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solv-int9801009.txt |@word consists:1 whose:2 isometric:1 paris:6 γr:4 swap:1 under:1 hermann:4 summarizes:1 saskatchewan:1 rise:2 georgia:1 every:23 coxeter:1 basics:1 suffices:8 solution:14 convenience:1 vector:6 shows:15 consistent:1 direct:5 second:8 rigorous:1 even:9 established:2 ˆs:1 iterating:1 ˆw:4 symes:1 birkhoff:9 ˆb:2 above:28 new:5 ˆj:4 consisting:4 coefficient:2 simultaneously:1 never:2 equals:2 here:14 q15:1 obtained:7 aks:1 study:1 settles:2 fourier:1 projection:4 9a:1 explained:1 replace:2 total:1 unit:2 derivatives:7 would:15 remainder:2 chooses:1 call:8 therefore:45 type:18 tell:2 brings:1 curvature:10 hold:1 must:1 word:1 rα:1 pursue:2 setup:2 work:8 reads:1 rλ:2 cocycle:1 root:10 example:19 give:4 cited:1 cartan:3 want:6 uxxx:1 end:8 turn:4 provide:1 verify:3 feature:3 how:9 nontrivial:1 sato:2 description:4 replacing:2 earlier:1 diagram:12 wrong:1 lax:1 summarize:1 meaningful:1 constants:1 third:2 deutsche:1 order:9 operations:1 restriction:3 xk:2 over:2 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solv-int9801012.txt |@word since:1 consider:4 chain:9 similarity:6 nauchn:2 results:1 leads:3 eds:1 scalar:4 proposition:2 houches:1 kowalewski:1 consists:1 gk:1 gj:2 gi:2 factorizing:1 const:2 montonen:1 tr:8 editors:2 γu:1 petersburg:2 semenov:1 include:1 applied:1 belonging:1 r12:8 sitting:1 very:1 rise:4 trigonometric:1 entries:8 matrices:41 condition:1 groups:1 four:3 solves:2 hamiltonian:7 turns:1 notes:2 sklyanin:13 solution:18 try:1 involution:1 commute:2 eigenvalues:1 shansky:1 upper:5 direct:1 second:4 substitute:2 canonical:2 spectral:10 brackets:1 maillet:1 poles:2 above:3 new:4 method:4 contrast:2 satisfy:1 exchange:4 respectively:6 here:14 q2:3 ansatz:6 sinh:2 equations:13 change:1 obtained:2 separating:2 institute:1 lomi:1 study:2 allows:6 hbc:1 tolstoy:1 products:1 poisson:1 permutation:2 usually:1 suitable:2 useful:1 family:2 extra:3 apply:1 use:8 yangian:3 prove:1 distinct:1 suppl:1 next:3 ψj:1 few:1 linear:3 therefore:1 twists:10 aut:1 zeroes:1 advance:1 iu:2 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solv-int9801013.txt |@word represent:2 managed:1 consider:12 chain:7 caused:1 forbidden:1 both:6 results:4 lr1:1 lr0:1 scalar:4 commute:1 generalize:1 grateful:1 parameterization:1 intricate:1 remarkably:1 reasoning:1 restrictions:1 layers:2 whose:10 certainly:2 compose:1 depend:2 remarkable:5 tu:1 trivial:3 finally:1 uniquely:1 indicate:4 those:35 elliptic:1 under:13 analogous:2 hints:1 passed:1 interchange:1 conservation:1 division:1 belonging:6 r12:1 string:36 straightforward:1 orthogonal:1 linked:2 reader:4 translations:2 primed:1 every:1 figs:2 formula:4 affect:1 difference:2 matrices:13 condition:15 four:6 annihilated:3 obvious:2 immediately:1 hamiltonian:4 did:2 turns:5 solution:2 try:2 discrete:1 vector:63 second:2 indices:5 eigenvalues:13 path:3 permutability:1 der:1 configurations:7 possibility:1 upper:7 revolution:1 says:1 version:1 foundation:1 dealing:2 consistent:3 somewhere:3 direct:2 prevents:1 sergeev:8 go:1 zero:8 pass:4 further:3 rectangular:2 odd:1 situated:7 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solv-int9801014.txt |@word is0:4 consider:2 remarkable:1 funct:1 equalities:1 results:2 neigborhood:1 consists:1 inverse:5 depend:1 kζ:4 under:3 amplitudes:1 advantage:1 frequencies:1 springer:1 dokl:1 wave:1 putting:1 capillary:1 condition:7 roy:1 solution:36 large:2 discrete:3 vector:6 small:5 neighborhood:4 σa1:1 direct:1 tex:1 imply:3 pass:1 further:1 substitute:3 spectral:3 index:1 nonlinear:2 const:3 diag:1 section:1 current:1 poles:2 new:1 method:1 component:4 here:2 q2:3 consideration:2 equations:8 z2:1 deduced:1 obtained:1 parameters:8 institute:1 shift:1 study:2 vectors:3 usually:1 fourier:1 changes:1 kates:1 york:1 modulated:1 unit:1 use:2 asymptotic:7 would:1 positive:1 contains:1 next:1 call:1 therefore:2 m2:10 type:1 more:4 nauka:1 formally:1 composite:2 solitons:6 εu1:1 odinger:1 carrying:1 nauchn:1 known:1 djordjevic:1 potential:1 k02:3 ma:1 science:1 equation:29 work:2 following:6 example:2 give:1 calculation:5 overbar:1 verlag:1 s0:2 pure:2 parameter:1 σb1:1 mar:1 mat:1 after:2 lump:1 waves:2 data:20 constants:2 realized:2 effective:1 explicit:2 so:2 expression:1 decreasing:2 representation:1 order:4 davey:4 over:2 soc:1 stability:1 paper:1 london:1 existence:3 its:3 solitary:2 ld:3 fiz:3 interesting:1 conjugation:1 forms:1 parts:1 main:1 lz:6 them:1 uspekhi:1 sssr:1 maslov:3 yu:1 2t:2 represents:1 term:6 equality:5 hereafter:1 2q:1 im1:1 inequality:1 l2:8 l1:4 2i:3 homogeneous:1 series:1 elementary:1 frequency:1 expect:1 lθ:4 extract:1 out:2 shown:2 matrix:4 since:1 rev:2 investigation:1 εq1:1 formula:6 correct:1 math:7 shows:3 folowing:1 theory:1 kulish:1 kaup:2 reason:1 collection:1 e1:9 interaction:1 asymptotical:4 kivshar:1 ist:4 turn:1 hence:3 teor:8 first:5 there:2 omitted:1 transform:2 rasmussen:1 another:1 carry:3 zh:3 zap:1 perturbation:13 introduction:1 adjoint:2 system:7 construct:3 their:3 perturbations:1 calculations:1 siam:2 continuous:1 newell:2 part:3 focusing:1 than:3 approximation:1 mclaughlin:1 liquid:1 second:1 determined:3 str:1 russia:1 bordag:1 correction:3 4k0:1 exper:3 exchanging:1 any:3 petviashvili:1 εz:1 εt:2 latter:3 note:1 sciences:1 k0:42 take:1 unperturbed:1 gε:1 akad:1 analize:1 shall:3 most:1 formulae:2 phase:2 eigenfunctions:2 soliton:20 considered:3 clear:1 physica:2 typeset:1 uε:2 segur:1 principle:2 exp:35 kz:21 supported:1 solutions:3 substituting:4 principal:2 q1:15 q0:19 slow:2 spite:2 rich:1 integrable:3 dl:1 dm:2 εb1:1 fluid:1 solvability:6 aβ:1 dz:10 dx:1 dy:1 ds:14 dp:1 evolution:2 kadomtsev:2 transversal:1 arxiv:1 nauk:2 dpb:1 qi:2 scott:1 4πi:1 view:1 requirement:1 ser:1 exists:1 see:2 result:6 w0:5 close:1 sem:1 dlb:1 phases:1 inequalities:1 nondegenerate:3 boundary:1 conditions:1 terms:3 shabat:1 matveev:1 however:2 manakov:2 vanishing:1 solv:1 jetp:1 come:2 both:1 essentially:2 taking:2 passing:1 zk0:4 ci:4 point:1 simple:3 σc1:1 corresponds:2 dimensional:7 bε:6 pole:6 respect:9 destroyed:1 transformations:3 due:4 int:1 asymptotics:29 topics:1 define:1 corresponding:3 quantities:1 sufficient:2 c2:1 c1:2 general:1 case:5 exponential:3 value:1 will:1 lomi:1 karpman:1 characterizing:1 iy:1 thus:3 constructible:1 surface:1 ii:16 reads:4 rfbr:1 different:3 pis:1 same:2 complex:1 finite:2 independent:1 used:1 infinity:1 hand:3 v0:2 ablowitz:2 mech:1 schr:1 disappears:1 depending:2 analysis:1 components:4 lim:1 self:1 obtain:10 scattering:21 pushkarev:1 stewartson:4 previous:1 blow:1 zakharov:4 reasons:1 setting:1 combine:1 lett:1 mod:1 iτ:3 disappearance:1 2iπz:2 increases:1 using:1 ams:1 unique:1 formal:2 necessary:1 follows:3 unstable:2 arbitrary:1 sesquilinear:6 reduced:2 acad:1 some:1 b0:1 b1:8 b2:4 moreover:1 scale:1 describing:1 affects:1 centre:1 integration:2 linearly:1 summand:1 turitsyn:2 proc:1 philadelphia:1 kiselev:9 ufa:2 equivalent:2 expansion:7 step:1 become:1 column:3 novikov:1 dependence:4 o:9 side:1 important:1 2iπ:3 perturbed:9 presence:1 kuznetsov:2 into:2 integral:4 pair:1 right:1 references:1 sov:1 operator:1 support:1 initial:6 iq1:1 u0:19 fast:2 iq2:1 appl:2 m1:8 malomed:1 was:3 naturally:3 function:4 form:31 but:1 construction:2 gain:2 russian:1 absent:1 consist:1 gravitational:1 smooth:1 up:3 uj:1 problem:25 2πz:2 similar:2 called:2 taylor:1 associated:1 conserves:1 computing:1 defined:3 aj:1 denote:2 proves:1 dζ:4 formalism:1 constructed:7 functions:1 qε:11 no:7 when:1 vanishes:1 other:3 fokas:1 mathematics:1 shin:8 2it:1 separate:1 preceding:1 problems:2 variation:3 a1:9 a2:4 variable:4 structure:6 implies:8 u1:2 time:5 original:1
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solv-int9801015.txt |@word represent:2 consider:9 pointing:1 limited:1 alg:1 global:1 results:3 leads:1 scalar:2 commute:2 generalize:1 go:1 na:4 remarkably:1 cases:4 factorizing:2 ihep:1 whose:4 inverse:4 collisions:1 graph:1 segments:5 tu:1 centers:1 passage:2 finally:3 petersburg:2 th:1 under:1 fermionic:1 presentation:1 belonging:1 string:22 g1:3 very:4 primed:4 isomorphism:2 every:3 orientations:1 onsager:1 difference:2 exact:2 condition:2 four:2 din:1 presented:1 irreducible:1 list:1 solution:1 try:1 discrete:4 convenience:1 multiplicities:1 math:3 small:1 relation:5 expanded:1 ten:1 dealing:1 consistent:2 direct:4 sergeev:4 consists:1 integrability:3 pass:3 situated:2 theory:2 even:1 gnb:2 what:1 nonlinear:1 stands:1 imagined:1 section:11 associate:1 expressed:3 d3:5 goes:3 new:4 row:1 ever:1 method:2 filled:2 movement:2 devoted:1 outgoing:7 degree:2 fiz:1 respectively:3 never:1 here:5 objects:5 free:1 others:1 directions:6 along:3 equations:7 change:4 intersect:2 obtained:1 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solv-int9801017.txt |@word represent:1 partial:2 gr:1 pointing:1 funct:1 alg:1 demand:1 four:1 inverse:3 depend:2 tr:1 helps:1 th:1 under:3 semenov:1 insights:1 worth:1 advantage:1 very:1 rise:1 springer:1 hµν:2 difference:1 matrices:9 condition:2 entire:3 riemann:1 solves:2 level:1 turns:3 sklyanin:1 solution:2 try:1 vector:1 indices:8 gauge:1 anal:2 noted:2 elegant:1 second:4 accompanying:1 linear:4 even:2 index:4 abc:8 trivial:1 version:3 above:1 new:5 satisfy:1 edited:1 here:6 understanding:2 china:1 others:1 represented:1 equations:2 appears:2 change:1 19b:2 box:1 shansky:1 institute:1 study:2 subcase:1 commonly:2 periodic:1 resulting:1 poisson:3 published:1 involves:1 named:2 regardless:1 explained:1 replace:3 lanczos:1 unit:1 derivatives:1 use:6 working:1 covariant:27 next:1 classically:1 therefore:6 taken:2 type:6 theoretical:1 more:3 flat:5 elliptic:1 becomes:3 curvature:2 carrying:2 labelled:1 particular:2 known:3 must:2 account:1 moser:1 sheds:1 rα:1 equation:24 work:1 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solv-int9801018.txt |@word partial:2 consider:11 remarkable:1 results:1 existing:1 leads:3 generalize:1 mnm:6 sci:1 expressions:2 devoted:2 kowalski:4 referring:1 pˆi:2 pˆk:1 technique:12 passage:3 recurrence:7 finally:9 stable:1 analogous:1 applied:2 straightforward:1 orthogonal:42 very:1 lyapunov:1 difference:2 condition:4 entire:1 hamiltonian:11 did:1 turns:5 solution:16 vector:6 shows:2 inspection:1 noted:2 zm:1 zn:3 zi:16 zk:10 direct:2 fold:1 rate:1 l2w:2 further:1 dynamics:1 linear:20 spectral:1 will:1 nonlinear:39 section:12 11b:1 43b:1 brief:1 expressed:4 43a:1 version:3 above:3 overcomplete:1 ˆi:25 ˆj:3 method:3 satisfy:11 respectively:3 here:3 reported:1 ansatz:13 xα:1 equations:8 appears:4 obtained:1 remark:8 generalizing:1 inspired:1 vectors:22 allows:1 approaches:2 experience:1 amount:1 resulting:1 