integral:3 while:1 xkj:2 hermitian:1 because:2 references:1 nonperturbative:2 another:2 sgn:2 summation:1 respect:1 lastly:1 tracy:2 math:2 use:2 lecture:1 log:3 prepare:1 ψk:1 2u:1 dnl:1 eqs:1 rewrite:3 vandermonde:2 been:2 ψj:2 few:1 pf:9 those:1 usp:1 taken:1 pk:1 dt1:2 structures:1 abstract:1 pl:1 pm:1 function:5 field:1 determinant:3 corresponding:1 3d1:3 form:2 furthermore:1 quantities:3 operators:1 helpful:1 t3:3 heat:1 6u:1 hep:1 known:1 cases:2 j3:1 iii:1 present:1 case:5 observed:1 springer:1 applying:2 tokyo:3 was:1 equation:6 work:1 det:6 toda:2 evaluated:2 komaba:1 aim:1 ohkubo:1 limit:2 hope:1 aij:1 following:2 toward:1 similar:1 example:2 unitary:1 associated:1 they:1 coupled:15 int:2 ny:1 refs:1 them:1 edge:1 denote:1 morozov:2 dxn:5 expressions:1 yj:2 conf:1 identities:1 physical:1 d14:2 functions:3 forthcoming:1 twofold:1 relationship:2 petviashvili:1 d13:1 distributions:1 formulations:1 when:1 pfaffian:3 pp:2 note:2 sciences:2 other:1 scientists:1 department:2 ordinary:2 constructed:1 ensemble:2 tic:1 conserved:1 formulas:2 investigated:1 kinds:1 exp:6 kazakov:1 may:3 correlation:1 nj:1 dx1:5 acknowledges:1 algebraic:1 multisoliton:3 3d2:1 mulase:2 date:1 4d1:3 φk:4 a2n:5 4e:2 give:1 observation:1 2d3:2 2d2:1 considered:2 physics:1 clear:1 author:1 well:1 xjk:2 strings:1 dr:1 kp:22 ohta:3 ku:1 hirota:3 4f:1 comments:1 4d:1 4a:2 4b:1 4c:2 fact:2 quantity:2
solv-int9909024.txt |@word partial:1 consider:7 funct:1 results:3 leads:1 scalar:2 generalize:1 gk:5 gj:7 gi:6 whose:2 inverse:2 depend:1 technique:2 tn:29 uniqueness:2 tm:3 tj:1 manifolds:1 th:1 dressing:14 worth:1 case:11 g2:2 g1:2 orthogonal:3 wave:4 putting:1 matrices:2 condition:9 four:1 school:1 presented:1 induction:1 integrating:1 t2:5 solution:6 t1:2 fredholm:1 zhu:1 anal:1 zn:2 wronskian:1 consistent:1 direct:2 integrability:1 further:1 substitute:1 zs:2 bilinear:5 will:3 what:2 nonlinear:1 appear:1 invertible:2 section:1 near:1 expressed:4 d3:1 version:2 d0:8 kyoto:1 ˆi:3 ˆj:3 method:11 satisfy:6 respectively:1 component:13 here:1 desired:2 b2k:2 represented:1 along:1 marchenko:2 equations:32 change:2 obtained:7 waseda:2 antisymmetric:1 glm:4 studied:1 g2n:1 geng:1 suitable:1 g2k:2 via:1 tau:1 ipj:1 ipk:2 sgn:1 apply:1 univ:1 use:2 dodd:1 prove:2 dnl:1 jpn:5 suppl:1 next:3 mse:1 volterra:2 type:8 becomes:1 operators:21 under:4 appendix:3 cases:1 valued:1 tokyo:1 science:1 equation:21 modified:1 85a:1 following:9 making:1 example:3 proof:2 f1:1 f2:1 renormalization:1 calculation:2 indicates:1 assumptions:1 viewpoint:1 rather:1 holds:1 how:2 pure:1 sato:3 algebra:1 may:1 derived:1 bkp:3 fi:5 fj:5 fk:5 revealed:1 dynamical:1 explicit:1 parameterized:1 element:3 order:1 neglect:1 dyj:1 hierarchy:37 paper:2 y1:2 japan:1 satisfies:7 y2:1 its:1 solving:2 conjugation:1 choose:1 fij:4 mail:1 them:1 yj:1 introduce:1 scaling:1 pfaffians:10 they:4 now:1 discuss:1 2u:1 term:1 hereafter:1 university:1 theory:1 each:1 found:2 2n:47 differential:9 series:1 reduce:1 related:2 t3:4 toda:1 investigated:3 quantum:1 our:1 eq:7 special:1 shown:2 matrix:13 space:1 furthermore:2 since:3 induces:1 denotes:5 formula:1 ref:1 shows:2 benjamin:1 linear:4 reformulated:1 quite:1 publ:1 generate:1 derivation:1 could:1 impose:2 pfaff:6 hence:1 lax:3 adjoint:10 first:2 xk:1 xn:19 symmetry:3 miura:1 variables:3 powerful:1 xx:3 relations:4 another:2 representations:2 ut2:1 given:6 introduction:1 eqs:4 system:1 construct:4 their:3 appl:1 vxy:1 kokyuroku:1 scheme:1 structures:2 gives:2 commutativity:4 3d1:2 relationship:2 tool:1 part:1 t4n:1 x2:2 x3:1 than:2 coefficients:5 wide:1 future:1 contrary:1 f12:1 f11:1 collecting:1 symmetries:1 rewrite:1 lines:1 seen:1 recover:1 lie:1 wilson:1 petviashvili:2 studying:1 note:3 sciences:1 k1:3 generalized:1 new:1 formulas:4 shall:2 t2k:2 z2:1 algebraic:2 pair:1 class:5 fand:2 soliton:11 especially:1 considered:1 ckl:2 coincides:1 km:2 kp:22 ohta:7 ckp:11 exp:8 vries:3 fact:1 show:4 dy1:1 relation:3 solutions:11 d2:2 find:2 decade:1 d1:4 based:1 f21:1 should:2 only:2 explicitly:2 vxxx:3 constant:1 hope:1 dn:4 dm:5 notation:2 get:1 dependent:1 de:2 dz:3 dx:3 dy:3 report:1 during:1 gel:2 kadomtsev:2 determinants:4 arxiv:1 gram:3 kernel:12 set:4 sep:1 j4:1 j1:4 j2:3 j3:2 mentioned:1 depends:1 bare:6 existence:1 recently:1 j2n:6 shabat:4 affine:1 commutation:1 symmetric:2 f22:1 written:4 between:2 subscript:1 conditions:2 terms:3 uux:3 rims:2 jp:1 however:2 reproduces:1 solv:3 article:1 δai:2 jb:1 wx:2 last:1 f2k:2 many:1 f2n:1 symplectic:2 expression:1 otherwise:1 ch:1 cn:4 cm:3 caianiello:1 simple:1 dimensional:1 concluding:1 anti:1 respect:2 throughout:1 levitan:2 kernels:1 transformations:1 addition:1 moerbeke:3 been:7 int:3 reduction:4 