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solv-int9612011.txt |@word represent:1 logarithms:2 since:5 arrives:1 consider:2 funct:1 alg:1 t2i:1 leads:12 edu:1 go:1 follow:1 expressions:1 dα:4 compact:1 whose:1 inverse:1 referring:2 tw:4 equivalence:4 young:1 passage:1 tn:22 quasi:1 does:1 tj:11 th:10 ti:7 atlas:1 grinevich:3 analogous:1 circumstances:1 ℜk:7 kσ:6 p2:7 fay:13 proved:2 abelian:1 very:1 rise:2 martinez:1 springer:8 choice:1 crosses:1 ωsm:1 lecture:1 condition:1 treating:1 entire:1 school:1 dubrovin:4 riemann:34 solves:2 hamiltonian:1 positions:1 notes:3 t2:5 solution:2 t1:8 large:5 solved:1 vector:1 stipulated:1 indices:1 relation:3 anal:1 referred:1 straight:2 work:1 neighborhood:1 zi:2 zj:6 farkas:1 dealing:1 qms:8 zg:2 za:1 zb:1 jump:1 across:1 second:9 qmj:2 zz:6 qmn:5 further:7 zw:1 odd:4 reina:1 canonical:4 bilinear:11 aim:1 gibbons:3 nonlinear:4 shrunken:1 gβγ:1 contemp:1 section:9 expressed:3 russ:3 consistently:1 version:4 poles:10 above:4 boundary:2 construction:2 contributes:2 equivalent:4 q1:7 degree:3 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solv-int9701003.txt |@word logarithms:1 consider:10 lack:1 truncated:3 results:6 ds:38 four:2 proposition:1 computation:2 edu:2 consists:2 follow:3 research:1 displaying:1 dα:2 devoted:1 whose:4 certainly:1 replacements:4 depend:2 analytic:9 b386:1 contained:2 reverting:1 tn:1 finally:1 critical:4 those:5 under:6 t10:1 analogous:1 norm:8 ingredient:1 conjecture:1 orthogonal:1 homogeneous:2 putting:1 entries:6 little:1 exact:1 condition:16 immediately:1 t6:1 suffices:1 t4:5 integrating:3 list:1 solution:7 occurs:2 large:2 differential:3 announced:1 science:1 small:22 upt:1 alternatively:1 upper:1 says:1 periodicity:3 coefficient:3 direct:1 sign:2 approximation:4 go:2 painlev:6 lines:1 interval:1 3a:1 dynamics:1 residue:1 trick:1 what:2 t2j:1 t2m:1 appear:3 invertible:31 brackets:1 section:8 near:3 uniform:4 poles:2 above:20 boundary:2 obvious:3 yv:1 contributes:1 method:4 contrast:1 satisfy:3 compact:4 degree:3 respectively:5 l1:2 component:1 equals:14 here:10 met:1 cylindrical:9 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solv-int9701004.txt |@word represent:1 consider:3 chain:5 arnol:1 skip:1 equalities:2 trigonometric:3 integration:1 four:2 hurtubise:1 proposition:9 follow:1 expressions:4 denotes:1 ejk:1 row:1 extra:1 lkl:2 γx:1 depend:6 calculate:1 skii:1 technique:1 tr:13 quasi:1 equate:2 petersburg:4 elliptic:14 under:2 tr1:14 analogous:1 tr2:13 magnetic:3 gekhtman:1 applied:4 proved:1 federation:2 straightforward:3 sitting:1 very:4 implicitly:1 dell:1 choice:3 every:1 jack:1 entries:5 difference:2 matrices:10 deformations:1 condition:5 arrange:1 generalised:3 entire:1 dubrovin:1 hamiltonian:5 turns:1 notes:1 sklyanin:15 enol:1 prototypes:1 leave:2 admissible:1 commute:1 phase:1 eigenvalues:1 anal:1 shows:1 lagrangian:1 zj:6 zk:1 mi:1 integrability:3 further:2 reine:1 odd:1 substitute:2 canonical:18 spectral:9 what:1 gl:2 appear:3 iterating:1 brackets:12 section:11 expressed:3 agrees:1 version:1 poles:7 above:6 new:7 method:9 satisfy:6 degree:5 newyork:1 respectively:6 aij:9 component:1 here:7 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solv-int9701005.txt |@word dewitt:1 consider:2 results:1 leads:2 proposition:5 oevel:2 expressions:2 localized:1 row:6 