action:3 fourier:1 via:2 useful:1 hermite:9 brought:8 coinciding:2 unit:1 tn:1 use:4 takes:3 would:3 recalling:1 positive:1 negative:1 properties:4 vol:2 therefore:10 taken:3 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solv-int9801019.txt |@word partial:1 consider:6 focus:1 leads:2 scalar:5 gd:21 generalize:2 edu:3 follow:2 tw:3 dickey:8 tr:7 finally:2 tk:5 under:2 case:8 provides:1 construction:1 results:1 wishes:1 putting:3 li:1 hamiltonian:38 did:1 turns:1 ferreira:1 correct:5 solved:1 science:2 gauge:2 anal:1 equation:14 nthu:2 consistent:5 second:12 further:2 substitute:1 spectral:1 what:1 brackets:5 section:5 xφ:11 near:1 expressed:2 above:2 fractional:1 ˆi:5 ˆj:1 ˆk:2 method:1 ˆn:4 coefficient:1 ibid:2 respectively:2 here:3 desired:3 identifications:5 tangent:1 ansatz:1 address:3 concluding:2 equations:11 obtained:6 remark:2 antisymmetric:1 rigorously:1 study:2 studied:1 accomplished:1 resulting:2 poisson:3 chang:1 via:1 huang1:1 put:1 use:1 would:5 commun:5 remains:2 ψq:2 next:2 ψj:4 ψk:7 ψi:3 ψm:1 ψf:3 theoretical:1 ψd:4 more:2 sort:1 introducing:1 sokolov:3 operators:2 validity:1 zimerman:2 virtue:1 particular:1 cases:1 iii:2 must:3 ml:1 originally:1 work:3 modified:5 paragraph:1 hope:1 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solv-int9801020.txt |@word sci:1 consider:3 existing:1 3a4:2 kowalski:2 inverse:1 depend:1 graph:1 bx3:3 finally:1 advantage:1 very:4 condition:6 presented:1 deals:1 vector:1 biological:1 noted:1 zn:1 rate:18 cost:1 design:1 dynamics:2 chem:2 linear:2 even:1 will:2 nonlinear:7 sum:1 supplied:1 above:1 new:10 method:2 satisfy:1 respectively:1 here:1 behaviour:2 reported:2 modelling:1 relaxation:1 represented:2 strong:1 equations:20 αip:2 αir:3 obtained:2 great:1 substance:1 study:1 vectors:1 resulting:2 action:1 suitable:2 via:1 discontinuous:1 brought:3 colloq:1 use:1 working:1 remains:3 positive:1 properties:2 narendra:1 chaotic:1 therefore:2 type:1 theoretical:1 more:1 introducing:6 flaw:1 iip:2 herein:1 particular:1 cases:1 account:1 fulfils:1 recall:2 equation:1 work:1 mi:1 following:5 making:1 arrive:2 example:4 theorems:2 predict:1 numbers:2 counting:1 species:2 szeged:1 renumbering:1 clarke:1 six:1 chemical:26 how:1 criterion:1 oscillatory:1 applications:1 plane:1 fi:1 law:1 data:1 attempt:1 dynamical:13 whenever:1 light:1 complexity:1 cannot:1 ultimate:1 order:2 typical:1 knots:1 unsolved:1 holds:1 indeed:1 years:1 paper:1 mentioned:2 kinetic:2 its:1 thank:1 fit:1 lj:2 coordinates:2 systems:27 practice:2 introduce:2 they:2 krzysztof:1 now:3 easily:4 term:1 volpert:2 university:1 lorenz:2 fields:1 found:1 reactions:8 differential:2 there:2 reduce:1 owing:1 our:1 really:1 shown:1 furthermore:2 denotes:1 increase:1 math:2 theory:3 mechanisms:2 possibility:1 complicated:1 york:1 besides:1 asymptotical:1 persists:1 nonnegative:1 int:1 first:2 xj:11 xk:3 xi:1 xn:4 omitted:1 variables:8 nonnegativity:1 nir:1 2a4:4 2a5:2 2a1:2 open:1 given:3 checked:1 system:21 xip:2 observations:1 essays:1 cycle:1 sixteenth:1 moscow:2 zeroth:1 part:1 x2:11 x3:6 x1:13 x6:2 coefficients:1 x5:6 scheme:1 showed:1 zero:1 bolyai:1 future:1 pairwise:1 maybe:1 colour:1 perturbative:1 viewed:1 mechanism:6 mip:1 mis:1 who:1 complexes:1 connected:1 letter:1 successive:1 nonlinearity:1 kj:2 kr:2 wasserman:1 mri:4 mrj:1 mechanical:1 physics:2 reactor:2 show:1 find:3 spite:1 written:2 should:2 jan:1 reactive:1 only:1 atmos:1 x4:11 interested:1 do:1 mixture:1 means:1 trees:1 ones:1 words:1 progress:1 designates:1 processes:1 covering:1 approach:1 arxiv:1 summary:1 geller:1 locating:1 requirement:1 set:2 observed:1 namely:1 result:1 kerner:2 satisfying:3 irj:2 classes:1 x24:3 x21:1 discovery:1 recently:1 ability:1 nature:1 jq:2 job:1 ji:4 key:1 solv:1 reaction:7 x2n:1 taking:1 according:1 anos:1 embedding:1 finds:2 experimental:1 point:1 simple:2 asymptotically:1 dimensional:3 polynomial:11 respect:1 σx1:3 σx2:3 σx3:1 been:3 quickly:1 carleman:2 reduction:5 pi:2 hardly:1 universal:4 oth:2 direction:1 arises:1 corresponding:8 restrictions:1 stoichiometric:2 present:1 case:1 pacs:1 aim:1 suppose:1 formats:1 iq:2 ip:3 ir:1 thus:3 surprisingly:1 ii:2 different:2 algorithmically:1 same:1 complex:3 difficult:1 used:1 see:1 singapore:1 i1:2 sums:1 hand:3 usually:1 infinite:2 recent:1 acknowledgement:1 nevertheless:3 poland:1 well:1 analysis:1 academic:1 without:1 bykov:1 model:1 arising:1 dimension:1 gorban:1 underlying:3 distant:1 world:1 differentiation:1 alternative:1 adv:1 seems:1 other:2 theorem:2 real:1 spectacular:1 format:1 showing:1 posed:1 possible:2 department:1 five:1 press:1 imposed:1 formal:1 necessary:1 like:1 systematically:1 qualitative:1 overdot:1 steps:2 arbitrary:1 reduced:6 grouping:2 mathematical:1 satisfactory:1 classical:2 sequence:2 some:2 understood:1 autocatalytic:2 describing:1 comments:1 conservative:1 everything:1 demonstrated:2 limitations:1 object:1 scientific:1 βis:3 βip:2 relating:1 hilbert:1 stage:1 integers:1 would:3 most:1 od:2 concentrations:2 soc:1 ars:2 into:3 within:1 down:3 linearization:1 appropriate:1 references:1 novosibirsk:1 elementary:1 additional:1 initial:1 quadratic:6 was:3 form:4 feinberg:1 construction:1 russian:3 removed:1 made:1 embedded:1 us:1 ul:1 limit:1 demonstrate:2 problem:4 called:3 constant:1 nauka:3 ai:5 abstract:1 aj:4 nri:4 general:11 single:1 referee:2 exist:1 constructed:1 ni:2 functions:1 graphs:4 vanishes:1 reality:1 field:1 valid:1 rx1:4 chemist:1 models:1 time:1 polynomials:1 helpful:1 a1:13 a3:9 a2:8 a5:2 a4:10 variable:3 pomorska:1 structure:1 implies:1 algorithm:1 kinetics:5 original:2 mass:1 embracing:1 having:1
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solv-int9801021.txt |@word concept:1 consider:5 chain:1 crucial:2 results:1 leads:1 eds:2 proposition:3 generalize:1 mℓ:1 edu:1 skip:1 follow:2 expressions:3 denotes:2 issues:1 whose:1 inverse:2 terms:5 superspace:2 dickey:1 ts:2 tn:1 finally:1 alvarez:2 tk:14 th:9 under:1 analogous:2 must:2 indicating:1 belonging:1 supported:2 advantage:1 zhang:2 multi:1 wave:3 entries:1 associated:2 manin:4 gurion:1 wronskians:1 turns:1 t2:2 solution:1 t0:1 t1:3 solved:1 commute:1 indices:2 relation:2 becker:2 equation:3 akns:2 wronskian:7 consistent:5 discover:1 b21:1 l2n:8 fold:1 integrability:1 further:4 odd:3 zs:2 even:7 will:5 what:3 nonlinear:5 power:1 chicago:2 sum:1 ψl2:1 expressed:1 henceforth:1 consistently:1 version:2 above:3 krivonos:3 new:2 wn:8 nes:2 contrast:1 coefficient:1 nas:1 condensed:1 full:2 respectively:1 mr:34 spacing:1 objects:2 free:6 active:1 equations:6 box:1 remark:3 ref:1 institute:1 study:3 allows:2 contradiction:1 later:1 products:1 wdw:1 action:2 mulase:1 fourier:1 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solv-int9801022.txt |@word represent:2 customary:1 consider:8 chain:3 pairing:1 equalities:1 nauchn:1 trigonometric:4 extensively:1 leads:4 roy:1 abelian:1 latter:2 ice:1 computation:6 edu:1 types:1 remarkably:1 zhedanov:1 contributions:2 eτ:1 dα:12 pril:4 ihep:1 whose:1 preserves:1 inverse:2 dα2:2 pˆi:1 spin:16 equivalence:1 γk:4 list:1 kη:43 funk:4 th:4 under:4 include:1 indicating:1 degeneration:1 belonging:2 r12:2 r13:2 straightforward:5 orthogonal:1 very:1 sα2:3 rise:1 conditions:1 choice:1 corollary:1 putting:2 ga:3 difference:23 matrices:2 condition:10 four:6 tokyo:1 obvious:2 riemann:1 presented:1 irreducible:7 t4:3 sklyanin:43 itep:3 solution:8 magnet:1 pˆ0:1 vector:8 section:8 indices:1 gauge:2 anal:4 smith:1 fashion:1 hasegawa:1 upper:2 zn:2 zi:9 renormalized:3 det:3 consistent:1 direct:2 iα0:5 sergeev:1 fold:1 second:4 pass:1 further:1 odd:1 substitute:1 linear:13 spectral:7 established:2 what:1 plays:2 appear:1 trivial:3 sum:1 version:1 poles:3 above:3 new:8 method:3 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solv-int9801023.txt |@word neighbors:1 limited:1 code:11 partial:1 consider:3 saves:1 results:4 leads:4 eds:1 concept:1 computation:4 edu:2 consists:1 follow:1 expressions:1 causes:1 gr:1 inverse:1 depend:1 tt:1 equivalence:8 βc2:1 program:24 those:2 under:5 include:1 ramani:1 fax:1 stud:2 very:1 later:1 differently:1 splitting:1 discretizations:1 difference:2 condition:3 four:5 school:1 solves:1 presented:2 proc:1 list:9 solution:4 enon:1 large:3 discrete:2 vector:2 prevent:1 force:1 consistent:1 batch:1 elegant:1 integrability:10 design:1 implemented:2 substitute:1 theory:1 spectral:1 trick:1 what:1 nonlinear:14 brackets:4 trivial:1 section:5 3w:2 analogously:1 serna:1 uniform:10 access:1 version:1 d0:2 fractional:3 new:3 method:2 coefficient:1 full:1 simultaneously:2 modify:3 here:3 desired:2 alone:1 quite:1 equations:16 change:2 obtained:1 search:1 ragnisco:1 shift:2 study:2 studied:2 allows:6 ignoring:1 amount:1 periodic:1 resulting:3 suggestion:1 pick:2 suitable:1 involves:1 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solv-int9801024.txt |@word concept:1 partial:3 lack:1 results:1 mines:1 leads:1 computation:8 depend:3 equivalence:1 under:3 applied:2 connects:1 wave:2 every:1 summarized:1 discretizations:1 difference:1 treating:1 school:1 presented:1 notes:1 list:2 discrete:1 vector:3 integrability:3 implemented:1 odd:1 substitute:2 theory:1 nonlinear:8 appear:2 sum:1 3v:1 uniform:3 version:1 fifth:1 new:1 satisfy:2 respectively:1 equals:1 here:1 equations:13 change:1 items:1 leaves:2 studied:1 allows:2 resulting:5 u3x:5 golden:1 projection:1 replace:2 apply:1 total:4 linearly:1 derivatives:13 use:4 uniformity:1 give:1 next:1 associated:1 volterra:5 more:2 introducing:1 known:1 hold:1 iii:1 must:4 equation:11 modified:2 ρn:5 infinitesimal:1 following:3 example:4 do:1 linearized:1 lacks:1 boussinesq:1 how:1 parameter:1 wolfram:1 fr:4 ubiquitous:1 after:1 lax:1 law:5 constants:1 algorithms:1 order:11 paper:1 through:1 its:7 systems:5 derivative:5 main:1 non:2 combination:3 material:1 erdmann:1 introduce:1 scaling:4 they:3 identically:1 term:1 2w:1 invariants:21 hamiltonian:2 2x:1 iff:2 each:1 monomials:9 arxiv:1 related:1 extended:2 obtains:1 our:3 eq:1 special:1 shown:2 u2n:5 since:2 research:2 equate:2 performs:1 u2x:17 integrated:2 math:1 linear:8 given:2 free:1 completely:1 pairs:1 language:1 recast:1 itoh:2 keep:1 hence:1 first:4 symmetry:12 variables:4 symbolic:3 number:1 rank:17 electronic:1 differ:1 similarly:1 system:13 their:3 echet:4 listed:4 shifted:1 centered:1 continuous:1 part:3 x2:1 x3:1 coefficients:2 λun:1 determines:1 require:2 second:1 submitted:1 classes:1 were:1 lotka:3 vx2:2 symmetries:22 say:1 obviously:1 any:1 lie:1 zero:1 latter:1 note:1 sciences:1 generalized:2 so:3 4u3:1 most:1 involving:1 class:1 soliton:1 physica:1 proceedings:1 vries:2 section:3 laws:2 show:1 supported:1 find:2 dilation:2 make:3 based:1 parameters:7 