treat:1 expected:1 pk:2 abstract:1 define:1 corresponding:3 commutes:2 xxx:1 6u:1 6v:1 c2:1 c1:3 c0:7 present:1 applied:3 k2:1 multi:6 means:1 engineering:1 aim:1 ohkubo:1 shiota:1 coupled:16 ir:1 systems:1 ii:1 89a:2 ij:7 vt:1 vx:2 d14:1 different:2 cji:1 d13:1 identities:4 make:1 same:2 complex:3 k2n:1 hierarchies:1 several:1 independent:1 used:2 satsuma:5 flows:2 hand:1 infinite:3 frequently:1 4d1:1 a2k:2 sattinger:3 identity:2 lower:1 solve:1 horozov:1 manifold:1 obtain:2 differentiation:3 scattering:1 preprint:3 infinitely:1 zakharov:4 seems:1 lattice:6 wu:2 lett:4 easy:2 real:1 rules:1 know:1 using:8 formal:1 follows:3 korteweg:2 integrals:3 δi:1 evolutions:1 uy:2 reduced:12 δa:1 mathematical:4 some:2 b2:1 kdv:3 neglecting:1 shinjuku:1 extensively:1 decomposition:3 provides:1 assuming:1 prog:1 bm:1 equivalent:2 bj:2 substitution:1 fordy:1 quotients:1 discussed:3 dependency:2 obeys:4 introduced:4 slightly:1 skew:1 soc:5 into:1 integral:6 remarks:1 references:1 operator:9 van:3 log:2 prepare:1 combinatorics:1 3u:2 dispersion:2 quadratic:2 function:5 form:3 regard:1 hu:1 2vt:3 elimination:1 adler:4 he:1 applying:2 ux:1 cij:4 up:1 us:1 problem:1 called:1 ac:1 proved:1 defined:2 universal:1 aj:2 general:1 single:1 formulation:2 commuting:2 constructed:2 grassmann:2 functions:5 no:2 wxx:1 pfaffian:5 field:1 other:2 department:1 theor:1 elements:1 denote:1 ku:1 hirota:15 problems:2 polynomials:1 massachusetts:1 variable:2 structure:1 implies:1 2d3:2 assume:4 physics:1 together:1 time:3
solv-int9909025.txt |@word inverse:1 12r:2 gt:1 partial:2 consider:14 chain:5 illustrates:1 crucial:1 separates:2 focus:1 bc:1 2c1:3 illustrated:2 quadrature:7 proposition:7 generalize:1 gb:2 broader:1 parameterization:1 expressions:2 gl:3 2r3:3 2n1:1 2r1:6 discern:1 devoted:1 whose:1 hold:1 depend:7 calculate:5 axial:3 revisited:2 equivalence:4 tr:13 including:1 presents:1 answered:1 quasi:9 rg:1 those:1 th:2 under:4 γa:4 include:1 r16:1 case:42 belonging:3 r15:1 r12:5 r13:1 straightforward:4 orthogonal:2 very:1 homogeneous:1 implicitly:1 rise:3 translations:1 springer:1 fat:1 results:5 corollary:3 every:7 difficult:2 lrw:1 entries:7 application:5 affect:1 parameter:10 matrices:41 condition:15 arrange:1 preserve:1 leads:3 obvious:1 riemann:1 hamiltonian:31 turns:1 list:1 accidentally:1 enon:6 integrated:3 leave:2 solved:6 vector:17 bq2:3 math:3 harry:4 indices:2 eigenvalues:1 originally:1 inserting:5 mn:1 force:21 ga:3 oscillator:1 consistent:1 b22:19 b21:6 sign:4 translating:1 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solv-int9910004.txt |@word represent:3 consider:2 caused:1 results:5 leads:1 discreteness:1 displaying:1 preserves:1 depend:1 program:1 γl:12 characterised:1 presentation:1 straightforward:1 choice:1 electron:1 summarized:1 discretizations:1 condition:3 solves:1 eds:1 solution:10 t0:6 deals:1 discrete:18 convenience:1 math:2 gauge:2 subindex:1 upper:1 force:7 periodicity:1 direct:2 cosh:7 zero:3 hδ1:2 concludes:1 chen:1 qualitatively:1 dynamics:4 even:3 index:1 what:1 nonlinear:4 stands:2 diag:1 3n:1 new:2 solitonic:1 satisfy:1 fiz:1 respectively:1 here:2 behaviour:4 sinh:7 address:1 equations:2 interpret:1 obtained:6 great:1 study:1 allows:2 periodic:3 4a2:1 eiφ:1 pp:1 unit:2 conventional:1 takes:1 recalling:1 positive:2 next:1 few:1 associated:2 more:2 formally:1 becomes:2 odinger:2 curvature:1 correspondingly:1 particular:3 known:3 cases:1 must:4 account:1 quantized:1 recall:1 equation:5 mh:5 values:2 following:1 about:1 example:1 renormalization:1 figure:2 give:1 purposes:1 sense:1 evidently:1 azquez:2 needs:1 end:2 caption:1 holds:1 maps:1 nontrivial:1 instead:1 parameter:2 sin:3 oscillatory:1 simplicity:1 product:1 mat:1 algebra:1 may:1 after:1 fa:2 levi:1 plane:1 fd:2 data:2 constants:1 introduced:2 hα0:6 hα1:3 grant:1 explicit:2 element:1 so:2 allow:2 acknowledges:1 playing:1 indeed:1 years:1 through:1 looks:1 jimenez:1 mentioned:2 existence:1 satisfies:1 its:1 fis:1 chosen:2 interesting:1 temporal:2 conjugation:1 fig:1 derivative:1 main:1 them:1 affected:2 introduce:3 emphasised:1 now:3 yu:1 transparent:1 bigger:1 2t:4 eigenvalue:2 february:1 2w:9 university:1 possibilities:1 truth:1 each:1 2n:1 referred:1 homogeneous:3 ei:1 related:1 inhomogeneous:9 obtains:1 shown:2 matrix:8 since:1 rev:2 stud:1 rn:6 independence:1 ibidem:2 numerical:1 linear:4 diagonal:1 possibility:1 quite:1 aei:2 reason:1 transition:3 times:2 counterpart:1 2πi:2 assumed:1 hence:1 teor:1 view:1 first:2 initial:1 features:4 xm:3 number:2 restrict:1 2a2:3 πl:2 illustrate:1 given:5 oscillation:1 introduction:2 eqs:1 system:3 relations:1 πp:2 appl:1 zeros:1 scheme:2 konotop:4 continuous:3 x0:2 than:2 determines:1 require:1 cimento:1 