inverse:1 analytic:1 tr:2 tn:6 alvarez:2 spain:1 under:1 te:1 very:1 wave:1 entries:1 manin:5 condition:2 school:1 presented:1 solution:9 t0:6 leave:1 solved:1 vector:2 harry:1 indices:2 eigenvalues:1 becker:1 wronskian:3 matrices:4 elegant:1 zero:3 odd:6 linear:10 even:9 index:1 nonlinear:2 iterating:1 section:1 version:1 goes:1 new:8 preserved:1 satisfy:1 respectively:2 here:3 china:1 represented:1 along:1 sine:1 equations:1 appears:2 differential:1 obtained:6 remark:1 shift:1 inspired:1 placing:1 studies:1 composed:1 formulated:1 family:1 skdv:1 tools:1 use:3 commun:2 next:4 therefore:1 taken:1 type:7 until:2 more:1 solitons:3 company:1 dressing:1 odinger:3 particular:2 known:3 cases:1 iii:1 springer:1 chaichian:1 ma:4 recall:1 equation:13 det:31 soul:1 following:4 making:1 arrive:1 proof:4 beijing:2 give:1 process:1 organized:1 lψ:2 indicates:2 sense:1 verlag:1 needs:1 end:1 notation:2 θ2k:4 rather:1 holds:1 write:3 how:1 pure:1 exponentially:1 cicyt:1 b77:1 replacing:1 after:2 hence:3 lax:3 δj:1 representations:1 choice:2 compatibility:1 physical:1 clarkson:1 kulish:1 whenever:1 lemmas:1 ueno:2 explicit:5 darboux:19 so:5 representation:1 order:2 wronski:2 help:1 ith:1 hierarchy:3 indeed:3 paper:4 during:1 its:13 superdeterminant:3 thank:1 ln:5 interesting:1 solving:1 actually:1 supermatrix:1 absence:1 systems:5 main:1 non:1 noticing:1 introduce:3 framework:1 now:3 yu:1 easily:3 several:1 university:1 2d:1 realistic:1 found:1 2k:10 en:1 ei:1 ek:2 ej:3 doing:2 ed:1 allan:1 obtains:1 combining:1 quantum:1 our:9 eq:1 matrix:7 furthermore:1 since:2 vectorial:1 research:1 attracted:1 formula:2 math:7 provide:1 theory:1 kaup:1 ısica:1 mψ:1 departamento:1 standard:2 ask:1 derivation:1 applications:1 konno:1 turn:2 int:3 gordon:1 δij:1 universidad:1 consequence:2 ltn:1 first:3 initial:1 roelofs:1 variables:2 powerful:1 number:1 set:2 given:7 toy:1 similarly:1 introduction:2 system:17 construct:1 their:1 final:1 supermanifolds:1 gives:1 para:1 alonso:1 newell:1 segur:1 natural:1 coefficients:2 determines:1 iteration:3 second:2 were:1 tion:1 dθ1:1 dθ0:2 say:1 seed:1 need:1 any:1 viewed:1 kersten:1 gravity:1 liu:4 take:2 salle:1 established:1 simplify:1 formulae:1 remarks:1 iterate:2 a2k:15 soliton:10 constructed:2 considered:1 clear:1 ibort:1 physica:1 kp:3 berker:1 exp:28 kx:1 vries:1 particularly:1 show:2 supported:2 notations:1 gauge:3 solutions:16 manifold:1 decade:1 should:2 jan:1 lemma:5 only:1 integrable:3 jth:2 do:2 above:2 viewpoint:1 get:3 de:3 itoyama:1 dym:1 dv:3 dw:30 gen:1 fields:1 arxiv:1 nes:2 gaum:2 mapped:1 body:3 multiplying:1 constructing:1 reference:1 achieved:1 espa:1 θ2i:3 morosi:1 see:1 result:1 written:1 αd:1 geometric:1 available:1 publishers:1 notice:4 matveev:1 terms:3 shabat:1 extend:1 attention:1 vanishing:1 berezinian:1 solv:1 aim:1 both:1 last:7 context:1 proyecto:1 expression:1 finds:1 cj:3 reconsidered:1 conclude:1 simple:1 ca:4 dimensional:1 iterations:1 mathieu:1 transformations:7 lt:2 been:6 mart:1 defined:3 reduction:2 much:1 3u2:1 universal:1 choose:1 θj:4 θi:13 supersymmetric:16 ϑw:1 ınez:1 quantities:1 ϑc:1 ϑb:1 berezin:1 emparan:1 ϑk:1 general:1 present:2 case:5 developing:1 will:2 while:1 replaced:2 orica:1 property:1 thus:3 them:1 ii:2 reads:2 claimed:1 binary:1 different:2 perform:1 make:1 gets:1 used:1 superanalysis:1 