implementation:3 jan:1 only:2 explicitly:4 integrable:4 hereman:3 get:2 dependent:2 champaign:1 de:2 dx:7 lattices:2 dt:14 evolution:5 densities:5 differential:3 remove:4 common:1 set:3 computed:4 exists:2 computes:2 computer:1 result:1 prototypical:1 pattern:2 representatives:2 determined:1 various:1 invariant:7 conditions:2 available:1 terms:2 comp:1 jn:9 key:1 solv:1 both:1 many:6 density:2 equal:1 etc:2 pde:4 expression:3 ddes:8 ci:7 co:1 point:1 corresponds:1 dimensional:1 maintained:1 polynomial:5 respect:1 willy:1 pp:3 due:1 treat:1 observe:1 c3:1 c2:3 c1:3 careful:1 those:1 c4:1 case:4 ǫg:8 remaining:1 will:1 dept:1 match:1 u3n:1 cons:1 thus:4 iv:1 ii:1 reads:1 vt:1 vx:2 vanish:1 different:2 grant:1 recursion:1 algorithmically:1 belong:1 same:1 shifts:1 parts:1 modification:1 several:1 higher:7 independent:2 used:1 infinity:1 see:4 upon:1 steps:1 investigates:1 invariance:4 com:1 well:1 analysis:2 ccr:1 solve:6 components:3 model:1 usual:1 monomial:2 select:2 adv:1 unable:1 infinitely:5 lattice:4 combine:1 lett:1 u4x:1 transformation:1 euler:1 bin:1 depends:1 using:1 like:6 semi:1 follows:2 flux:2 yields:2 integrals:1 arbitrary:1 mathematical:1 www:1 methods:2 sequence:2 phenomena:1 library:1 examples:2 table:9 kdv:4 matching:1 provided:1 lead:1 avoid:1 integration:2 ddt:1 eliminate:1 prog:1 korteweg:2 dde:4 cgi:1 slight:1 equivalent:3 bi:2 about:2 package:5 http:1 consequently:1 automatically:1 software:2 colorado:1 into:2 within:2 nsf:1 three:4 references:1 determine:5 operator:2 additional:2 u4:1 there:1 u3:4 u2:9 conservation:6 way:1 unal:1 3u2:3 files:1 complete:2 form:4 pdes:7 reset:1 compute:6 ux:12 ut:5 6uux:3 up:1 ranks:2 un:149 similar:1 constant:2 int:1 likewise:1 abstract:1 conserved:5 exist:1 inc:1 mathematica:7 vanishes:1 illinois:1 details:3 test:1 theor:1 gets:2 structure:2 auxiliary:2 algorithm:3 assume:1 weights:7 time:1 quantity:1
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solv-int9801025.txt |@word lakshmanan:6 consider:1 results:1 eds:1 sci:1 expressions:1 xxii:1 equivalence:3 tr:2 finally:1 p2:1 orthogonal:1 very:1 iux:1 exact:1 qv2:1 alma:2 gue:1 presented:1 vector:3 10b:1 takhtajan:1 10a:1 b22:1 second:2 equation1:1 subscripts:1 nonlinear:3 g22:1 new:3 satisfy:2 respectively:1 γlij:1 here:2 tangent:1 b2j:1 equations:15 19b:1 box:1 study:1 studied:1 glg:1 4a2:2 ipt:1 unit:1 derivatives:1 iαs:1 m1:7 m3:2 m2:5 type:2 solitons:2 berlin:1 appendix:1 particular:1 known:1 cases:1 iv:1 ii:1 springer:1 sy2:1 equation:16 r3:1 following:6 example:1 14b:1 14a:1 61a:1 motion:1 end:1 s3:2 s2:1 mclachlan:1 ryx:1 ryy:1 algebra:1 after:2 lax:4 bks:1 representations:1 compatibility:1 sy:9 sx:11 st:1 so:2 fundamental:1 representation:2 ry2:1 g12:1 davey:1 symbols:1 paper:1 peterson:1 ln:1 coordinates:1 forms:1 13c:1 13b:1 13a:1 introduce:2 γkij:2 now:5 university:1 2f:1 l2:1 2a:3 2b:5 each:1 2l:1 found:1 ei:5 ej:1 series:1 magnets:1 eq:1 es:1 rt:1 shown:2 matrix:1 rs:2 robert:1 rx:12 ry:9 denotes:1 dxdy:2 blk:1 blj:1 ref:2 math:1 codazzi:1 8b:1 8c:1 8a:1 8d:1 8e:1 admits:2 usual:1 e1:5 e3:2 e2:3 ata:2 ist:3 counterpart:6 place:1 hence:1 first:1 xj:2 xk:1 xl:1 xx:1 2a2:1 given:3 unknown:1 eqs:8 1a:1 1b:1 too:1 2ab:4 segur:1 x2:3 x1:1 coefficients:1 18b:1 18c:1 kind:1 18a:1 were:1 20a:1 20b:1 lumps:1 weingarten:1 note:2 take:2 normal:1 soliton:5 kl:1 g11:1 kz:1 kx:1 reductions:2 notations:1 gauge:5 solutions:4 find:3 q1:1 q2:1 jan:1 integrable:9 local:1 v1x:2 ssx:1 notation:1 get:1 kxx:1 dy:1 qr:1 qt:1 arxiv:1 yield:1 qi:2 fixed:1 set:3 w3:2 w2:3 w1:2 ke3:1 satisfies:1 harvey:1 state:1 between:1 conditions:1 wj:3 solv:1 both:2 according:1 admit:2 v2x:1 dimensional:1 simply:1 mainardi:1 19a:1 int:1 basic:2 pi:2 po:1 partial:1 arises:1 families:1 denote:1 spin:3 present:1 case:2 p1:1 eit:1 eiy:1 eix:1 choices:1 viii:7 almaty:3 ix:5 vectors:3 metric:1 surface:2 uxy:2 vp:1 vq:3 2uy:1 ready:1 vy:1 different:2 φt:1 φx:2 complex:1 counterparts:2 hand:1 v1:3 moving:1 prescribed:1 well:3 position:1 dimension:1 21c:1 gdy:1 drdr:1 stewartson:1 previous:1 preprint:4 bullough:1 zakharov:3 lett:2 transformation:1 bil:1 bij:2 bik:2 iα:1 papers:1 21b:1 know:1 21a:1 bis:1 theor:1 like:2 follows:1 reduces:1 temporally:1 gjl:1 gji:2 myrzakulov:8 qxx:2 some:5 understood:1 dimensions:1 centre:1 vortex:1 11a:1 11b:1 equivalent:12 pq:2 2m:1 generated:1 christoffel:1 bji:1 references:1 question:1 gil:1 was:1 gij:4 function:2 form:3 gauss:1 uy:1 ux:8 whether:1 iqt:3 ishimori:1 called:1 defined:1 abstract:1 general:1 exist:1 sxx:2 functions:2 us:1 nx:1 ny:1 other:2 b12:1 b11:1 rx2:1 briefly:1 4i:2 problems:1 a1:2 rv2:1 sx2:1 a2:3 structure:2 nonintegrable:1 b1j:1 rxy:1 rxx:1 time:1 starting:1
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solv-int9801026.txt |@word customary:1 consider:5 yasuhiro:1 results:4 scalar:1 commute:1 go:1 gn:4 expressions:5 nakayashiki:2 whose:1 compose:1 const:1 calculate:4 former:1 finally:2 present:1 elliptic:2 under:1 stochastic:1 eβ:3 encircle:2 conjecture:1 vǫ:6 r12:7 r13:2 straightforward:1 mpa:29 very:1 regional:1 fan:1 summarized:1 difference:3 matrices:10 identity:1 school:1 hamiltonian:8 affinization:4 sklyanin:2 correct:2 vector:3 originally:2 zf:27 second:2 value:1 further:3 gm:1 even:1 plays:1 appear:1 section:7 expressed:1 3k:1 vega:1 above:1 new:1 method:2 satisfy:5 justification:1 construct:1 respectively:2 prescribe:1 proc:1 here:2 reported:1 ansatz:6 situation:1 represented:1 observing:1 obtained:2 zpn:1 parameters:1 technical:1 matsuo:1 schadschneider:3 prior:1 products:2 action:1 chain:6 studies:3 cancellation:1 ξk:15 uniquely:2 formulated:1 scaler:1 f1:6 unitarity:1 analyzing:1 evans:1 apply:2 use:2 takes:1 would:1 next:2 calculation:1 nucl:4 doubt:1 call:1 candidates:1 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solv-int9802001.txt |@word consider:1 alg:2 invent:2 commute:4 polinomials:1 particles:7 inverse:5 excluded:1 under:2 fermionic:2 di2:1 straightforward:1 very:1 wave:1 jack:8 affect:1 difference:1 exact:1 condition:7 annihilated:1 hamiltonian:9 solved:1 subscript:1 eigenvalues:14 degeneracy:4 zi:12 zj:9 mi:2 sin2:1 further:1 linear:1 subscripts:2 nonlinear:1 stands:1 deeply:1 expressed:2 version:2 concisely:1 fractional:3 new:3 unrestricted:1 d1:3 bn:6 contrast:1 body:1 condensed:1 lee:1 exchange:7 here:2 operating:1 others:1 represented:3 laughlin:1 coupling:3 equations:5 z1:1 deduced:1 obtained:3 antisymmetric:1 institute:1 involved:1 vectors:1 allows:1 reason:2 suggests:1 products:1 permutation:1 formulated:1 useful:1 hermite:1 altshuler:2 decrease:2 sgn:1 redefining:1 total:2 univ:1 use:1 dunkl:2 would:1 commun:2 recalling:1 positive:3 jpn:1 nagoya:4 nonsymmetric:3 next:2 nucl:2 examination:1 ki2:1 taken:1 type:1 theoretical:1 lowering:7 duality:2 operators:34 known:2 cases:2 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solv-int9802002.txt |@word partial:1 consider:5 rev:5 focus:1 gx:1 illustrated:1 scalar:4 cooperative:1 go:1 3a2:1 issues:2 whose:1 depend:1 violate:1 ruck:1 presents:2 charge:1 th:1 under:1 anharmonic:1 advantage:1 very:2 wave:2 iut:2 condition:4 solves:1 presented:3 ref:1 having:1 discrete:1 science:2 configurations:3 sign:3 translating:1 second:2 follow:1 further:3 odd:4 scientific:1 even:1 nonlinear:12 plays:2 appear:5 giving:1 expressed:1 current:1 above:8 fractional:1 new:3 method:2 degree:1 component:1 here:7 water:1 departamento:2 galileo:2 sine:4 equations:22 appears:3 change:2 obtained:2 remark:1 ctp:1 institute:1 allows:1 resulting:1 usually:2 makes:1 jackiw:4 via:2 private:1 use:2 would:1 recalling:1 simons:1 next:1 nucl:2 theoretical:1 more:3 introducing:2 knows:2 engender:3 solitons:11 odinger:5 instantons:1 known:4 cases:1 dey:1 recall:4 equation:36 work:3 modified:2 values:1 following:1 modifies:1 example:3 fc02:1 solved:2 relativistic:9 states:1 sense:1 evidently:3 provide:1 write:2 far:1 94er40818:1 adjacent:1 sin:1 map:2 fx:3 after:1 dx2:3 mag:1 waves:9 summarize:1 branches:1 caixa:1 whenever:1 sech:1 b167:1 chern:1 explicit:9 maintain:1 so:4 order:8 paper:1 excitations:1 its:1 thank:1 interesting:9 writing:1 systems:13 derivative:5 travelling:9 main:1 setting:1 non:3 introduce:2 break:1 they:1 das:1 now:8 hall:1 coffey:1 term:1 identified:1 2a:1 each:1 found:3 aglietti:1 side:1 l9:1 griguolo:2 differential:5 another:3 simplicity:1 energy:1 reduce:1 related:7 investigated:2 static:1 quantum:1 laboratory:1 mapping:1 beyond:1 eq:11 shown:1 space:3 restricted:1 since:2 lagrangian:2 research:1 may:1 contained:1 suffices:1 math:3 wiley:1 linear:1 ısica:2 possibility:3 standard:3 york:1 pairs:1 chiral:21 impose:1 motion:5 gordon:4 generalizations:2 first:7 already:3 symmetry:4 restrict:1 done:2 directly:4 given:4 start:1 interact:1 system:8 least:1 assumption:1 e54:1 siam:1 ribeiro:2 gives:2 para:2 contains:1 whitham:1 part:1 debnath:1 natural:1 x0:2 x1:2 than:1 vxxx:2 kind:1 holland:1 richer:1 matter:1 determined:2 amplitude:1 were:2 providing:2 jpn:1 boston:1 generalization:1 manuscript:1 seem:1 ideas:1 note:1 instance:5 potential:4 generalized:25 mit:1 rabello:1 play:1 shall:2 birkh:1 extending:2 connected:1 jul:1 pair:5 class:2 soliton:4 nonlinearity:5 considered:5 phil:1 breather:1 points:1 exp:1 velocity:8 physics:2 show:2 supported:1 tecnol:1 gauge:1 solutions:32 d2:14 find:1 realizing:1 parameters:4 situations:2 topological:1 should:2 only:1 integrable:1 local:1 hereman:1 dh:5 get:3 de:9 seminara:2 da:1 dx:3 dy:15 dv:8 du:7 gen:2 nicely:1 fields:7 arxiv:1 acknowledgments:1 recife:1 set:2 see:6 result:1 recently:4 subject:2 brazil:3 federal:2 nuclear:1 definite:3 santos:3 written:1 identification:1 simplest:1 progress:1 boundary:2 reading:1 conditions:1 terms:2 extend:1 attention:2 weak:1 however:1 vanishing:2 jo:1 solv:2 both:1 cos:1 contrasted:1 ıfico:1 b516:1 reproduces:2 propagation:1 connection:1 context:3 argue:1 finds:1 point:1 bδ:1 mkdv:5 ct:5 considering:3 combines:2 xα:3 been:4 defined:3 reduction:1 basic:1 pessoa:1 pi:2 define:1 corresponding:2 relaxing:1 concerning:1 search:1 plasmas:1 former:2 present:10 case:12 multi:1 tanh:3 cast:1 behavior:4 investigating:1 du2:1 property:1 planar:1 coupled:8 them:2 uxx:3 obeying:1 vt:2 crystals:1 vx:2 uxxx:6 technology:1 different:1 make:2 roman:1 same:4 arguments:1 several:3 higher:1 used:2 singapore:1 cubic:1 effect:1 hand:1 ion:1 auser:1 takaoka:1 invariance:2 recent:2 relies:1 schr:6 center:1 scenario:2 changes:1 solve:1 model:5 dimension:1 manifold:1 just:1 being:1 dφ2:1 identify:2 ogico:1 enters:1 preprint:2 density:3 seems:1 nacional:1 other:6 lett:6 take:1 real:6 iθ:1 iν:1 sytems:1 possible:1 game:1 know:1 vacuum:1 world:1 postal:1 formal:1 dimensional:4 like:3 specific:3 imposes:1 korteweg:4 arbitrary:1 works:3 parity:2 because:2 deal:2 some:5 searching:1 examples:3 kdv:32 happens:1 provided:1 describing:4 investigations:6 comments:1 ıba:2 does:1 provides:1 pernambuco:2 conselho:1 refer:1 obey:3 novelties:2 agreement:1 acoustic:2 between:1 central:1 desenvolvimento:1 o:1 distinct:2 carries:1 extensions:1 obeys:1 introduced:5 soc:1 cambridge:1 presence:2 communication:1 within:3 right:1 references:1 amsterdam:1 hep:1 additional:1 u5:1 u4:1 there:6 cient:1 u3:4 u2:8 dispersion:2 width:1 quadratic:1 way:1 naturally:1 function:5 north:1 form:6 offer:1 funds:1 but:2 bazeia:4 cnpq:1 ux:6 ut:6 smooth:4 us:4 unveils:1 dχ:1 similar:1 constant:1 int:2 abstract:1 describe:1 ao:1 general:1 exist:1 controlled:2 universidade:2 physical:1 functions:3 when:5 vanishes:1 arctan:1 field:1 valid:1 role:3 details:1 department:2 offered:1 models:2 important:1 bounded:1 massachusetts:2 dos:1 structure:1 rajaraman:2 coupling:1 dφ:7 vries:4 governed:2 dρ:2 presenting:1 hirota:1 appl:1 requires:2 original:2