see:1 limiting:3 determined:1 pra:1 lines:1 say:1 any:3 strength:2 convenient:1 taha:1 note:1 instance:1 potential:1 take:1 analogy:1 degenerated:1 praxis:2 spectral:1 exactly:1 electric:1 centre:2 sets:1 paid:1 involving:1 connected:1 formulae:2 phase:1 soliton:10 especially:2 consequences:1 considered:3 order:1 points:1 exp:7 velocity:1 physics:2 dot:1 χh:1 phenomenon:1 v12:1 v11:1 bright:1 relation:1 solutions:4 analogue:3 label:1 trivial:1 find:2 d0:2 parameters:6 situations:1 analytic:1 only:3 µn:11 integrable:9 circle:2 local:1 oct:1 do:2 means:4 express:1 generalise:1 ones:1 words:1 suris:1 report:1 during:1 justified:1 liu:1 evolution:6 bar:1 continuum:2 approach:1 arxiv:1 imposed:2 hλ2:2 qn:6 hλ:2 requirement:2 exists:1 achieved:1 physically:1 depends:1 result:2 arg:1 ur:1 nonlocality:1 subject:2 phases:1 yet:1 µm:3 written:1 smallest:1 ladik:5 simplest:1 boundary:3 αj:2 conditions:6 preserve:2 notice:2 comp:1 attention:1 however:1 reproduces:1 concentrate:3 solv:1 cos:5 last:4 equal:1 attributed:1 ln:1 fix:1 among:1 relevant:1 point:2 continuation:1 ca:1 corresponds:3 coincidence:1 dimensional:1 respect:4 2nw:2 considering:1 ensures:1 source:1 trajectory:1 three:2 been:4 reduction:1 cauchy:1 treat:1 interest:1 fluctuation:1 define:1 v22:1 v21:1 corresponding:1 xxi:1 present:1 case:14 will:1 while:2 property:1 portugal:1 iq:1 ir:1 thus:1 ih:2 reads:1 different:3 author:1 same:2 complex:2 pauli:1 defines:1 φl:1 used:1 trajectories:1 effect:1 hand:2 moment:1 purpose:1 ablowitz:6 schr:2 center:2 well:3 finds:1 lim:4 coordinate:2 position:1 model:21 ae:2 minima:1 being:1 obtain:1 transforms:1 λe:5 using:1 scattering:2 underline:2 53a:1 sciences:1 lattice:3 lett:1 transformation:2 iχ:11 real:5 iθ:1 spatial:2 possible:2 period:10 integer:7 necessary:1 follows:4 reduces:1 specific:1 δj:2 arbitrary:2 disorder:1 replacement:1 mathematical:1 right:1 deal:2 some:2 b0:1 choosing:2 oscillations:19 scale:2 feder:1 lead:2 does:2 linearly:1 steps:2 scientific:1 bm:2 use:1 step:10 eiχ:1 substitution:1 between:1 constrains:2 vh:4 world:1 dependence:4 o:2 sake:2 a2:1 stand:1 reproducing:1 bloch:12 discretization:21 computational:1 communication:1 into:4 due:1 down:1 references:1 institut:1 additional:1 comparing:1 transfer:1 support:1 there:2 question:1 transform:1 describes:1 naturally:1 form:5 phenomena:1 construction:1 hm:1 made:1 nonlinearity:1 evident:1 whether:1 inside:1 us:2 2πn:1 discretized:1 below:2 limit:1 problem:2 constant:4 int:1 abstract:1 chubykalo:1 deep:1 proper:1 exist:1 periods:1 funchal:1 bishop:1 physical:3 nh:8 when:5 bremen:1 arctan:1 rewriting:1 field:1 other:3 role:1 solitons:2 department:1 nr:1 elements:2 bruschi:1 models:3 ragnisco:1 a1:3 a0:2 important:1 sides:1 implies:1 assume:2 4w:3 curve:1 governed:1 4n:1 iψ:1 time:15 n0:1 requires:1 having:1 4a:3
solv-int9910005.txt |@word ψ1x:2 lakshmanan:9 consider:4 ψ1t:2 results:4 eds:1 φ1x:3 expressions:3 ward:1 devoted:2 whose:1 inverse:4 depend:1 paris:1 equivalence:4 finally:1 spain:1 th:1 under:1 te:1 case:7 rise:1 geometrical:3 every:1 summarized:1 resonant:2 exact:1 condition:5 alma:4 level:1 permits:1 solution:7 ri:3 strachan:3 possibility:1 sign:1 jump:1 integrability:2 dynamics:1 substitute:1 ψ2x:2 bilinear:2 xψ:1 nonlinear:2 section:11 tabor:1 foregoing:1 version:1 above:1 abx:1 new:1 solitonic:21 method:7 satisfy:4 simultaneously:1 hern:1 respectively:1 here:1 l21:1 eci:2 represented:1 equations:23 obtained:6 ishimori:1 study:2 studied:4 allows:1 reports:1 suggests:1 useful:2 apply:2 ψx:11 ψy:8 positive:3 h1t:1 negative:2 ψt:10 few:1 therefore:4 iteratively:1 type:1 more:2 becomes:1 odinger:6 berlin:1 appendix:4 particular:2 known:1 cases:1 iv:1 iii:1 easiest:1 must:1 springer:3 integrating:1 equation:23 mj:1 values:1 following:8 my:10 mx:6 f1:2 f2:2 figure:10 give:2 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solv-int9910006.txt |@word consider:2 chain:2 maximum:1 results:3 eds:1 kc3:1 expressions:1 contributions:1 localized:3 inverse:2 depend:2 quasi:1 anharmonic:1 ωt2:1 amplitudes:3 straightforward:1 very:2 ǫan:1 wave:6 difference:2 condition:2 vibrational:2 hamiltonian:2 t2:12 solution:3 t1:4 large:1 vector:2 biological:1 optics:1 direct:1 pulse:1 sign:3 approximation:2 zero:4 chen:2 further:3 odd:1 linear:5 nonlinear:10 plays:1 trapping:1 giving:1 find:1 above:1 solitonic:1 method:8 coefficient:1 lee:2 here:2 atoms:1 behaviour:1 ansatz:1 sinh:1 address:1 active:1 along:1 equations:1 appears:2 change:1 obtained:2 institute:1 stretching:1 published:1 usually:1 resonance:2 spacetime:1 followed:1 scales:3 manna:1 plenum:1 santini:2 linearly:1 derivatives:2 use:2 ayn:1 asymptotic:5 would:4 positive:1 played:1 vibron:1 next:4 call:2 therefore:1 