counterparts:1 a2i:1 uˆ:10 ablowitz:1 schr:3 acknowledgement:1 well:2 academic:1 solve:1 usual:1 λw:1 sdet:21 when:2 obtain:4 yamada:1 facts:1 preprint:1 kluwer:1 field:2 zakharov:1 except:1 transformed:3 lett:2 theorem:1 relevance:1 transformation:19 cramer:3 crum:6 breaks:1 possible:1 background:1 press:2 using:4 advanced:1 mod:2 like:1 lost:2 follows:2 reduces:3 separately:1 continue:1 korteweg:1 δi:1 stationary:2 mathematical:1 parity:3 because:2 methods:1 classical:1 madrid:1 some:4 understood:1 examples:3 kdv:15 δn:1 schief:1 does:1 prog:1 steps:2 bd:3 pp:1 step:6 super:10 fordy:1 publishing:1 about:1 extension:3 constraint:2 column:1 wadati:1 o:1 seeds:2 extensions:2 introduced:1 block:2 cambridge:1 reidel:1 into:2 obtaining:2 three:1 down:2 references:1 operator:7 rows:1 mt0:1 there:1 transform:1 noticed:1 start:1 way:3 was:1 sanuki:1 form:4 but:1 line:1 removed:2 partially:1 embedded:1 whether:1 up:1 us:3 those:1 iterated:1 ki:2 associated:3 ai:4 abstract:1 denote:3 dα:3 effected:1 grassmann:2 functions:1 na:1 supermatrices:1 graduate:1 nas:2 interested:1 mathematics:1 theor:1 may:2 complutense:1 models:2 radul:5 medina:1 a1:4 a0:5 a3:2 a2:2 a7:1 variable:1 a8:1 parities:1 structure:2 supersymmetrized:1 rule:3 time:2 once:1
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solv-int9701006.txt |@word secondly:1 miwa:1 consider:21 remarkable:4 exponentiation:1 lagrangian:4 magnetic:1 global:6 results:7 integration:2 leads:5 eds:4 scalar:1 commute:4 generalize:1 rebbi:1 broader:1 talks:2 liao:2 expressions:2 involved:2 go:2 localized:1 corrigan:1 gˆj:1 inverse:1 const:2 analytic:1 re:1 paris:1 montonen:1 b260:1 simplify:1 tr:18 mη:1 tn:24 charge:11 tm:2 those:17 th:11 dressing:30 semenov:1 connecting:1 ev2:1 te:1 ev3:1 worth:1 indicating:1 ın:1 summarizes:1 case:11 conjecture:5 kπ:1 economical:1 advantage:1 parameterize:2 very:13 could:3 gˆm:15 conditions:5 choice:5 mν:1 electron:2 witten:2 formula:4 application:2 matrices:1 condition:13 four:2 annihilated:3 obvious:1 evn:1 level:8 bn:4 issue:2 notes:1 72b:1 t2:2 solution:44 olive:9 large:4 f1m:2 insights:1 vector:9 math:7 relation:6 hospitality:1 shansky:1 finiteness:1 upper:1 smaller:1 century:1 arctan:1 8k:1 dealing:1 aρn:3 direct:1 sign:2 approximation:1 elegant:1 zero:13 zx:1 value:4 zz:5 further:2 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solv-int9701007.txt |@word consider:2 rev:1 unhatted:1 results:3 scalar:1 proposition:1 consists:1 localized:3 c0i:12 technique:3 tr:2 βxx:3 alvarez:3 present:3 th:1 dressing:2 analogous:1 te:1 ingredient:1 straightforward:2 very:1 wave:2 valued:1 manin:7 condition:3 bxx:3 school:1 presented:2 list:1 solution:15 large:3 vector:4 brezin:1 becker:2 wronskian:1 dealing:1 coefficient:1 direct:1 matrices:2 zero:1 further:3 odd:4 linear:10 even:11 established:1 appear:1 giving:1 diag:2 section:2 selected:1 expressed:1 ˆb:2 above:1 new:4 method:2 satisfy:3 edited:1 simultaneously:1 κj:10 respectively:1 here:3 behaviour:1 desired:1 objects:1 china:1 will:2 represented:2 equations:5 appears:1 obtained:3 search:2 generalizing:1 algebra:1 involved:2 study:4 constitutive:1 pick:1 plotted:4 yamada:1 family:1 vij:3 replace:1 supervector:1 select:1 virasoro:2 plot:1 use:1 takes:2 commun:3 bx:5 ψt:1 next:2 nucl:1 therefore:4 taken:1 type:5 more:1 started:1 solitons:1 