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solv-int9802003.txt |@word consider:3 gg:2 gd:3 generalize:2 gb:3 antichiral:2 expressions:1 gl:10 gj:1 gi:8 superspace:2 tr:2 tn:2 under:2 analogous:1 include:1 lkp:1 rise:3 hamiltonian:5 turns:1 t2:14 solution:1 item:1 math:4 indices:2 consistent:2 l2n:2 second:10 further:2 residue:1 what:1 brackets:3 section:4 3u:1 3j:2 suspect:2 above:1 krivonos:8 new:17 ever:1 acknowledgments:1 contrast:1 coefficient:1 lukierski:1 here:7 consideration:2 equations:17 z1:8 z2:8 obtained:3 institute:2 resulting:1 lred:2 poisson:1 hospitality:1 via:1 family:3 extra:3 ls:2 summation:2 research:1 standing:1 derivatives:1 use:1 covariant:3 contains:1 nucl:1 bases:2 therefore:3 theoretical:3 more:2 operators:13 correspondingly:1 known:3 cases:1 fermionic:12 keeping:1 chaichian:1 equation:12 work:2 values:1 following:9 example:2 gallot:2 give:2 pieces:1 numbers:1 boussinesq:2 provide:1 write:1 how:2 nontrivial:1 plus:1 parameter:1 gnls:2 description:2 algebra:5 derived:2 fa:3 lax:49 realized:1 natural:1 third:3 labelle:1 explicit:2 su:4 rather:1 so:1 representation:4 hierarchy:15 indeed:2 over:2 years:1 course:1 through:1 looks:1 dw:7 still:1 its:3 before:1 thsun1:2 la:3 ln:5 interesting:2 conjugation:1 forms:1 djd:2 mail:1 hidden:2 might:1 supersymmetry:10 non:1 junction:1 propose:1 daj:1 break:1 they:3 bogoliubov:1 now:2 hierarchies:13 nor:1 ift:2 easily:1 term:1 2w:1 january:1 university:1 2f:9 2g:3 l1:1 characterized:1 constraints:1 spinor:1 differential:2 dωj:1 t3:4 laboratory:1 borna:1 ep:1 out:1 shown:1 matrix:4 discrete:1 since:1 denotes:3 got:1 red:1 foundation:1 standard:2 complicated:2 flows:4 dubna:3 e2:2 pairs:3 chiral:3 could:1 turn:1 first:2 symmetry:2 ǫdd:2 number:3 peculiarity:1 bellucci:1 least:1 another:1 checked:1 rewritten:3 introduction:1 system:3 construct:4 their:4 realization:2 dfg:1 dfa:1 gives:3 moscow:1 stress:2 part:3 somewhat:1 ivanov:5 kind:1 sections:1 integrability:2 providing:1 russia:1 symmetries:1 delduc:4 mind:1 generalization:3 close:1 self:1 note:1 internal:1 take:1 εj:1 εg:1 subscripts:1 letter:2 pair:5 class:2 surprising:1 considered:1 t2n:1 flow:8 hints:1 kp:6 physics:3 laws:1 reductions:2 supported:1 purely:1 find:1 sorin:5 based:2 just:1 parameters:1 should:1 jan:1 only:5 explicitly:3 integrable:5 hamiltonians:3 local:1 do:2 dj:19 means:2 df:14 dg:41 straightforwardly:1 ones:4 dz:5 during:2 du:5 subscript:1 evolution:3 exhibiting:2 fields:4 arxiv:1 yield:1 redefined:1 including:1 j1:3 j2:2 j3:1 see:1 wroc:1 written:1 simplest:2 µd:1 neither:1 terms:6 extend:1 wn:1 however:1 js:3 comm:1 solv:5 thank:1 both:1 last:1 limits:1 region:1 uni:1 mean:1 relevant:1 point:1 superfield:5 grants:1 moreover:1 better:1 mathieu:1 described:1 transformations:2 basis:1 three:3 been:6 appears:1 int:5 reduction:4 describes:1 basic:3 algebras:1 pl:2 systems:1 aj:2 families:3 6g:1 6j:2 covariance:1 understand:1 derivative:1 spin:6 present:7 case:12 look:1 single:1 evaluated:1 aim:2 while:4 intas:1 conformal:1 procedure:1 wroclaw:3 bonora:2 coupled:2 thus:7 reads:3 itself:1 supercurrents:1 superconformal:4 currents:1 rfbr:1 different:4 grant:2 generic:2 same:1 proved:2 finite:2 yung:1 dgb:6 extended:2 dgd:2 again:1 dgi:6 dgl:4 infinite:6 popowicz:3 poland:1 well:1 analysis:1 coordinate:1 possesses:2 proposed:4 obtain:1 gdg:2 multiplet:1 previous:1 field:2 belongs:1 conjugated:1 lett:9 easy:1 mod:1 2u:1 read:2 immediately:2 bit:1 coincide:1 formal:1 like:2 follows:3 reduces:1 δj:3 byproduct:1 δg:4 conclusion:1 sissa:1 parity:1 some:1 understood:2 respect:1 kdv:34 pashnev:1 toppan:1 superfields:19 provides:1 ddg:3 equivalent:1 bj:4 super:7 extension:4 discussed:1 mutually:1 extensions:4 2j:4 act:1 introduced:1 latter:1 square:1 references:1 operator:34 bosonic:12 additional:2 conservation:1 way:3 jinr:5 was:2 function:1 form:6 but:1 repeated:2 construction:1 hn:4 delta:1 russian:1 partially:1 ut:1 inside:1 us:5 ωj:2 limit:3 uj:1 demonstrate:1 problem:1 detailed:1 constant:2 defined:3 recognize:1 abstract:1 describe:2 general:12 conserved:1 our:1 supersymmetric:11 check:3 constructed:5 grassmann:3 no:2 commutes:1 ext:1 2dd:2 other:1 2dj:6 star:1 problems:1 includes:1 structure:3 corresponding:4 together:3
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solv-int9802004.txt |@word neighbors:1 code:8 partial:4 consider:10 chain:2 aids:1 rev:1 varying:1 results:3 invent:1 leads:2 eds:1 computation:32 edu:1 go:1 gn:1 expressions:2 involved:1 plasmas:1 soc:3 whose:1 inverse:4 depend:5 calculate:1 technique:1 finally:4 program:4 those:2 under:7 discretization:3 unit:1 applied:3 lack:2 g2:22 straightforward:2 connects:2 wave:3 p1:2 should:2 suggests:1 surprise:1 discretizations:1 nonlinearity:2 difference:7 exact:1 condition:7 treating:1 school:1 solves:1 presented:2 forth:1 list:4 solution:5 enon:1 large:1 discrete:5 vector:6 fourier:1 optics:2 nagata:1 force:1 euler:1 consistent:2 coefficient:1 direct:4 suffices:1 sign:1 carefully:1 integrability:18 follow:1 further:1 dynamics:1 implemented:2 substitute:3 theory:2 established:1 gibbons:1 nonlinear:33 appear:1 trivial:1 section:9 3w:2 analogously:2 expressed:1 hereditary:5 access:1 version:1 fifth:4 above:3 new:6 method:6 contrast:1 instructions:1 satisfy:2 investigating:1 degree:5 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solv-int9802005.txt |@word lakshmanan:1 consider:5 leads:1 gj:3 sch:1 devoted:1 γz:5 γx:1 tz:4 schiff:2 tx:1 tt:1 tn:13 program:1 those:2 th:2 analogous:1 include:3 song:1 choice:1 sons:1 2γx:2 difference:1 condition:3 specify:1 positions:1 notes:1 t2:2 t3:2 adjust:1 manifestly:1 anal:1 optics:1 concluded:1 neighborhood:1 consistent:1 second:1 7th:4 further:1 dynamics:1 substitute:1 even:1 what:1 nonlinear:3 section:4 analogously:2 consistently:2 poles:1 fuchssteiner:1 above:2 new:3 method:4 coefficient:1 full:1 respectively:4 modify:1 here:7 inverse:1 ansatz:1 others:1 represented:1 path:1 equations:34 appears:2 z2:6 z3:5 obtained:8 remark:1 larger:1 leaving:1 professor:1 resonance:3 useful:1 problematic:1 plenum:1 replace:1 santini:1 recurrence:2 use:3 feb:1 proceed:1 would:1 positive:1 jpn:1 negative:1 depicted:2 therefore:1 rearranging:2 more:2 becomes:3 ρxx:2 occurred:1 known:1 must:5 ramani:3 springer:2 room:1 equation:67 ρj:7 ρl:1 little:1 following:2 root:2 degenerate:1 figure:6 give:2 calculation:2 contradicts:1 performed:2 want:1 sense:2 times:2 verlag:2 respective:2 lacks:1 painlev:9 discussion:2 means:1 feature:1 pure:1 singular:1 may:4 after:1 derived:1 movable:2 routes:2 lax:11 coming:1 fj:3 φ2x:11 types:1 short:1 physical:1 imply:1 explicit:2 liner:1 so:4 allow:1 φy:1 representation:2 order:19 davey:1 help:1 hierarchy:23 mainly:1 satisfied:2 course:1 paper:5 through:3 mentioned:1 japan:1 its:1 derive:1 thank:1 directional:1 gen:1 forms:3 choose:1 constitutes:1 setting:1 non:3 fukuyama:3 fokas:2 they:1 singularity:1 now:2 yu:2 hierarchies:3 possess:1 represents:2 february:1 equality:1 university:1 each:1 2n:3 differential:2 constitute:2 toda:2 γx3:3 our:1 special:1 shown:1 space:1 furthermore:1 since:1 chaos:1 replacing:1 investigation:1 izv:4 conjectured:1 denoted:1 correct:1 math:7 shiga:1 wiley:1 differ:1 free:1 quite:2 admits:1 clarify:1 complicated:1 pairs:1 applications:1 could:1 ist:1 hence:2 ritsumeikan:1 first:1 variables:3 powerful:1 number:3 xx:2 relations:2 stage:1 equating:1 passes:1 given:3 checked:2 rewritten:1 similarly:2 introduction:1 leading:1 5th:11 system:5 construct:5 their:5 appl:2 calculations:2 scheme:1 structures:2 tool:1 part:1 x2:8 x3:6 x1:3 coefficients:3 x5:2 john:1 unfortunately:1 double:1 namely:4 determined:2 takeshi:1 contrasted:1 powers:7 lowest:1 rewrite:1 7j:1 correspond:1 enforces:1 conjugate:1 apparently:1 orders:1 solitons:1 lec:1 instance:1 potential:12 schematically:1 lectures:1 unless:1 though:4 uyy:1 reach:1 simplify:1 pair:1 inconsistency:1 soliton:2 laurent:3 clear:1 later:1 coincides:1 physica:1 kp:5 exp:1 hietarinta:3 physics:2 specification:1 laws:1 nls:5 joshi:1 solutions:5 substituting:1 find:1 parameters:2 title:1 should:1 analytic:1 only:1 explicitly:1 x4:2 ambiguity:2 integrable:23 local:1 dominant:1 get:1 dependent:2 kusatsu:1 ds:1 kadomtsev:1 approach:1 arxiv:1 acknowledgments:1 investigate:1 ut:3 fixed:2 requirement:1 set:2 up:1 depends:1 computer:1 sec:3 existence:1 discussions:1 said:1 ways:1 review:1 between:1 conditions:1 terms:4 ju:1 jp:3 however:9 wtc:1 comm:1 extent:1 solv:4 both:1 kruskal:2 etc:2 comes:1 point:2 appeared:1 hoppe:1 dimensional:10 mkdv:1 applicability:1 proved:2 described:1 three:1 been:3 z1:5 kouichi:1 logarithmic:1 abstract:1 systems:2 quantities:1 concerning:1 understand:1 func:1 c2:1 affirmative:1 present:2 case:8 choices:2 situation:1 property:2 procedure:1 coupled:3 thus:1 tzn:1 different:6 φx:43 recursion:5 φz:22 formulations:1 matsuno:1 same:6 unity:1 complex:1 φj:7 several:1 φl:1 higher:9 extended:1 cubic:1 carnevale:1 purpose:1 infinite:2 nevertheless:1 well:1 analysis:1 consistency:2 coordinate:1 dimension:1 manifold:2 proposed:1 grammaticos:3 obtain:2 using:1 facts:1 scattering:1 succeeding:1 previous:2 candidate:1 zakharov:1 conclude:1 seems:2 except:1 weiss:1 add:1 other:3 transformed:1 lett:2 trilinear:3 transformation:1 possible:2 department:1 integer:1 bit:1 unique:1 δz:9 like:3 follows:1 arose:1 discarded:1 arbitrary:10 essential:1 replacement:1 because:1 some:2 examples:1 kdv:19 dimensions:13 lead:1 resonances:4 defined:1 does:3 eliminate:1 faddeev:1 tabor:2 equivalent:1 expansion:3 bs:32 takes:2 2cy:1 extension:1 most:1 discussed:1 dependence:1 o:4 reduced:5 extensions:6 konopelchenko:2 2iπ:1 soc:1 own:1 φxx:34 φxt:8 into:5 integral:1 ussr:4 references:1 determine:2 operator:11 log:1 indispensable:1 there:5 transform:1 conservation:1 102a:1 was:2 function:4 form:12 but:2 construction:1 ux:1 uz:3 whether:2 characteristic:1 γx2:3 us:5 kawahara:1 similar:1 called:1 ac:3 constant:3 int:4 universal:1 conserved:1 exist:1 formulation:1 check:2 constructed:4 functions:4 integrability:6 no:2 mathematica:1 detail:1 application:1 valid:1 branch:1 spatial:2 test:7 mathematics:1 vanished:1 operators:7 odinger:1 variable:1 structure:1 algebraic:2 bkc:3 assume:1 uncovered:1 sasa:1 4d:1 starting:1 having:1