reductive:1 taken:1 type:2 theoretical:1 more:1 introducing:2 solitons:3 odinger:1 ip1:1 jmn:3 known:3 encountered:1 must:1 account:2 quartic:1 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solv-int9910007.txt |@word consider:1 fitch:1 results:11 leads:5 entropy:13 grateful:1 consists:2 follow:2 paris:2 does:2 those:3 th:1 under:3 case:29 conjecture:1 straightforward:1 choice:3 every:2 ζn2:1 redefinition:1 matrices:1 condition:11 four:1 p4:1 presented:4 turns:3 solution:1 large:1 discrete:15 bxn:1 gauge:2 referred:1 zn:18 findings:1 nonautonomous:18 go:1 second:2 value:1 further:1 implemented:1 odd:7 d4:5 even:7 established:3 what:5 plays:1 appear:3 iterating:1 d3:4 version:1 3m:7 new:2 method:4 satisfy:1 full:1 led:1 degree:26 here:1 analysed:1 behaviour:1 q2:2 hkn:1 q12:2 strong:1 equations:8 appears:2 obtained:15 remark:2 study:4 studied:1 example:2 suggests:1 bol:1 action:1 implement:2 changes:1 divide:2 family:1 extra:3 requiring:2 vii:1 brought:1 limn:1 p42:1 infinitum:1 asymptotic:1 would:3 nijhoff:2 next:3 few:1 doubt:1 m2:2 simpler:1 entails:1 more:5 introducing:1 elliptic:5 ecole:1 validates:1 factor:3 validity:2 particular:1 known:2 cases:5 must:4 ramani:11 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solv-int9911006.txt |@word represent:1 partial:1 gr:1 chain:3 leads:1 scalar:1 bicomplexes:4 consider:2 depend:1 tx:3 charge:1 th:1 matrices:1 solution:2 enon:1 vector:1 demonstrated:1 samos:1 further:1 canonical:1 appear:1 trivial:1 sj0:2 current:1 above:4 new:1 satisfy:3 respectively:1 hδs:1 consideration:1 quite:1 equations:3 obtained:2 ekl:1 allows:1 via:4 dimakis:2 modifying:1 planck:1 unit:1 use:1 eφ:1 next:2 linear:6 axx:1 introducing:1 becomes:3 correspondingly:1 particular:3 known:1 mf:2 recall:1 equation:11 work:1 χk:2 mt:1 obvious:1 following:4 example:6 lχ:4 calculation:1 organized:1 recursive:1 provide:1 get:1 maps:5 parameter:1 product:1 ft:2 algebra:1 fx:2 max:1 hence:2 st:1 so:4 pleasure:1 order:1 help:1 indeed:1 over:2 satisfied:1 years:1 course:1 e2φ:5 through:1 satisfies:2 its:1 lf:2 thank:1 fit:1 how:2 exact:2 coordinates:1 writing:1 forms:2 lt:1 choose:2 derivative:1 lx:1 they:1 identically:1 nov:1 now:2 finite:9 2r:1 university:1 iff:1 arxiv:1 ei:10 ek:5 ej:3 series:1 reduce:1 related:1 toda:12 expect:1 our:2 special:1 really:1 acknowledgment:1 space:2 furthermore:2 since:2 rev:1 denotes:2 formula:2 rn:6 forth:1 math:3 mχ:3 theory:2 associate:1 standard:1 completely:1 hep:1 e1:2 generate:1 r2:2 iterative:2 motion:1 consequence:2 promotion:1 generalizations:1 δia:2 restrict:1 xx:1 δjb:1 directly:1 given:1 system:3 eqi:7 their:1 eqk:2 vxx:1 eqn:2 scheme:1 lot:1 eq1:2 iteration:1 str:1 bicomplex:3 w2:1 symmetries:1 outstanding:1 topics:1 modern:1 element:1 convenient:1 note:1 k2:1 calculus:1 systems:2 germany:2 φk:2 especially:1 professor:2 sf:2 occasion:1 physics:2 solutions:1 d2:2 q1:2 q2:3 only:3 integrable:2 his:3 dj:2 means:1 df:4 dg:1 dx:1 lattices:2 dt:3 him:1 regarding:1 qt:1 qx:1 differential:2 qi:9 qk:2 qn:3 set:2 aegean:1 δjk:2 j0:6 j1:2 see:2 us:2 greece:1 sei:1 satisfying:2 doebner:2 closed:6 conditions:2 terms:1 se1:1 however:1 solv:1 wx:1 collaborators:1 last:2 expression:1 finds:1 point:1 simple:1 dimensional:1 respect:1 actually:1 hoissen:2 basis:1 calculi:1 ph:2 fig:2 corresponding:2 quantities:1 c3:2 c2:1 c1:4 denote:2 c4:2 case:2 conserved:15 will:1 euclidean:1 replaced:1 eii:2 eij:3 eil:1 procedure:1 conferences:1 thus:1 vt:2 exterior:1 ax:4 vx:1 currents:4 recover:1 φx:9 recursion:1 several:1 independent:2 used:1 trivially:1 infinite:1 recent:1 charges:7 well:1 coordinate:1 graded:1 φtx:2 obtain:3 underlying:1 uller:3 λm:1 previous:2 retirement:1 lattice:5 extends:1 possibly:1 using:2 like:1 δj:3 integrals:1 arbitrary:2 δf:2 qxx:1 mathematical:3 some:3 examples:2 choosing:2 kdv:1 lead:1 does:1 linearly:1 yields:1 participation:1 equivalent:5 bi:2 bt:1 bx:3 properties:1 anything:1 nonvanishing:1 introduced:1 therein:1 φxx:1 j1i:1 into:1 en:1 references:2 determine:1 elementary:1 ricatti:1 institut:1 support:1 there:2 long:2 way:2 function:3 hx:1 construction:3 made:1 smooth:1 differentiable:1 ur:1 liouville:4 iterated:1 demonstrate:1 define:5 called:1 associated:5 int:1 abstract:1 chao:1 general:1 single:1 ottingen:1 constructed:1 ni:2 functions:1 nk:1 field:5 setting:1 department:1 mathematics:1 elements:4 models:2 variable:1 structure:1 matrix:1 implies:3 assume:2 dχ:6 n0:1 rep:1
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solv-int9912001.txt |@word since:1 lakshmanan:1 chain:5 magnetic:1 trigonometric:3 leads:1 eckern:1 remarkably:1 compact:1 preserves:1 depend:1 including:1 include:1 belonging:4 g0:2 results:1 antipode:1 entries:2 exact:6 encounter:1 hamiltonian:3 proc:1 notes:1 sklyanin:1 t2:1 solution:2 discrete:2 c01:4 c02:5 consistent:1 matrices:1 integrability:6 chen:1 canonical:1 spectral:2 nonlinear:3 appear:1 version:1 above:1 new:2 coefficient:1 patt:1 c0j:1 here:1 explore:1 cylindrical:4 concluding:1 along:3 sine:9 equations:2 change:2 convert:1 institute:1 study:1 allows:1 usually:2 suitable:2 spacetime:1 inducing:1 use:2 takes:1 would:3 iαs:4 comparing:1 nucl:2 therefore:3 taken:1 introducing:2 formally:2 becomes:1 operators:11 constructs:1 odinger:1 particular:1 known:5 eα:1 springer:1 tnp:1 deformed:1 equation:6 mj:4 values:1 making:1 omer:1 relativistic:4 india:1 arise:1 tan:1 schmitteckert:1 s3:6 parameter:5 sin:8 lal:1 fs:1 mat:2 algebra:9 may:10 derived:1 levi:1 lax:8 representations:1 choice:3 kulish:1 explicit:4 korepin:1 inhomogeneity:10 enter:1 representation:1 playing:1 bidhan:1 through:5 japan:1 still:1 its:4 group:1 thank:1 euj:2 fiz:1 interesting:2 presence:1 forms:1 lt:1 lr:1 systems:1 deformation:1 non:1 seeking:1 propose:2 introduce:2 they:1 nov:1 now:2 represents:1 february:1 several:1 2s:1 level:2 possibilities:1 2e:2 2m:1 baxter:2 mikhailov:1 financial:1 series:2 related:1 inhomogeneous:12 toda:5 obtains:2 quantum:24 our:2 tarun:1 shown:1 matrix:6 space:7 casimirs:1 rev:5 chaos:1 eprint:1 rational:5 print:1 math:2 foundation:1 theory:1 standard:3 eigenvalues:5 retained:1 saha:2 could:1 gordon:9 teor:1 essler:1 first:1 sanchez:1 humboldt:1 bed:1 variables:2 simplified:1 defects:1 another:1 impossible:1 given:5 derives:1 1t:1 introduction:1 system:4 construct:3 their:9 1c:2 1e:2 scheme:8 konotop:1 exactly:1 serve:1 coefficients:4 cimento:1 submitted:1 exhibit:1 acknowledgment:1 b489:1 depending:1 eter:1 note:3 liu:1 k1:1 k0:1 generalized:1 forces:2 destroy:2 play:1 gλ:1 impurities:2 algebraic:2 involving:1 germany:1 calcutta:1 remarks:1 class:6 soliton:1 constructed:2 yang:2 exp:1 hietarinta:1 physics:1 fact:1 nls:9 b41:1 attempts:1 relation:1 counit:1 find:1 based:2 parameters:1 situations:1 should:2 analytic:1 only:1 going:1 generators:2 integrable:15 hopf:1 g02:1 dependent:7 dx:1 dy:2 lattices:1 ux:1 evolution:3 continuum:3 fields:1 arxiv:1 yield:1 coproduct:1 anjan:4 constructing:1 depends:1 result:3 sen:1 αs:2 αu:1 nuclear:1 symmetric:1 written:1 αe:1 ladik:3 approach:1 email:1 2αu:1 2αs:2 however:1 solv:1 uσ:2 both:3 cos:3 taking:2 annual:1 etc:3 objects:1 casimir:5 generalisation:2 nonrelativistic:3 simple:1 corresponds:1 mkdv:1 simply:1 associated:1 considering:1 lect:1 due:1 pj:1 algebras:1 generating:3 corresponding:3 various:1 schwab:1 external:2 systematic:4 c2:2 c1:1 c0:1 spin:4 case:2 eip:1 intriguing:1 novel:5 organisers:1 replaced:1 conformal:1 procedure:2 almost:1 ip:2 im:1 thus:3 site:1 vt:1 conf:1 ernet:1 different:4 media:2 fractals:1 φj:2 gets:1 independent:2 counterparts:1 inhomogeneities:4 ablowitz:3 prescribed:1 schr:1 nevertheless:1 poland:1 well:6 coordinate:2 position:1 model:18 vazquez:1 spherical:1 cj:3 being:2 enters:1 preprint:1 53a:1 density:1 zakharov:1 conclude:1 seems:1 except:1 param:1 lattice:5 belongs:1 lett:5 c12:4 c11:4 cond:1 transformation:1 realisations:3 take:1 frahm:1 using:1 c1j:3 like:4 arbitrary:4 become:1 reduced:4 gauge:1 often:1 classical:3 nagar:1 examples:1 choosing:3 proper:1 eiα:1 scale:1 radha:1 provides:1 chains:4 inserting:1 retains:2 equivalent:1 properties:1 central:3 kundu:3 o:2 introduced:1 automatically:1 homogeneous:1 soc:1 undeformed:1 into:2 sol:1 down:1 references:1 operator:11 bosonic:1 realisation:3 support:1 there:2 start:1 quadratic:4 way:2 ed:1 malomed:1 m0:1 function:5 form:4 but:2 anisotropic:1 construction:6 removed:1 applying:1 builds:1 ut:2 limit:5 uj:4 fluctuations:1 similar:1 inspite:2 constant:3 af:1 int:1 certain:1 abstract:1 physical:2 functions:4 no:1 when:1 hpt:1 field:6 other:3 role:2 solitons:1 izergin:1 elements:3 bruschi:1 models:19 ragnisco:1 important:1 variable:9 ξc:2 sides:1 structure:2 impurity:4 together:1 equivalently:1 mass:10 time:9
solv-int9912002.txt |@word consider:1 expressions:1 inverse:1 graph:5 elliptic:2 ti:1 semenov:1 td:1 tb:3 mpg:1 r12:9 r13:6 wave:1 antipode:2 difference:1 matrices:3 disconnected:1 jurˇco:3 solves:1 hamiltonian:8 t2:8 solution:1 t1:10 solved:1 vector:1 manifestly:1 reyman:1 hasegawa:2 zero:3 canonical:1 index:1 what:1 appear:1 sum:1 contracted:1 expressed:1 symes:1 subspaces:1 capital:1 new:3 method:1 component:1 here:1 provides:1 groups:2 path:7 equations:3 obtained:1 shansky:1 eij:4 ekj:1 shift:3 pictorial:3 action:1 t23:1 via:1 projection:1 family:1 vii:1 koji:1 planck:1 bra:1 use:1 would:2 contains:1 axioms:3 nucl:2 kostant:2 duals:1 operators:8 eλ:3 known:1 eη:2 iii:1 springer:1 endpoint:1 equation:6 