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solv-int9802006.txt |@word lakshmanan:5 consider:2 results:2 gy:1 gx:1 eds:1 sci:1 xxii:1 33a:1 equivalence:1 tr:3 29a:1 finally:1 p2:2 orthogonal:1 geometrical:1 iux:1 ay:1 exact:1 qv2:1 alma:1 34b:1 presented:3 vector:1 strachan:2 takhtajan:1 b22:1 second:2 zx:1 zy:1 subscripts:1 nonlinear:1 g22:1 section:1 lifshitz:1 new:3 method:1 3e:2 eω2:1 respectively:2 γlij:1 here:2 b2j:1 19a:1 19b:1 box:1 glj:1 vectors:1 bry:1 29b:1 ipt:3 unit:2 derivatives:1 feb:1 m1:9 m3:6 m2:10 type:2 becomes:3 jmp:1 curvature:1 berlin:1 known:2 cases:2 iv:3 iii:2 33c:1 33b:1 ii:3 springer:1 2bc:1 equation:24 work:1 mj:1 following:8 example:1 ready:1 61a:1 counterpart:5 end:1 s3:3 s2:4 s1:3 write:1 mj0:1 ryx:1 ryy:1 konopelchenko:1 description:1 algebra:1 after:2 23a:1 23b:1 lax:4 bks:1 representations:1 compatibility:1 sy:11 sx:11 st:5 so:3 sn:1 fundamental:1 representation:2 ry2:1 g12:1 davey:2 multidimensions:1 symbols:1 paper:2 looks:1 peterson:1 mclachlan:1 ln:1 interesting:1 coordinates:1 forms:1 τy:2 main:1 13b:1 13a:1 introduce:1 landau:1 γkij:2 22a:1 now:3 34a:1 university:1 34c:1 2e:1 2f:1 2a:3 2b:6 each:3 found:1 en:1 ei:2 ek:2 series:1 magnets:1 our:1 es:1 rt:2 shown:2 matrix:1 space:2 rx:14 ry:11 denotes:1 dxdy:2 blk:1 blj:1 ref:3 math:1 codazzi:1 admits:2 e1:17 e3:9 e2:18 ata:1 aj0:1 m20:2 ist:4 motion:1 int:1 isotropic:1 hence:3 first:1 xj:3 xk:1 already:1 xl:1 2a2:1 given:3 introduction:1 1x:1 eqs:4 construct:2 too:2 final:1 2ab:4 17b:1 17a:1 segur:1 x2:2 x1:1 coefficients:1 kind:1 were:2 w2:2 iφt:1 7b:1 7a:1 curves:1 solitons:3 lumps:1 note:3 centre:1 qxxx:2 class:2 32b:1 soliton:5 32a:1 kl:1 g11:1 kz:1 ky:3 12a:1 12b:1 reductions:5 gauge:3 solutions:4 find:2 q1:2 q2:2 only:2 em3:2 em2:1 integrable:12 local:1 v1x:2 ssx:1 notation:1 get:4 dx:1 dy:1 dt:1 evolution:2 qr:1 qt:3 conditions:1 arxiv:1 yield:1 qi:2 view:1 set:3 arx:1 see:1 us:2 w1:2 state:1 approach:4 solv:1 31b:1 31a:1 both:1 many:1 rijk:2 according:2 admit:4 cn:1 point:1 cb:1 v2x:1 dimensional:9 m10:4 mkdv:2 ct:1 pq:3 equations:29 ai:2 basic:1 pi:2 po:1 partial:1 qx:1 xxi:2 denote:1 spin:3 present:2 case:7 p1:2 will:2 viii:4 almaty:4 a20:1 ix:5 metric:1 surface:3 uxy:1 vp:2 vq:4 reads:1 2uy:1 vx:2 vy:1 different:2 az:1 φt:3 φx:2 φy:1 same:1 singapore:1 counterparts:9 hand:1 v1:3 older:1 well:2 position:1 usual:1 26b:1 26a:1 gdy:1 drdr:1 obtain:2 world:1 stewartson:2 previous:1 nlse:1 preprint:5 4a2:1 bullough:1 zakharov:3 lett:2 real:1 bil:1 bij:2 bik:2 iα:1 papers:1 using:5 bis:1 theor:1 like:3 28a:1 28c:1 28b:1 cy:1 gjl:1 gji:2 myrzakulov:16 qxx:3 reduces:1 terminology:1 2eq:1 some:13 examples:2 30a:1 kdv:2 30c:1 vortex:1 manipulations:1 scientific:1 equivalent:20 mainardi:1 2m:1 bx:1 15a:1 generated:1 15b:1 km2:2 km1:1 φxy:1 φxx:1 christoffel:1 22b:1 bji:1 references:1 ixa:1 gil:1 was:1 gij:4 form:8 uy:1 ux:7 iqt:4 ishimori:5 below:2 defined:1 abstract:1 aj:1 general:1 sxx:2 formalism:1 30b:1 functions:1 nx:1 ny:1 other:4 b12:1 b11:1 rx2:1 conclusion:1 elements:1 a10:1 time:3 problems:2 a1:2 rv2:1 a3:1 a2:5 nonintegrable:2 2d2:1 starting:2 rs:2 b1j:1 rxy:1 rxx:1 4i:3 4f:1 4d:1 4e:1 4b:1 4c:1 4a:1
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solv-int9802007.txt |@word partial:1 consider:14 rev:6 focus:3 gx:1 illustrated:1 eds:1 scalar:18 cooperative:1 follow:5 contributions:2 issues:2 concerned:1 trivial:1 containing:1 presents:8 charge:3 helps:2 th:3 under:1 case:32 µuv:1 straightforward:1 zhang:2 very:10 conditions:1 results:2 every:1 difference:1 iut:2 condition:1 leads:4 ref:5 tanh:8 solution:9 leave:1 solved:6 vector:2 science:1 relation:1 configurations:14 dealing:1 direct:1 sign:3 burges:1 second:10 further:6 dynamics:2 odd:3 scientific:2 even:6 what:1 nonlinear:19 appear:3 fine:2 section:4 expressed:1 find:1 current:4 fuchssteiner:1 above:24 fractional:1 new:6 3a:1 method:2 edelstein:1 satisfy:1 led:1 respectively:3 component:1 here:19 growing:1 identifications:1 possibility:3 xα:7 equations:82 appears:7 z2:1 obtained:4 search:5 ctp:3 spite:2 singapore:2 institute:1 inspired:3 studied:1 allows:4 reason:1 example:5 trial:1 chemical:1 resulting:2 usually:1 makes:5 jackiw:5 named:1 via:4 controls:2 use:3 feb:1 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solv-int9802008.txt |@word represent:1 concept:2 homomorphism:14 consider:16 chain:3 bernard:1 induces:1 results:9 existing:1 leads:8 proposition:3 karimipour:2 computation:3 hyperboloid:1 expressions:2 contributions:2 devoted:2 whose:2 certainly:2 inverse:2 depend:2 bivector:3 paris:1 equivalence:5 b264:1 recurrence:4 finally:4 preserved:1 th:32 under:8 worth:1 p2:34 expressing:1 straightforward:4 very:1 implicitly:1 rise:11 pressley:1 dokl:1 geometrical:1 corollary:1 should:4 antipode:2 fall:1 emphasized:2 matrices:1 deformations:17 condition:9 preserve:1 illustrated:1 basics:1 obvious:1 immediately:2 presented:12 turns:1 xyz:7 nucl:1 magnet:3 involution:12 vector:2 math:11 fadeev:1 manifestly:1 il:1 y2:14 possibility:1 sapienza:1 coordinate:1 dealing:1 sin2:4 direct:4 suffices:1 cosh:7 integrability:14 omez:1 j22:4 further:3 dynamics:2 implemented:1 analogue:1 quite:3 canonical:25 even:1 aim:2 what:1 nonlinear:1 appear:2 brackets:3 cone:1 section:13 expressed:1 3j:2 3i:2 version:1 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solv-int9802010.txt |@word replacing:2 precise:1 logarithms:1 partial:1 consider:9 establishes:1 mnp:1 results:6 interpret:1 commute:2 entropy:5 zˆl:1 go:1 follow:4 expressions:2 gl:3 hole:11 whose:2 inverse:7 depend:2 calculate:1 spin:2 γv:7 finally:3 does:2 manifolds:5 th:2 stable:3 exposition:1 analogous:1 γg:3 spec:1 norm:5 kσ:3 kρ:4 comm:1 g2:5 straightforward:1 outside:1 very:1 holds:2 assuming:1 ψk:1 wave:21 electron:1 every:2 ηir:4 entries:1 resonant:1 li:2 difference:3 matrices:2 condition:11 umn:1 immediately:2 hamiltonian:8 suffices:1 tokyo:2 solution:38 yˆk:1 magnet:1 admissible:1 convenience:2 vector:3 phase:1 math:5 yale:1 indices:1 eigenvalues:2 noted:2 solutions:14 zl:15 prevent:1 approximately:2 force:1 periodicity:6 zk:11 subtracting:1 coefficient:2 direct:1 sign:1 jump:2 consists:2 zero:7 ǫm:1 pass:4 rigorous:1 writing:1 zp:4 even:3 established:1 what:1 nonlinear:2 minimize:1 richard:1 g21:1 partition:1 trivial:1 sum:5 near:1 expressed:2 gj:2 version:5 subspaces:1 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solv-int9802011.txt |@word represent:1 partial:3 consider:7 φ1c:1 results:6 segr:1 illustrated:1 eds:4 scalar:3 proposition:13 consists:1 follow:2 research:1 reasoning:2 row:1 compact:1 whose:1 preserves:1 depend:2 mallet:1 paris:2 subjected:5 acting:1 finally:4 tj:37 preserved:1 th:2 dressing:2 tc:4 ingredient:1 case:5 conjecture:1 algebraization:1 straightforward:2 orthogonal:4 rc:8 conditions:1 geometrical:1 corollary:9 every:1 cellular:1 formula:2 difference:6 matrices:1 condition:7 arrange:3 leads:3 riemann:1 presented:4 x0c:8 turns:1 notes:1 applicable:1 2xt:4 evy:1 convenience:1 vector:13 inscribed:1 relation:1 warszawa:1 rk:3 permutability:1 zn:4 lecture:1 coordonn:2 za:1 integrability:15 pass:1 further:1 reine:1 quite:1 linear:3 bilinear:3 fℓ:2 const:1 appear:4 brackets:1 fact:2 section:12 expressed:1 sur:2 above:11 new:11 net:1 connected:2 method:4 satisfy:12 supporting:1 even:1 component:2 here:2 diagonal:4 les:3 address:1 based:2 sine:1 equations:33 obtained:9 remark:11 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solv-int9802012.txt |@word represent:1 consider:6 remarkable:1 results:1 four:1 scalar:3 commute:1 consists:3 wholly:1 cases:1 gh:18 ihep:1 depend:1 re:3 tu:1 λn1:1 γk:27 kβ:11 kα:11 tk:1 th:1 analogous:1 fermionic:4 xtk:1 division:1 amplitudes:6 g2:3 advantage:1 orthogonal:1 very:2 translations:2 isomorphism:1 formula:1 li:3 difference:3 matrices:8 condition:2 scholar:1 solves:3 hamiltonian:5 solution:2 ri:2 large:1 discrete:3 vector:4 indices:3 eigenvalues:3 equation:15 configurations:1 zm:7 zn:1 dealing:1 direct:5 zb:3 sign:3 sergeev:6 integrability:1 further:2 zp:4 linear:8 spectral:1 established:1 nonlinear:1 appear:1 giving:1 sum:5 layers:1 international:1 acknowledgments:1 ek1:2 3d:6 devoted:1 chose:1 maillard:1 quasimomenta:1 tangent:1 expansion:1 represented:1 path:3 shortness:1 equations:5 z1:3 z2:3 z3:1 obtained:2 ekm:2 remarks:1 institute:2 vectors:4 allows:1 example:6 p2:12 p4:10 action:8 fourier:3 changes:2 via:3 useful:3 divide:1 family:2 extra:1 private:1 p3:14 dζ:1 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solv-int9802013.txt |@word consider:7 osp:2 explicit:2 splitting:2 integration:1 leads:8 scalar:7 commute:2 gr:3 whose:6 depend:1 superspace:7 show:2 tr:8 trivial:2 containing:2 charge:2 tk:3 th:2 under:1 include:1 tb:14 ta:1 applied:1 belonging:1 g1:4 g0:6 very:3 kψ:1 conditions:2 dokl:1 choice:10 matrices:2 condition:8 dim:3 trl:1 hamiltonian:10 turns:1 t2:1 t3:1 t1:1 involution:2 vector:3 second:7 gauge:26 superalgebras:3 inspection:1 freidel:1 degeneracy:1 upper:1 consistent:3 coefficient:4 direct:2 hti:1 sign:1 zero:15 choices:2 odd:24 panda:1 scientific:1 even:14 established:2 nonlinear:2 appear:2 invertible:2 brackets:4 giving:1 diag:4 section:6 m33:4 maillet:1 nondegeneracy:2 version:2 suspect:1 above:7 krivonos:3 satifies:1 principal:3 method:1 groupe:1 led:1 gathered:1 aij:2 here:5 dψx:1 along:1 equations:12 z2:1 obtained:8 remark:1 generalizing:1 kanno:3 commutant:1 study:2 studied:3 allows:2 mx:1 resulting:1 loop:11 poisson:33 uniquely:1 equivalence:1 projection:1 family:2 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solv-int9802014.txt |@word partial:1 consider:10 remarkable:1 results:2 four:2 consists:2 remarkably:1 contributions:5 row:1 ihep:1 looking:1 inverse:1 graph:4 technique:1 quasi:1 th:1 analogous:1 tb:7 ta:7 belonging:1 kφ:1 translations:3 geometrical:3 difference:1 matrices:2 condition:1 hamiltonian:1 list:1 solution:2 try:1 discrete:8 ten:1 sergeev:11 surrounding:2 integrability:2 further:2 linear:15 spectral:1 nonlinear:1 plays:1 brackets:2 giving:2 section:3 current:6 version:1 3n:3 new:1 equivalent:1 3d:13 here:4 ansatz:2 directions:1 path:1 shortness:1 equations:10 