work:1 following:4 relativistic:2 taa:2 r23:6 coalgebra:1 end:4 provide:1 acts:1 theresienstr:1 feature:1 ordinary:2 parameter:1 yangbaxter:1 product:1 algebra:9 max:1 lax:6 physik:1 representations:1 unchen:2 short:1 natural:1 dynamical:6 correspond:1 element:1 rather:1 encyclopedia:1 allow:1 representation:5 help:1 over:3 displayed:1 symbols:1 including:1 statistical:1 mentioned:1 satisfies:1 quasitriangular:2 its:1 group:1 thank:2 interesting:1 fix:2 coordinates:1 systems:2 van:1 jacobi:1 mail:1 main:3 deformation:1 non:3 eµ:1 nov:1 homomorphisms:1 university:1 bonn:2 each:1 found:1 universit:1 baxter:3 arxiv:1 ei:10 ek:3 ej:4 ed:1 contracting:1 combining:1 quantum:5 special:1 rt:2 jimbo:1 matrix:6 rr:1 space:5 particles:1 denoted:1 math:6 foundation:1 theory:1 tian:1 indices:3 complicated:1 york:1 institut:1 ruijsenaars:7 generate:1 incorporates:1 motion:2 length:5 δij:3 onto:1 first:1 origin:1 there:3 humboldt:1 sutherland:1 given:4 their:1 introduction:2 relations:2 indicate:1 pavel:1 scheme:2 xith:1 gives:1 commutativity:1 tfe:1 exactly:2 x2:2 x1:2 second:2 dtd:1 winternitz:1 boston:1 argument:1 seen:1 apparently:1 paths:13 generalizes:1 convenient:1 calogero:1 inv:2 oriented:1 sciences:1 generalized:1 heisenberg:1 continuous:1 unless:2 trace:2 shall:3 object:1 boltzmann:4 connected:1 coincides:1 vertices:3 face:13 graphs:2 yang:2 exp:3 physics:2 ending:1 miwa:1 spaces:1 solutions:2 state:1 controls:1 jan:1 integrable:1 moser:1 local:2 hopf:7 de:1 rt1:1 international:2 tba:11 dt:2 alexander:1 differential:1 factorization:3 acknowledgments:1 felipe:1 coproduct:1 common:1 fixed:8 set:1 tilde:1 relative:2 see:1 discussions:1 points:1 tensor:1 label:1 written:1 closed:2 theta:1 irf:1 terms:1 rims:1 neveu:1 weak:1 however:1 comm:3 key:1 solv:1 ket:1 diejen:1 last:1 equal:1 embedding:1 expression:2 co:1 δab:1 point:1 cocommutative:2 corresponds:1 dimensional:2 constant:1 commutative:2 int:2 interest:1 algebras:6 abstract:2 corresponding:4 suppress:1 mpim:1 hayashi:1 spirit:1 those:1 case:4 novel:1 jurco:1 look:1 will:2 theoretical:1 rbd:1 von:1 iagolnitzer:1 ii:1 dual:1 gervais:1 id:7 develop:1 make:1 shifts:2 finite:2 subalgebra:1 corepresentations:1 numerical:2 publ:1 edges:1 frequently:1 felder:1 academic:1 dashed:2 coordinate:1 model:5 latter:1 summed:3 sektion:1 source:2 interested:1 theorem:5 schupp:3 press:2 mod:1 like:4 continue:1 yields:1 arbitrary:1 become:1 δb:1 δa:1 mathematical:3 methods:1 respect:1 peter:1 avoid:1 t12:3 t13:2 proc:1 okado:1 tdc:3 kyoto:1 hilbert:2 mutually:1 range:3 obeys:1 act:1 germany:2 introduced:1 letters:1 h2:3 h3:3 h1:3 appropriate:1 references:1 span:1 weight:2 support:2 pairing:1 start:1 cocommutativity:1 inner:2 way:1 naturally:2 function:2 form:2 concatenated:1 but:1 construction:1 line:1 adler:2 coupling:1 versions:1 ur:1 problem:1 similar:1 ac:1 ordered:3 defined:1 universal:3 loops:1 single:1 formalism:2 commuting:1 functions:2 no:1 mathematik:1 when:1 valid:1 picture:1 corepresentation:2 elements:1 congress:1 models:4 setting:1 vertex:11 includes:1 structure:2 longer:1 assume:1 rule:1 weights:2 starting:1
solv-int9912003.txt |@word sector:1 pth:1 global:10 sca:29 results:3 ds:16 existing:1 four:4 olive:1 scalar:1 generalize:1 francesco:1 consists:1 follow:1 zinn:1 dsds:1 rd:1 preserves:1 aug:1 superspace:3 subjected:1 quasi:6 does:1 promoting:1 those:4 supplies:1 under:3 include:1 straightforward:2 far:1 rise:2 translations:4 seemingly:1 choice:1 witten:2 putting:1 summarized:1 redefinition:2 manin:1 vast:1 hdr:1 entire:1 presented:1 did:1 issue:1 troost:1 z12:76 deals:1 involution:3 small:8 iassns:1 superalgebras:10 consistent:1 direct:1 second:8 antichiral:1 odd:3 rrr:1 even:1 what:2 nonlinear:7 appear:1 brackets:10 giving:1 sum:1 supermultiplet:1 expressed:2 2df:1 version:2 concisely:1 above:2 krivonos:8 new:8 wn:1 consisting:2 satisfy:5 full:9 nonlinearly:1 jˆ:4 ibid:1 respectively:4 realizations:1 here:6 understanding:1 objects:1 supermultiplets:2 represented:3 enveloping:3 equations:8 z1:1 z2:2 obtained:2 remark:1 kanno:1 rdr:3 involved:1 study:1 drr:1 reports:1 poisson:19 wzw:1 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solv-int9912008.txt |@word gt:2 customary:1 consider:16 remarkable:1 rx:1 γn:7 splitting:10 leads:8 πgn:2 rˆ:3 proposition:13 edu:2 consists:1 gn:3 expressions:4 gl:2 gk:14 gj:5 gi:11 gr:9 whose:1 c0:39 equivalence:1 acting:3 tn:17 uop:1 finally:4 ie2:1 tj:13 tk:43 th:1 ti:83 semenov:2 c4:21 mehta:2 summarizes:1 applied:3 fay:1 string:2 straightforward:1 orthogonal:18 conditions:1 results:1 corollary:2 worst:1 entries:12 tridiagonal:7 matrices:39 condition:2 common:1 hamiltonian:7 bn:9 turns:1 notes:1 t2:2 solution:8 t1:33 deals:2 involution:2 vector:14 math:8 recall:1 reyman:1 bordering:1 inspection:1 upper:6 zn:1 mn:9 zi:11 zj:6 haar:8 lecture:1 qλq:5 direct:1 α2n:12 second:6 further:2 zp:3 zq:2 addition:1 bilinear:15 established:1 what:1 nonlinear:1 appear:3 invertible:2 t2n:9 β2n:7 diag:4 section:13 expressed:9 abo:3 symes:2 version:4 jq2:7 above:7 flowing:1 new:6 preserved:1 ˆn:3 ρt:57 satisfy:10 evolving:3 full:1 simultaneously:1 l32:1 degree:1 respectively:9 l1:17 component:1 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solv-int9912009.txt |@word consider:2 chain:9 similarity:1 global:1 results:3 commute:1 vega:1 inverse:2 const:2 xiong:1 tr:2 finally:1 ti:1 include:2 r12:6 r13:2 zhang:3 trigonometric:3 every:1 difference:1 matrices:6 condition:3 tang:1 trk:3 hamiltonian:4 tra:1 anisotropy:1 sklyanin:3 t2:2 solution:4 t1:2 solved:1 a123:1 trt:1 takhtajan:1 sin2:1 direct:4 integrability:2 further:1 theory:1 spectral:3 index:1 stands:1 sum:2 expressed:1 kun:1 version:2 above:3 new:1 ever:1 method:4 satisfy:1 here:4 diagonal:1 represented:4 consideration:1 equations:13 obtained:4 search:1 dec:1 allows:1 amount:1 periodic:5 permutation:1 formulated:1 followed:1 family:3 namely:1 apply:3 lima:2 use:1 commun:2 perk:1 chi:1 comparing:1 nucl:1 ψn:10 therefore:1 iαa:2 tell:1 operators:10 2w1:4 particular:1 effort:1 recall:1 equation:19 work:2 infinitesimal:1 following:8 arrive:2 compare:1 wang:1 figure:8 calculation:1 indicates:1 r23:2 r21:4 end:1 rather:1 verify:1 acts:1 write:1 how:2 get:2 mccoy:3 parameter:5 sin:41 product:1 singular:1 may:3 derived:2 different:2 lax:25 summarize:1 data:1 compatibility:1 constants:2 caixa:1 imply:1 correspond:1 alcaraz:1 fundamental:1 order:3 ith:1 satisfied:1 including:1 statistical:4 its:2 horizontally:2 derive:1 ln:75 continued:1 solving:1 systems:1 constitutes:1 mail:1 main:1 xyz:3 non:4 introduce:2 obeyed:1 framework:1 mezincescu:1 effects:1 cep:1 now:4 yu:1 easily:1 term:3 gets:1 equality:1 alez:1 identified:1 l2:1 l0:7 l1:20 crossing:2 carlos:2 referred:1 baxter:12 related:1 extended:1 remove:1 combining:1 quantum:11 out:2 matrix:15 space:6 since:1 rev:1 denotes:2 acting:4 rn:4 ref:1 math:7 linear:2 associate:1 ısica:1 given:11 departamento:1 completely:4 brasil:3 keep:1 motion:5 length:1 consequence:1 amparo:1 βi:1 first:6 number:1 ihn:2 relations:3 open:8 differ:1 introduction:1 system:6 construct:1 nepomechie:1 1d:1 calculations:1 gives:1 part:1 than:1 specify:1 σkz:1 kulish:1 cimento:1 second:4 determined:2 nouvo:1 ann:1 αln:3 depending:1 responsible:1 note:3 k2:11 k1:18 heisenberg:4 trace:1 shall:2 akutsu:1 most:1 automorphism:1 multiply:2 appear:1 ka:2 ke:1 considered:2 vertices:3 yang:10 usual:1 notion:1 dot:1 show:2 supported:1 spaces:3 relation:12 3u:1 substituting:1 trivial:1 find:4 q1:9 parameters:2 only:3 explicitly:1 integrable:8 hamiltonians:1 local:8 ruiz:1 do:2 triangle:1 means:1 de:6 a70:1 σ1z:5 compute:1 du:1 gen:4 prime:1 evolution:1 places:1 transposition:2 arxiv:1 expansions:1 factorization:1 involutive:1 qn:8 set:2 exists:1 see:1 w4:16 w3:16 result:1 w1:5 satisfying:1 commutation:3 federal:1 sites:1 identification:2 between:1 invariant:1 boundary:22 conditions:5 αl:1 terms:9 importance:1 ju:1 wu:3 solv:2 σk:5 both:2 cos:13 σn:30 iln:3 etc:1 context:1 expended:1 wall:1 continuation:1 dimensional:4 associated:1 considering:1 commutative:1 basis:1 been:1 defined:1 yan:1 sogo:2 corresponding:6 xxz:4 great:1 commuted:2 derivative:4 spin:6 those:1 cot:2 case:3 pokrovsky:1 ǫk:1 ǫl:1 will:1 cast:1 monodromy:2 property:2 vi:1 vj:1 thus:1 site:2 vn:2 rij:1 il:3 id:1 santos:2 same:2 paulo:1 iα:8 pauli:1 finite:1 difficult:1 independent:1 used:1 rmatrix:1 trivially:1 parametrized:1 v1:3 v3:12 v4:12 estado:1 normalization:2 b275:1 off:4 reflection:6 well:1 concrete:1 consistency:2 model:8 left:5 unified:1 being:3 σnz:9 solvability:1 scattering:2 previous:2 adding:1 regarded:1 guaranteed:1 nacional:1 lett:3 iσ:4 solvable:1 2u:3 read:4 rna:1 b56:1 using:4 postal:1 mod:1 vertically:1 follows:1 specific:1 yields:1 right:3 deal:1 some:2 moreover:1 describing:1 l17:1 fapesp:1 prog:2 chains:2 pr:1 faddeev:1 power:1 equivalent:1 each:2 expansion:2 br:1 substitution:2 constraint:1 desenvolvimento:1 o:3 thacker:1 considerations:2 presence:1 into:3 h1:2 pair:11 2v1:4 because:1 references:1 operator:13 iαl:1 transfer:6 h01:1 there:2 signifies:1 noticed:1 way:1 m1:4 was:4 form:7 regard:1 hn:25 cnpq:1 funda:1 factorized:1 made:2 applying:1 consist:1 us:1 limit:2 demonstrate:1 problem:2 similar:2 called:1 mechanics:2 interchanges:1 constant:1 int:2 abstract:1 describe:1 ao:4 general:2 conserved:1 au:1 formulation:2 commuting:2 universidade:1 gonz:1 functions:1 locality:1 application:1 conselho:1 quantities:1 theor:3 elements:4 star:1 zhou:1 models:3 pesquisa:1 vertex:3 wadati:3 a2:1 graphically:4 xing:1 acknowledgment:1 bulk:2 auxiliary:5 assume:1 interval:1 together:2 time:1 starting:1