appears:1 z2:2 obtained:2 institute:1 shift:2 vectors:2 completely:1 mx:1 periodic:1 poisson:2 published:1 action:3 appropriately:1 equivalence:4 useful:1 namely:2 marked:3 elude:1 protvino:1 use:2 feb:1 nijhoff:1 contains:1 direction:1 finally:1 ψk:16 taken:1 type:6 bethe:2 elliptic:1 operators:1 curvature:1 appendix:3 iii:1 must:2 states:1 account:1 quantized:1 recall:2 equation:11 det:5 modified:1 ferro:1 values:2 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solv-int9802015.txt |@word nwu:1 consider:1 similarity:1 alg:1 trigonometric:3 scalar:1 edu:1 depend:1 b262:1 equivalence:1 tr:1 elliptic:22 enjoying:2 degeneration:1 fax:1 r12:20 r13:4 results:3 difference:3 matrices:5 condition:1 hamiltonian:3 nondynamical:10 t2:2 t1:2 relation:2 anal:2 freidel:1 direct:1 integrability:1 further:2 dynamics:1 canonical:3 appear:1 expressed:1 maillet:1 current:1 version:3 above:1 new:5 satisfy:1 here:2 china:2 address:1 quite:1 obtained:5 great:2 antisymmetric:1 institute:1 study:1 changed:1 poisson:11 classification:1 univ:1 feb:1 problems:1 would:1 nijhoff:3 motivate:1 nucl:4 call:1 type:6 th:3 solitons:1 operators:4 known:2 hold:1 mc:1 equation:4 work:1 theories:1 following:4 beijing:1 calculation:1 relativistic:6 sense:1 r23:4 occur:1 r21:2 counterpart:2 hou:1 parameter:1 map:1 algebra:2 may:1 lax:30 choice:1 realized:1 dynamical:12 effective:1 light:1 schneider:8 twisting:1 element:2 complexity:2 so:1 fundamental:3 representation:6 funct:2 over:1 paper:4 through:3 satisfies:3 still:3 its:8 group:2 ln:1 lk:1 li:1 lr:26 mail:1 main:1 overcome:1 non:1 good:6 oxford:1 yu:1 hall:1 february:1 university:1 level:1 l2:2 l1:2 crossing:1 found:4 baxter:9 sklyanin:5 independent:1 ed:1 related:1 quantum:7 our:3 eq:14 special:1 shown:3 matrix:33 ejj:3 rs:19 nuovo:2 semi:1 denotes:2 particles:3 investigation:1 rational:4 ref:1 math:4 standard:4 admits:1 completely:3 besides:1 van:1 ruijsenaars:17 could:3 hyperbolic:4 motion:1 δij:1 first:2 variables:4 number:1 restrict:1 relations:3 another:2 open:3 given:9 checked:1 degenerations:1 introduction:1 system:7 construct:4 appl:2 b338:1 kind:1 see:1 ann:1 modern:1 generalization:2 lie:3 depending:1 calogero:7 potential:1 generalized:3 finding:1 δil:1 qalg:1 most:3 eight:1 why:1 b414:1 kj:1 yang:8 exp:1 mailing:1 fact:1 drastically:1 show:1 purely:1 gauge:3 hasegawa:1 find:5 avan:1 bernard:1 only:1 arutyunov:1 factor:1 integrable:5 moser:7 do:1 dependent:1 ones:2 suris:2 evolution:1 babelon:1 arxiv:1 qi:6 qk:1 qj:3 body:1 exists:1 δjk:1 namely:1 w2:1 discussions:1 braden:2 subject:1 nekrasov:1 interacting:2 review:1 symmetric:3 written:2 difficulties:1 various:1 closed:2 between:1 invariant:1 enjoys:1 conditions:1 terms:3 importance:2 however:2 comm:1 wr:1 extent:1 solv:4 bracket:9 diejen:1 taking:1 equal:1 among:1 cn:1 cm:6 nonrelativistic:4 q12:15 cf:1 2nd:1 dimensional:3 polynomial:1 constant:1 due:2 been:1 a212:1 int:4 describes:1 pj:1 pi:5 define:1 box:1 corrigan:1 corresponding:6 cotangent:2 general:2 former:1 present:1 case:8 will:2 eii:4 situation:1 eij:4 procedure:1 vol:2 xian:1 ik:1 ij:2 im:1 generic:1 make:1 ep2:4 same:9 ep1:4 antisymmetry:1 complex:1 northwest:1 hierarchies:2 development:1 qji:3 qjk:7 rmatrix:1 numerical:6 upon:2 purpose:1 recent:1 well:1 s21:2 epj:1 epk:1 model:34 just:1 being:1 obtain:1 aspect:1 speed:1 gorsky:1 adv:1 wen:1 macdonald:2 lett:6 transformation:3 press:1 world:1 particle:2 success:1 follows:1 specific:1 integrals:1 classical:12 some:9 q21:15 moreover:2 ccast:1 ourselves:1 lead:2 s12:6 equivalent:1 bo:1 polynomials:1 properties:1 theirs:1 o:3 consequently:1 dorey:1 kuznetsov:1 compos:1 lies:1 references:1 operator:27 hep:3 transfer:1 there:2 quadratic:5 way:1 was:5 lnσ:1 function:2 form:1 longer:2 u12:3 whether:1 up:2 us:6 limit:2 demonstrate:1 problem:3 b436:2 associated:1 qik:2 qij:3 defined:3 certain:1 abstract:1 denote:1 presented:1 exist:1 laboratory:1 commuting:4 check:1 sasaki:2 constructed:3 functions:2 cim:2 no:2 when:2 field:1 other:1 mathematics:1 frolov:1 a12:3 vertex:1 bundle:2 important:1 variable:2 b317:1 structure:13 eji:1 coupling:1 physics:1 governed:2 mass:1
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solv-int9802016.txt |@word represent:3 casimirs:1 partial:2 consider:14 remarkable:2 funct:2 rev:1 equalities:2 commun:4 results:6 ala:1 eds:1 scalar:4 generalize:1 consists:3 follow:3 remarkably:1 gl:3 row:1 kh:12 whose:2 certainly:1 inverse:7 pb1:6 calculate:6 pb2:14 similar:1 concerned:3 tu:2 tr:3 nonlocal:8 former:2 γk:5 tl:22 program:2 tj:12 those:1 under:10 discovering:1 connecting:1 analogous:4 sent:1 belonging:4 proved:2 izv:3 advantage:3 zhang:2 very:2 intriguing:1 ieice:1 choice:3 putting:1 remarks:1 discretizations:15 li:2 associated:5 difference:19 matrices:44 deformations:7 condition:13 look:3 tri:1 notations:6 immediately:4 hamiltonian:20 bn:3 turns:6 notes:1 tre:1 applicable:2 t1:6 large:2 discrete:36 vector:2 rj:2 section:3 small:1 biological:1 reyman:1 governing:1 work:2 says:1 bψ:1 consistent:3 direct:6 hti:5 approximation:3 second:12 arnold:1 incidentally:1 further:4 defines:1 expressions:1 substitute:1 linear:30 subscripts:3 aim:2 what:8 nonlinear:8 stands:1 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solv-int9802018.txt |@word partial:1 sca:11 superfields:12 antichiral:3 expressions:3 inverse:1 depend:1 superspace:2 equivalence:1 quasi:1 tk:1 th:5 marks:1 analogous:1 straightforward:4 desirable:1 choice:4 difference:1 condition:2 look:1 pbs:7 hamiltonian:5 t2:7 solution:1 discrete:1 small:9 relation:6 second:10 follow:2 even:1 what:1 invertible:3 brackets:2 trivial:1 remain:1 above:3 krivonos:5 fixings:1 respectively:1 component:1 residual:1 here:3 objects:2 quite:1 equations:11 z1:1 z2:1 obtained:2 remark:1 involved:1 elaborate:1 allows:1 poisson:2 stressed:1 via:1 extra:1 merely:1 expect:1 gallot:2 apply:1 establish:1 standing:1 derivatives:3 use:5 feb:1 would:2 prove:1 distinct:1 substitutions:1 comparing:1 theoretical:1 more:6 operators:6 under:2 particular:3 known:3 cases:1 fermionic:3 keeping:1 unessential:3 equation:2 jdf:2 suggestive:1 following:6 making:1 arrive:1 example:1 persists:1 give:4 sense:1 topic:1 allowed:1 mutually:2 acts:1 feature:2 write:1 how:2 gnls:1 description:3 algebra:12 our:1 lax:13 representations:3 wave:1 meaningful:1 constants:1 realized:1 natural:1 imply:1 explicit:3 correspond:1 su:1 so:2 allow:1 representation:7 interpretation:1 dx:1 gauges:9 hierarchy:15 indeed:1 course:1 through:7 mentioned:2 existence:4 still:1 its:5 seeming:1 thsun1:1 acknowledge:1 chosen:2 interesting:2 fix:2 lk:1 exhibits:1 forms:1 choose:2 mail:1 defining:3 supersymmetry:7 correspondence:3 them:5 they:4 bogoliubov:1 now:1 ift:1 easily:1 february:1 dirac:1 2d:5 mode:1 each:2 characterized:1 mean:1 spinor:3 differential:4 directly:2 arbitrariness:2 related:3 constitute:2 extended:1 obtains:1 laboratory:1 eq:1 special:2 out:1 dgd:2 crucial:1 acting:1 dλ2:4 dλ1:3 ref:3 math:2 reformulated:1 possibility:1 standard:3 admits:2 dubna:2 e2:2 pairs:1 chiral:8 could:1 impose:1 turn:1 support:1 first:1 features:2 possessing:1 primary:1 preservation:1 peculiarity:1 another:6 precisely:1 given:5 salient:1 eqs:5 achieved:1 system:5 relations:8 their:3 master:1 realization:5 dfg:1 popowicz:1 final:1 commutativity:2 moscow:1 convention:1 part:1 convinced:1 than:1 ivanov:6 kind:1 skdv:20 integrability:1 aims:1 matter:1 were:3 russia:1 symmetries:1 entail:1 rewrite:2 mind:1 need:1 any:4 zero:1 latter:3 note:4 absorbed:1 coincide:1 though:1 involving:1 considered:1 later:1 flow:4 ext:1 physics:1 notion:1 fact:1 precise:1 show:5 analogously:1 gauge:27 substituting:4 d2:1 find:2 sorin:2 based:1 proposed:4 parameters:2 should:4 only:4 explicitly:3 local:4 do:2 dj:4 notation:2 get:1 df:10 dg:2 dd:10 express:1 ones:1 words:1 new:1 dv:3 reveal:2 evolution:3 arxiv:1 fixes:1 common:1 including:1 fixed:1 view:1 declared:1 set:1 constructing:1 exists:1 observes:1 imposing:2 differs:1 namely:1 result:1 analog:2 written:4 between:6 invariant:2 subscript:1 before:2 conditions:3 knowing:1 notice:1 terms:16 vanishing:1 solv:7 both:1 parentheses:1 last:2 freely:1 region:1 uncertainty:1 adapted:1 otherwise:1 relevant:2 point:3 simple:1 superfield:10 grants:1 associated:1 ddφ:1 transformations:3 basis:1 delduc:4 chirality:3 due:3 been:2 pb:2 int:7 reduction:1 describes:1 basic:3 expected:1 djd:3 supersymmetric:5 quantities:1 subspace:1 covariance:2 spin:9 present:2 case:1 ǫf:2 ǫd:3 evaluated:1 choices:3 will:1 while:2 proves:1 intas:2 applies:1 property:3 conformal:1 procedure:1 supercurrent:1 redefinitions:1 non:6 claimed:1 supercurrents:7 superconformal:2 ig:3 rfbr:2 different:6 make:1 formulations:2 same:2 complex:5 hierarchies:2 gets:1 higher:1 used:4 see:2 grassmann:4 upon:2 flows:2 hand:2 subvariety:1 v1:2 v2:1 purpose:1 recent:1 acknowledgement:1 expression:2 well:2 obviously:1 sets:1 firstly:1 dimension:2 just:4 being:2 identify:1 dφd:2 2jj:2 preprint:1 2dd:2 valid:1 conjugated:2 lett:4 easy:4 transformation:3 match:1 identical:3 lacking:1 read:1 possible:3 harmonic:1 using:5 unique:1 brought:1 like:2 follows:5 manifest:1 δj:3 either:1 arbitrary:2 δf:2 δg:1 reduced:2 right:2 classical:2 existing:1 obliged:1 some:2 respect:1 kdv:4 pashnev:1 toppan:1 unavoidable:1 ddv:2 ddj:2 does:1 ddg:2 ddf:5 equivalent:8 stem:1 relating:2 freedom:5 commun:1 discussed:1 covariant:3 whence:1 extensions:1 act:2 presence:1 previously:1 into:2 appropriate:1 references:1 determine:1 operator:13 bosonic:2 prepotentials:16 hep:5 assumed:2 strictly:1 there:3 noticed:1 start:2 way:1 jinr:4 was:7 function:2 form:9 true:1 applying:1 characteristic:1 inside:2 up:7 us:5 those:1 demonstrate:2 jφ:3 similar:2 called:1 recalling:1 constant:3 prepotential:4 defined:2 abstract:1 general:11 single:1 invertibility:1 dλ:2 formulation:2 identities:1 check:3 constructed:1 again:2 functions:2 no:1 amounts:1 fixing:1 when:1 detail:1 reality:1 field:1 other:6 structure:5 matrix:1 implies:2 dψ:1 dω:3 dφ:5 restores:1 pseudo:1 together:2 equivalently:1 once:2