solv-int9912010.txt |@word secondly:1 sci:2 consider:2 chain:26 osp:1 madsen:1 global:3 sca:1 results:1 existing:1 leads:2 follow:1 expressions:2 gl:1 compact:1 inverse:1 calculate:1 superspace:23 b389:1 nonlocal:2 quasi:1 tk:7 th:10 under:3 andreev:1 eliminate:1 applied:1 string:2 associated:1 manin:1 presented:1 turns:2 t2:12 t3:7 t0:1 t1:2 discrete:9 unrelated:1 minimal:1 manifestly:2 anal:1 superalgebras:7 inspection:1 ρk:5 inconsistent:1 enjoy:1 consistent:2 direct:1 modified:11 zero:1 chen:1 odd:16 scientific:1 even:12 will:3 what:3 nonlinear:6 invertible:1 brackets:3 d2:1 section:2 3v:2 3u:2 krivonos:3 new:6 equivalent:1 satisfy:1 q1:5 led:1 lee:1 ibid:1 relationships:4 respectively:5 realizations:2 component:2 here:3 understanding:1 objects:1 consideration:3 method:1 equations:9 roˇcek:1 remark:3 parameters:3 reason:1 pics:1 products:1 grisaru:1 hospitality:1 system:1 changes:1 involves:1 via:3 classification:3 tau:1 merely:1 tp:8 tools:1 unit:1 derivatives:9 use:4 would:6 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solv-int9912011.txt |@word sci:3 they:1 over:4 supported:1 results:1 russian:5 through:2 solutions:1 previous:1 slow:7 rapidly:2 decay:2 ln:5 parametrization:2 lemma:4 only:2 under:7 integrate:1 mail:1 deformation:5 norm:1 do:1 within:1 triangle:1 means:2 very:1 secular:4 wave:1 differential:1 property:2 ones:2 additional:1 background:1 unique:1 decomposes:1 condition:3 formal:2 well:1 term:2 finite:1 2r:1 2s:2 conditions:4 arxiv:1 t2:3 solution:22 teoret:2 solved:1 grants:1 arbitrary:3 small:3 fixed:1 side:4 depend:3 homogeneous:1 kernel:1 requirement:1 acad:1 ser:1 deal:1 series:1 sbornik:2 journ:1 some:1 direct:1 calculated:1 second:1 been:1 result:1 nonhomogeneous:1 remainder:1 into:1 close:1 ode:3 linear:5 ru:1 scale:4 affects:1 centre:1 expressed:1 research:2 does:1 rb:1 tends:1 formula:5 boundary:1 reading:1 approach:2 method:3 math:2 available:1 foundation:1 terms:1 theory:1 ufa:2 given:4 here:5 approaches:1 expansion:1 substitution:1 solv:1 const:3 equations:10 change:1 pointed:1 obtained:4 both:2 remark:1 piece:1 r2:4 institute:2 taking:1 dependence:2 o:18 times:1 a2:1 fisika:2 context:1 assumed:1 corrections:2 pde:2 view:1 first:5 perturbed:2 formulated:1 follows:1 simple:1 variables:2 asymptotically:1 integral:1 solve:1 u0:1 represented:1 because:1 references:1 long:5 operator:3 appl:1 per:1 use:2 perturbation:9 described:2 asymptotic:8 rection:1 remains:1 leading:2 initial:11 u1:1 transform:1 construct:3 defined:1 cauchy:6 asymptotics:3 way:1 suit:1 taken:4 was:2 correction:2 gives:2 function:2 2x:2 pare:2 relations:1 corresponding:1 matem:1 form:4 becomes:1 theorem:1 idea:2 integrable:1 x2:3 hold:1 than:5 case:2 account:1 potentials:1 characteristic:1 equation:14 smooth:5 fast:3 hopf:1 liouville:10 determined:7 values:1 str:1 ussr:1 problem:12 dec:1 similar:1 russia:1 cor1:1 f1:4 f2:4 piza:1 give:1 int:1 december:1 abstract:1 spectrum:2 ann:1 general:5 ar:1 right:5 linearized:3 any:1 constructed:1 functions:13 zero:1 no:1 provide:1 εt:7 travel:1 same:1 matching:2 εn:2 pure:1 mathematics:2 εf:1 unperturbed:5 used:2 infinity:5 fundamental:1 see:1 singular:1 may:3 time:7 uniformly:4 parametrized:1 a0:2 nonlinear:1 bounded:2 purpose:1 waves:3 variable:2 choice:1 data:4 sides:1 structure:1 soliton:2 super:1 considered:3 bianchi:2 4t:5 interval:5 explicit:1 dσ:2 original:2 so:5 exp:7 decreasing:1 position:1 order:7
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solv-int9912015.txt |@word consider:12 rev:3 results:3 invent:1 fapesp:1 eds:3 αr2:1 ρjl:4 computation:2 takhtajan:1 go:4 gn:6 expressions:2 research:1 gk:1 gj:10 gi:23 row:3 whose:1 inverse:1 calculate:1 bll:1 tn:34 finally:1 νim:4 those:1 nσn:2 dressing:10 uma:1 te:4 presentation:1 third:1 amplitudes:1 g2:18 g1:21 very:1 ρj1:2 choice:2 every:1 reordering:1 exact:1 condition:2 annihilated:1 facilitate:1 level:3 bn:27 turns:1 t2:5 solution:15 t1:4 mm:4 vector:14 eigenvalues:1 optics:1 ρk:2 zn:17 mn:2 ρjn:2 zj:8 zk:1 mi:2 cosh:5 zero:8 value:4 follow:2 linear:10 bilinear:1 nonlinear:1 plays:1 appear:1 t2n:3 d2:1 section:3 supplied:2 h0b:1 consistently:1 en:1 subspaces:1 bm:2 new:3 b449:1 method:6 satisfy:3 αil:16 full:1 transparency:1 degree:5 respectively:6 l1:4 component:1 residual:1 here:6 behaviour:2 zz12:2 groups:1 equations:22 z1:27 z2:10 suggest:1 obtained:6 instituto:1 hamiltonian:3 mathematics:1 study:6 studied:5 βil:17 aνj:1 resulting:1 procedure:1 published:1 action:2 proof:2 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