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solv-int9803001.txt |@word partial:7 consider:1 results:1 four:4 scalar:1 edu:1 lakshmanan:1 research:2 compact:1 inverse:2 depend:1 turkish:1 tr:1 nonlocal:3 kσ:1 p2:2 ginn:1 kτ:2 far:2 geometrical:2 ankara:1 difference:1 condition:2 generalised:1 vector:1 governing:1 sin2:1 direct:1 sign:3 integrability:2 bilkent:2 further:1 carmo:1 belief:1 spectral:2 established:2 what:1 nonlinear:13 abd:1 tetrad:2 diag:2 new:2 satisfy:1 q1:2 respectively:2 here:12 believed:1 q2:3 tangent:1 cos2:1 others:2 directions:1 sine:6 equations:45 change:2 obtained:9 convert:1 suitably:1 technical:1 study:1 tµ:23 products:1 usually:1 suitable:1 sci:1 family:2 total:1 tools:1 derivatives:3 feb:1 takes:1 recalling:1 negative:1 crampin:1 choosen:3 m4:1 m3:6 more:3 flat:5 becomes:2 dxµ:1 curvature:14 berlin:1 virtue:2 known:1 must:1 nutku:1 springer:1 valued:3 science:1 equation:16 work:4 modified:1 following:1 example:3 compare:2 give:4 sokolov:1 assumptions:1 council:1 arise:8 robinson:1 lamb:1 means:3 parametrised:1 write:2 very:1 pseudo:2 parameter:3 sin:1 dπ2:1 may:15 dπ0:1 plane:1 lax:1 faculty:1 choice:7 compatibility:1 eµa:2 eµb:1 greek:1 so:4 fundamental:1 sl:1 order:1 hierarchy:4 satisfied:2 including:1 urses:3 pirani:1 sciences:1 interesting:1 forms:3 choose:2 nakayama:1 derivative:2 main:1 decades:1 dxν:1 qs:1 they:2 hall:1 february:1 goldstein:1 university:1 orthonormal:2 each:8 serret:4 2k:2 mikhailov:1 defocusing:2 directly:1 ed:1 gaussian:6 related:3 obtains:1 eq:5 special:1 shown:2 matrix:4 space:16 since:2 rev:5 denotes:1 rn:1 math:5 common:1 theory:1 codazzi:1 free:1 quite:2 complicated:1 york:1 e3:6 interaction:1 geometry:5 could:2 ds2:6 keep:1 motion:8 gordon:6 dπ1:1 signature:6 hence:6 first:2 variables:1 philadelphia:1 utilized:1 done:1 another:4 given:9 eqs:1 system:5 their:1 eqn:1 dt2:2 siam:3 structures:1 gives:1 academy:1 segur:2 focusing:2 treatise:1 showed:2 sections:2 cimento:1 zero:3 determined:1 contrary:1 were:2 motivation:1 symmetries:1 boston:1 curves:18 manner:1 conjugate:1 flatness:1 curved:1 element:4 any:7 self:3 instance:6 k1:2 take:1 trace:1 normal:2 gauss:1 significant:1 class:2 xµ:13 soliton:16 tν:2 prolongation:1 kd:1 considered:3 clear:2 face:1 ks:1 properly:2 kw:8 principle:1 physics:1 reprinted:1 dover:1 nls:4 show:3 supported:1 spaces:3 gauge:1 akns:3 wahlquist:1 find:1 bν2:1 bν1:1 parameters:1 should:2 only:1 explicitly:1 integrable:15 local:5 do:1 notation:1 get:2 dependent:1 familiar:1 de:1 fluid:1 sss:1 dz:1 dy:1 during:1 dt:1 selfinteracting:1 ds:6 areas:1 evolution:5 cie:1 karasu:1 approach:1 differential:12 arclength:2 nν:2 fixed:1 communicated:1 set:1 exists:1 frame:2 see:3 w2:4 w1:4 w0:4 surfaces:14 interacting:2 its:4 written:2 between:4 progress:1 prentice:1 conditions:1 email:1 terms:6 shabat:1 bµ2:6 bµ1:6 vanishing:2 solv:1 both:1 last:1 many:3 connection:9 pde:1 finds:1 jersey:1 among:1 point:3 corresponds:3 dimensional:6 mkdv:11 respect:4 torsion:3 turkey:2 ps:1 mainardi:1 described:1 transformations:1 due:3 been:1 int:1 arxiv:1 define:2 corresponding:2 dimesional:1 relaxing:1 scalars:6 remark:1 estabrook:1 arised:1 denote:1 case:3 minkowskian:3 nski:1 value:1 choices:4 will:4 euclidean:6 sli:1 couplings:1 vectors:4 coupled:6 surface:3 need:1 examined:1 vanish:2 different:3 perhaps:1 recursion:3 make:1 same:1 orders:1 member:1 complex:3 resulting:1 sinegordon:1 physical:1 used:1 upon:1 sym:2 hand:2 parametrized:2 v3:15 moving:10 purpose:1 infinite:1 ablowitz:1 mech:1 without:1 position:1 left:1 obtain:4 bµ:10 correspondance:3 scattering:1 fokas:1 previous:2 letting:4 infinitely:1 zakharov:1 lett:7 hasimoto:1 transformation:1 frenet:4 nuov:1 possible:4 iη:5 using:3 like:1 follows:1 reduces:3 performing:1 korteweg:1 either:1 petrich:1 arbitrary:4 become:1 reduced:2 classical:1 some:4 examples:1 choosing:4 bν:1 proper:1 kdv:2 describing:1 dimensions:1 eiη:1 assuming:2 eisenhart:1 run:1 scientific:1 ωba:1 bi:1 properties:1 dependence:1 langer:1 fen:1 konopelchenko:1 introduced:1 considerations:1 letters:1 functional:1 three:12 references:1 operator:3 schrodinger:2 assumed:1 there:4 transform:1 why:2 torsions:1 way:4 was:2 function:10 complexified:1 elsewhere:1 form:10 relaxed:1 but:3 construction:1 line:4 trying:1 pdes:6 partially:1 embedded:1 versions:4 whether:1 ωs:2 variations:1 up:1 backlund:1 similar:2 nµ:21 constant:4 defined:2 certain:1 abstract:1 describe:3 general:3 exist:1 vn:1 check:1 defines:2 functions:9 locality:1 when:3 vanishes:1 other:4 solitons:1 department:1 mathematics:3 wadati:1 dψ:1 dω:1 vries:1 dτ:1 curve:14 dσ:7 4p:1 strings:4
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solv-int9803002.txt |@word consider:2 pointing:1 funct:1 equalities:1 focus:1 δi1:1 leads:2 scalar:4 edu:1 go:1 row:2 inverse:2 depend:1 chinese:1 tn:1 finally:1 under:2 u1i:1 proved:2 far:1 results:2 nijenhuis:1 hamiltonian:2 ref:5 t1:1 vector:11 math:14 indices:1 anal:2 application:1 direct:1 second:5 bilinear:1 will:9 what:2 nonlinear:19 appear:1 diag:1 section:5 hereditary:67 fuchssteiner:6 above:9 values:1 method:4 satisfy:3 meth:1 respectively:3 here:1 reported:1 concluding:1 along:1 quite:1 equations:6 obtained:3 involved:2 resulting:4 u3x:9 composed:2 examining:2 useful:1 plenum:1 diagonalizable:1 santini:2 unit:1 derivatives:3 use:3 would:1 prove:1 contains:1 next:3 noting:2 therefore:7 type:2 reflects:1 more:4 separated:1 βu:1 becomes:2 operators:64 berlin:1 particular:3 known:2 cases:3 hold:1 springer:1 ma:8 recall:1 equation:3 obvious:1 columns:1 following:10 example:16 proof:5 sokolov:1 accept:1 high:1 want:1 verlag:1 requirements:1 provide:2 discussion:1 holds:3 write:2 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solv-int9803003.txt |@word japan:2 consider:7 remarkable:2 crucial:1 results:2 leads:6 scalar:8 proposition:2 l12:1 grateful:1 foundations:2 partial:2 gm:1 gl:1 2r3:1 gj:1 gi:4 gh:3 devoted:2 whose:3 inverse:3 const:3 concerned:3 δhm:1 those:2 under:1 lyp:5 case:12 belonging:2 protective:1 wjk:1 g1:1 very:2 rise:2 geometrical:6 every:1 continued:1 condition:1 four:1 dij:1 presented:1 solution:4 d2:3 moldova:4 solved:1 vector:2 math:4 indices:1 noted:1 concluded:1 des:1 specially:2 f0i:2 za:5 substitutions:1 second:8 zx:1 further:3 dynamics:1 mj:3 ode:2 theory:3 subscripts:1 nonlinear:8 plays:1 appear:2 3s:17 3r:2 section:3 contracted:1 analogously:2 3t:2 wd2:1 sur:1 above:7 abx:2 satisfy:4 led:1 intas:1 degree:12 b2x:2 respectively:5 here:1 behaviour:1 l22:1 tangent:1 address:1 represented:1 xα:2 equations:14 change:6 obtained:1 remark:3 property:2 parameters:2 institute:1 study:1 contradiction:1 sx:8 p2:2 usually:2 makes:1 3p:5 followed:1 divide:1 analyzing:1 weierstrass:4 univ:2 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solv-int9803007.txt |@word partial:2 pointing:1 results:3 leads:1 generalize:1 lakshmanan:1 expressions:1 inverse:3 depend:1 calculate:1 ty:1 presents:2 finally:5 manifolds:1 under:3 te:1 worth:1 case:7 conjecture:1 stud:1 rise:1 martinez:1 wave:10 sons:1 trough:1 summarized:1 2rv:1 exact:1 condition:1 presented:2 u2y:1 large:1 akns:4 application:1 dealing:2 cosh:1 painlev:11 pass:1 dynamics:1 bilinear:3 3y:1 nonlinear:4 ˆt:2 appear:1 invertible:1 ˆx:2 ˆy:8 section:3 tabor:2 expressed:2 henceforth:1 version:7 establishes:2 method:5 λrt:1 satisfy:2 simultaneously:1 sinh:7 consideration:1 equations:30 appears:2 change:3 obtained:4 great:1 balance:1 studied:3 allows:1 subcase:1 suggests:1 suggestion:1 decouple:1 pickering:1 apply:1 use:3 ψy:2 takes:1 would:2 prove:1 ψt:3 next:4 call:1 therefore:2 type:1 more:1 successful:1 becomes:3 odinger:3 particular:4 known:6 cases:1 iv:4 iii:4 must:5 account:3 equation:77 modified:10 mt:6 obvious:1 following:4 trans:13 my:4 mx:3 compare:1 give:1 ηxx:1 purposes:1 calvo:1 numbers:1 boussinesq:6 darboux:1 verify:1 discussion:1 algorithms:1 nyt:3 write:3 how:1 2my:10 singular:6 after:1 singularities:1 movable:1 lax:13 physic:1 branches:2 clarkson:1 yielding:1 spain:1 allow:1 order:5 restriction:1 help:1 over:1 satisfied:2 l19:1 paper:2 through:2 2v:2 satisfies:2 its:4 le:1 interesting:4 ηo:1 systems:1 mail:1 versus:2 non:11 salamanca:2 mxy:13 lambert:2 propose:2 acklund:1 introduce:1 newman:2 qr:4 singularity:2 now:5 realize:1 above:1 easily:7 february:1 hereafter:2 designation:1 university:1 level:1 40k:1 2y:1 reasonable:1 each:2 2m:8 pb95:1 differential:2 prompted:1 series:1 2r:1 society:1 mar:1 obtains:1 our:1 es:1 out:2 rt:6 try:1 shown:3 ψxx:3 m2x:1 m2y:4 furthermore:1 since:6 rx:6 chaos:1 research:1 smm:1 multiply:1 kent:2 lecture:1 induced:1 u2x:1 integrated:4 math:10 wiley:1 linear:10 succesfully:1 kaup:7 ısica:2 publication:1 r2:1 could:3 gordon:5 universidad:1 first:2 already:4 miura:33 variables:3 xx:1 xy:8 another:2 ψxy:3 precisely:1 dispersive:10 given:4 exists:1 introduction:1 leading:1 carnevale:1 system:14 statement:1 final:1 adopts:1 relationship:2 alonso:1 newell:1 part:1 authors:6 attempt:1 double:2 integrability:1 express:1 gives:1 treated:1 decompose:1 constrained:1 clearly:1 solitons:1 jour:1 thoroughly:1 self:1 mills:1 note:1 generalized:4 kawamoto:1 finding:1 so:3 shall:10 pair:14 acknowledgements:1 extremely:2 class:1 soliton:1 considered:4 shortly:1 χx:2 yang:1 principle:1 physics:1 χj:2 fact:1 show:4 reductions:4 supported:1 gauge:1 solutions:13 x3:1 substituting:3 trivial:1 find:9 based:3 just:4 jap:1 should:2 analytic:1 explicitly:1 subsection:1 integrable:4 local:4 do:2 dominant:1 ϕx:1 means:1 dependent:1 ϕt:1 2mx:6 de:3 pave:1 truly:1 ones:1 dx:1 dy:1 gen:2 evolution:1 kadomtsev:1 qt:2 qx:2 dgicyt:1 arxiv:1 expansions:2 london:1 musette:1 view:3 set:1 reference:3 see:1 individual:1 result:2 eliminating:1 terms:1 forthcoming:1 techniques:2 written:5 between:12 invariant:1 notice:1 recently:2 shabat:1 conde:1 solv:1 jetp:1 both:4 pempinelli:2 taking:4 conclusions:1 ϕxx:1 ϕxy:1 expression:3 fields:2 point:3 appeared:1 corresponds:1 leon:1 proved:1 pp:1 transformations:3 been:13 reduction:8 interest:1 inv:1 define:1 conte:1 arises:2 corresponding:1 xxy:1 systematic:2 present:5 applied:2 pacs:1 mtt:1 aim:1 while:3 orica:1 property:4 real:2 boiti:3 thus:2 uxx:1 uxy:2 ii:1 n2y:3 n2x:3 converts:3 contract:1 dual:1 vy:1 different:3 mxx:7 author:1 φx:2 make:1 same:4 check:1 complex:2 firs:1 widely:1 auto:1 several:4 independent:1 used:1 upon:2 ablowitz:2 identity:1 schr:3 well:4 analysis:5 obviously:2 latter:3 manifold:7 proposed:5 λt:1 able:1 obtain:10 scattering:1 field:4 zakharov:1 ψˆt:1 weiss:3 qx2:2 simple:1 add:1 other:2 transformation:22 take:1 identical:1 rescaled:1 sonia:1 sytems:1 papers:1 possible:2 press:2 using:12 2q:4 like:1 alternatively:3 reduces:1 yields:3 arbitrary:3 qxx:5 qxy:1 stationary:3 reduced:1 2qv:1 deal:3 truncated:1 some:4 respect:2 chakravarty:2 conventionally:1 est:4 dimensions:11 integration:1 2xy:1 eliminate:1 prog:1 refer:2 inserting:1 usal:1 expansion:9 imaginary:1 constraint:1 discussed:3 ηxy:2 o:1 practical:1 mathematical:1 soc:1 cambridge:1 previously:1 into:6 obtaining:1 ηj:2 down:1 nothing:4 ηt:1 references:1 sov:1 ηy:4 ηx:4 classical:2 area:1 initial:2 long:4 u2:7 accordingly:1 appl:1 facultad:1 way:5 function:3 form:10 offer:1 regard:1 but:7 construction:1 segur:1 truncation:2 made:2 uy:5 ux:8 ut:6 us:5 uo:1 uj:2 called:6 detailed:1 constant:1 int:1 recognize:1 abstract:1 myt:2 general:1 examine:1 formalism:2 simplest:2 functions:1 no:1 when:3 nx:7 ny:8 setting:2 neighbourhood:1 branch:3 fokas:3 theor:1 nt:1 superposition:4 time:3 problems:3 medina:1 substract:2 a0:3 important:1 variable:1 radha:2 nxt:1 longer:1 assume:1 pilar:1 nxy:3 nxx:1 rxx:4 4m:1 presenting:1 hirota:1 starting:2
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solv-int9803008.txt |@word represent:4 partial:2 consider:5 remarkable:1 secondly:1 gz:8 llt:1 four:1 commute:2 comments:2 parameterization:1 consists:1 follow:2 expressions:3 depend:2 finally:4 weyl:1 aut:1 th:1 under:7 lks:2 preserved:1 returning:1 very:2 account:2 dokl:2 results:5 lrs:9 every:1 difference:1 exact:1 trudy:1 condition:2 leads:1 obvious:2 level:6 bn:1 irreducible:7 solution:31 correct:1 leave:1 discrete:4 proposition:3 indices:1 corollary:1 consistent:2 direct:4 zero:8 irreducibility:2 pass:1 further:3 remarkably:1 canonical:3 putting:1 brackets:8 section:7 consequent:1 version:1 3n:1 above:7 capital:1 new:6 method:4 satisfy:5 degree:6 realizations:1 equals:1 here:4 understanding:1 l21:8 canonically:2 objects:1 groups:2 represented:4 consideration:3 equations:21 change:1 chumakov:1 instituto:2 institute:1 involved:5 allows:2 poisson:8 permutation:1 usually:1 symmetrical:6 suitable:2 composed:1 formulated:1 divide:1 sistemas:2 replace:1 protvino:1 derivatives:1 use:2 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solv-int9803009.txt |@word secondly:1 partial:1 chinese:1 funct:1 equalities:1 leads:3 eds:1 computation:1 edu:1 constants:4 research:1 inverse:2 dickey:1 quasi:1 under:1 applied:1 far:1 choice:2 hamiltonian:30 ref:3 notes:1 solution:1 εkn:1 vector:6 enhance:1 anal:2 direct:1 second:1 theory:1 even:1 what:1 nonlinear:8 invertible:2 hereditary:8 fuchssteiner:5 above:3 new:4 method:1 coefficient:1 respectively:2 component:1 understanding:1 equations:12 obtained:1 search:1 sjk:1 resulting:3 poisson:1 ma1:1 derivatives:1 would:3 prove:1 jpn:1 fordy:1 ψi:1 m1:2 m0:3 associated:1 decomposable:2 more:5 sort:1 fokas:1 operators:8 berlin:1 known:3 must:1 springer:1 ma:6 equation:1 mn:1 mi:2 modified:1 theories:1 following:1 example:1 def:1 proof:1 f0:9 f1:1 degenerate:1 give:1 process:1 want:2 evidently:1 verlag:1 end:1 provide:1 verify:1 means:1 how:1 answer:1 acta:1 product:1 may:9 after:1 lot:1 lax:1 fn:2 realized:1 sx:1 council:1 ones:1 so:1 allow:1 order:2 typical:1 hierarchy:14 kong:4 paper:1 through:2 still:1 urses:2 thank:1 interesting:1 actually:1 forms:1 lu:1 choose:2 derivative:2 eventually:1 non:1 motivated:1 scaling:1 they:5 now:4 hierarchies:1 possess:3 easily:1 dirac:1 2r:1 university:2 presented:1 chowdhury:1 each:1 found:3 arxiv:1 financial:1 universities:1 idea:2 related:1 constitute:2 our:7 meth:1 special:3 really:1 matrix:3 integro:1 gradient:4 nuovo:1 since:3 rx:1 chaos:1 denotes:1 bkl:1 get:1 induction:1 math:7 wiley:1 linear:3 standard:1 york:1 e1:2 generate:2 pairs:2 chiral:1 sinica:1 ukx:2 u20:1 βl:3 βn:42 βi:3 first:6 already:2 xn:1 transform:1 relations:1 directly:2 size:1 city:2 given:2 perturbation:3 rewritten:1 f1m:2 system:6 construct:2 their:2 appl:3 master:1 xiu:1 statement:1 scheme:3 structures:3 final:1 observations:1 way:2 exactly:1 part:1 jordan:1 manipulation:1 x0:1 x1:1 coefficients:4 kind:2 1m:2 cimento:1 zero:2 determined:4 motivation:1 symmetries:3 involution:1 say:4 conjugate:1 need:2 seen:1 any:1 lie:2 note:3 instance:1 k1:4 potential:1 spectral:1 4u0:5 4u1:2 magri:4 algebraic:2 but:4 significant:1 pair:3 class:2 soliton:4 sometimes:1 kn:11 km:3 ways:1 bracket:1 principle:1 physics:1 fact:1 oevel:1 show:2 justifies:1 solutions:2 find:2 d0:12 d1:4 partners:1 proposed:1 should:1 explicitly:1 rji:2 integrable:4 local:6 do:1 di:10 express:1 aβ:1 dx:8 silk:1 gen:3 gel:2 evolution:4 fields:4 λu:3 differential:4 yield:1 common:3 contain:2 view:1 satisfy:2 requirement:1 computed:1 exists:2 see:3 bordag:1 techniques:1 fand:2 lux:1 functionals:4 symmetric:2 written:2 various:1 irn:1 αi:3 ui:7 jf0:1 email:1 αn:4 however:1 cijk:1 jj:2 solv:1 dorfman:3 pempinelli:1 kruskal:1 many:4 taking:1 equal:1 ck:1 among:1 ci:9 except:1 grants:1 kowloon:1 moreover:2 cu:1 considering:1 observing:1 due:1 been:4 int:1 reduction:1 aijk:3 systems:39 corresponding:4 quantities:1 xxx:1 observe:1 c3:1 c2:2 c1:5 c0:14 present:1 c4:2 case:4 choices:1 u1x:2 investigating:1 uit:1 2ui:1 coupled:10 vol:1 boiti:1 thus:4 according:1 reads:1 itself:1 bik:2 hong:4 author:1 journal:1 recursion:5 make:1 belong:2 φi:2 proved:1 φn:6 higher:2 singapore:2 moment:1 ablowitz:1 identity:1 locality:1 well:2 analysis:1 concrete:2 just:2 obtain:2 karasu:2 world:2 scattering:1 yet:1 accepted:1 infinitely:1 wen:1 lett:1 easy:1 cum:1 guarantees:2 transformation:1 scientific:2 bij:2 around:2 read:1 possible:2 using:3 unique:1 fractals:1 appearing:1 like:4 cu0:1 follows:4 δu:14 specific:3 either:1 δh:14 arbitrary:3 become:1 mathematical:2 because:2 namely:1 lectures:1 some:3 examples:6 respect:5 kdv:15 subclass:1 h1m:2 bm:1 equivalent:1 bi:18 although:2 bx:1 properties:1 extension:1 o:1 introduced:2 soc:1 ψf0:3 h0:5 h1:5 functional:1 references:1 operator:12 support:1 there:4 u1:11 u0:16 start:1 much:2 inner:1 u0x:10 resulted:1 ψn:5 was:1 therefore:2 complete:1 form:2 jul:1 hk:1 construction:1 hn:2 illustrative:1 made:1 compute:1 ux:12 whether:1 ut:12 us:3 un:5 jψ:1 uk:5 uj:8 called:1 separated:1 constant:1 defined:3 physica:2 abstract:1 aj:1 general:6 conserved:1 invertibility:1 dλ:3 formulation:16 commuting:2 check:1 physical:1 compared:1 integrability:1 no:1 when:2 field:4 other:4 solitons:2 department:1 mathematics:2 theor:2 expose:1 sijk:5 problems:3 important:1 acknowledgment:1 implies:1 assume:1 ghosh:1 required:1 starting:1 having:1
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solv-int9803010.txt |@word represent:5 consider:2 chain:8 exponentiation:1 osp:1 results:2 integration:1 ge:1 generalize:1 antichiral:4 expressions:1 gl:3 gj:36 ihep:1 whose:1 inverse:1 superspace:3 tp:1 tq:1 γj:32 aut:1 th:5 under:1 decomposition:1 norm:1 case:18 belonging:3 g2:1 advantage:1 g0:23 very:1 account:1 choice:1 entries:2 difference:1 matrices:6 brunelli:1 differentiated:1 dij:4 presented:4 turns:1 solution:6 involution:2 convenience:1 vector:3 progress:1 indices:3 gauge:7 markov:1 superalgebras:3 upper:2 decompositions:1 zero:6 further:1 linear:2 even:1 will:1 what:3 nonlinear:2 invertible:1 brackets:1 section:7 expressed:3 above:3 krivonos:3 new:9 method:4 exercise:1 satisfy:2 compact:1 simultaneously:2 respectively:7 component:1 here:9 chumakov:1 groups:2 represented:1 consideration:2 november:1 equations:25 z2:1 instituto:2 ultra:1 institute:1 shift:1 vectors:2 completely:2 example:2 resulting:1 suitable:1 g2j:4 via:2 useful:3 projection:1 classification:1 bonora:2 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solv-int9803011.txt |@word ψ1x:1 represent:1 concept:1 lakshmanan:11 consider:3 remarkable:1 ψ1t:1 results:1 gy:3 gx:4 leads:1 eds:1 scalar:1 nan:1 sci:1 expressions:3 research:3 gj:2 localized:7 compact:1 inverse:3 chain:1 re:2 equivalence:13 tr:4 29a:1 charge:3 daniel:2 th:1 dressing:1 106a:1 include:1 73a:1 g5:1 g3:11 84a:1 g1:23 orthogonal:3 rise:2 springer:1 geometrical:7 wishes:1 exact:5 condition:7 look:1 notations:1 obvious:1 alma:7 presented:4 turns:1 notes:1 tanh:3 φ1x:1 d2:1 large:1 vector:6 elsewhere:1 relation:2 originally:1 strachan:5 zl:5 work:1 10b:1 takhtajan:3 consistent:2 10a:1 literature:1 cosh:3 painlev:1 iσ3:1 further:5 dynamics:2 50a:2 substitute:1 linear:6 spectral:3 dissertation:1 nonlinear:11 diag:1 section:4 codazzi:1 analogously:1 bdu:1 version:1 abt:1 lle:2 above:9 lifshitz:1 3b:1 3a:1 method:5 satisfy:2 27a:1 27b:1 27c:1 30b:1 fiz:1 respectively:3 even:4 component:1 here:11 bi:1 l21:1 reported:1 them:1 κy:2 108a:1 κt:3 along:3 equations:30 19c:2 19b:1 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solv-int9803012.txt |@word science:1 represent:1 since:1 partial:1 indeed:1 over:1 grammaticos:3 obtain:1 carnevale:1 themes:1 paper:1 relation:1 solutions:4 ηi1:1 part:3 japan:1 parameters:1 find:1 cn:2 q1:6 accepted:1 q2:4 tz:4 schiff:2 tx:1 directional:2 izv:2 exact:1 tt:1 complex:1 weiss:1 completes:1 analytic:1 explicitly:2 transformed:1 systems:3 τx:1 miura:10 integrable:7 analogous:1 transformation:10 gave:3 pk2:2 eventually:1 conjecture:1 dj:2 2rj:1 fukuyama:4 dependent:2 ηin:1 possible:1 introduce:1 differential:1 schematically:1 q31:1 jp:3 combinations:1 using:2 singularity:1 kusatsu:1 yu:3 discuss:1 symbols:1 february:1 induced:1 always:1 university:1 arxiv:1 arrows:2 solution:9 applied:1 vector:1 yields:1 math:4 arbitrary:1 become:1 qk:2 unifying:2 reduced:1 wronskian:5 series:1 ψx:1 searching:1 summation:2 toda:3 elements:1 result:1 p22:2 kdv:10 nonlinear:1 dimensions:2 bottom:2 cubic:1 its:1 defined:1 ajk:1 jth:1 closed:1 respectively:1 new:5 construction:2 pj2:2 order:1 method:4 rj:2 shiga:1 τn:8 replaced:1 handside:1 written:1 ju:1 equivalent:1 each:1 modify:1 however:3 here:3 p2j:2 admits:1 completely:1 wtc:1 term:1 bs:7 solv:4 equations:8 z1:5 z2:7 z3:5 obtained:6 pairs:3 qj:8 central:1 r1:4 r2:2 column:1 study:1 title:1 allows:1 parts:1 o:3 called:1 p2:6 connection:1 strang:1 nothing:1 konopelchenko:4 hence:1 other:1 2iπ:1 fujita:1 cj:2 ucker:1 there:1 xn:2 φxx:3 follows:3 φxt:3 into:1 ηj:1 tabor:1 latter:1 dimensional:12 variable:2 mkdv:3 ussr:2 references:1 construct:1 another:1 ψxt:2 operator:3 moreover:2 ring:3 ψxx:1 infinite:1 mbs:5 ψz:3 derivatives:1 use:1 described:1 takes:1 leads:1 prove:1 previous:1 top:1 rewrite:1 ai1:4 system:2 relations:1 dispersion:1 kouichi:1 depicted:1 ed:1 editor:2 basic:1 pj:9 pk:4 scheme:1 was:2 pl:1 lett:3 corresponding:2 form:8 becomes:1 operators:3 mkp:3 but:1 taken:1 zero:1 derivative:1 x2:9 given:2 than:1 must:1 ramani:3 p1:7 holland:1 invariants:1 solid:1 type:1 equation:68 det:2 modified:14 us:2 easier:1 will:2 transformations:1 ain:1 p12:2 takeshi:1 were:1 following:1 property:1 root:1 example:1 proof:2 f1:5 ac:3 constant:1 figure:5 give:3 int:4 discussed:2 abstract:1 conjugate:1 thus:2 generalization:1 denote:2 indicates:1 a12:3 sense:1 fn:5 north:1 qj2:2 four:1 tzn:1 sato:2 painlev:1 φx:8 s2:2 φz:3 song:1 composing:2 same:3 p14:1 unity:1 potential:3 remarks:1 department:1 extensions:3 proved:1 ψzz:1 higher:6 mar:1 see:2 bkc:3 replacing:1 symbol:1 i2:1 hand:1 routes:2 lax:16 letter:5 hietarinta:3 pair:8 fj:1 analytically:1 concluding:1 constants:2 soliton:8 short:1 constructed:2 proceed:1 succeeded:1 ψx2:7 later:1 trilinear:3 analysis:1 ritsumeikan:1 sj:2 kp:8 sasa:1 does:1 exp:8 dashed:1 representation:1 left:1 physics:1 s1:4 typical:1
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