odinger:1 berlin:1 particular:5 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solv-int9701008.txt |@word proposition:4 represent:1 51b:1 partial:5 consider:20 funct:1 lagrangian:1 eλx:1 theoretical:1 results:11 interpret:2 scalar:1 commute:6 montr:4 computation:1 foundations:1 go:1 expressions:1 gl:20 gk:1 chaundy:2 rom:1 devoted:1 preserves:1 inverse:3 depend:3 calculate:3 dickey:4 editors:4 nonlocal:5 centerless:2 tn:48 list:1 charge:2 according:2 tk:11 th:3 under:10 tf:2 include:1 ingredient:1 case:12 conjecture:4 supported:1 proved:2 string:4 g1:3 very:2 rise:3 conditions:1 dokl:1 choice:3 implicit:1 corollary:1 putting:1 gerasimov:2 got:1 resonant:3 difference:3 condition:8 identity:2 entire:1 school:3 obvious:1 riemann:2 immediately:1 presented:1 turns:1 t4:18 t5:19 t2:10 t3:5 t0:87 t1:9 large:1 discrete:5 vector:26 phase:1 announced:1 ǫn:2 small:2 anal:2 shows:1 noted:1 related:1 possibility:1 ville:2 mn:9 zh:4 zi:16 zj:4 2k3:1 appearance:1 zg:3 nonautonomous:1 direct:7 sign:5 integrability:3 summer:1 yakimov:1 equal:1 link:1 further:2 dynamics:1 khesin:1 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solv-int9701011.txt |@word proposition:7 footing:1 homomorphism:4 consider:6 remarkable:2 similarity:1 rev:2 existing:1 leads:1 gf:1 ge:1 commute:4 generalize:1 montr:2 grateful:1 go:1 follow:1 expressions:10 gr:4 whose:1 preserves:2 inverse:7 sogo:1 chain:1 paris:1 exponentiation:1 containing:1 finally:2 those:2 th:2 under:5 semenov:6 geom:1 analogous:2 r12:75 g2:2 g1:4 zhang:1 very:2 rise:1 pressley:1 dokl:1 unchen:2 corollary:1 antipode:2 summarized:2 difference:1 matrices:2 condition:1 eit:7 jurˇco:3 dubrovin:1 solves:1 hamiltonian:11 did:1 turns:1 z14:1 sklyanin:7 t2:43 solution:13 t1:65 deals:1 discrete:2 vector:2 math:12 frolov:1 drop:1 shows:1 equation:27 zl:2 work:4 neighborhood:1 zi:1 takhtajan:1 direct:5 second:5 masson:1 further:1 dynamics:2 fonction:1 linear:6 even:1 index:1 what:2 nonlinear:1 plays:3 appear:3 invertible:1 section:7 expressed:3 maillet:1 symes:3 version:2 above:3 new:4 learned:1 factorizing:1 method:6 y2:25 full:1 simultaneously:2 notions:1 conf:1 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solv-int9701012.txt |@word consider:3 satify:1 results:2 integration:1 leads:2 eds:1 ferreira:2 consists:1 primes:1 c0:1 calculate:1 iii:1 equivalence:1 tn:3 swieca:1 tm:25 th:2 under:1 must:1 case:9 straightforward:1 2ra:1 choice:2 rm:3 difference:1 matrices:2 condition:1 tri:5 school:1 hamiltonian:12 solution:2 correct:1 try:1 math:4 manchester:1 solutions:1 α2a:1 sign:1 elegant:1 second:7 further:1 linear:2 established:1 stands:1 brackets:12 giving:1 section:1 above:7 expresses:1 satisfy:2 prescriptions:1 exchange:1 respectively:3 realizations:1 component:1 here:2 ansatz:2 equations:9 c0m:1 obtained:2 instituto:1 antisymmetric:2 studied:1 survey:1 poisson:2 involves:1 uniquely:1 explained:1 establish:4 recurrence:1 use:3 commun:1 contains:1 program:2 therefore:3 taken:1 associated:1 type:1 blas:1 more:1 introducing:1 formally:1 appendix:1 particular:1 hold:3 eα:5 eβ:1 account:1 te:1 equation:2 work:1 values:2 following:1 root:3 example:1 give:4 dnls:11 cartan:1 sense:2 write:3 fourth:1 rivelles:1 parameter:4 algebra:1 replacing:2 derived:1 different:1 compatibility:2 third:3 so:4 fundamental:1 sl:20 definitions:1 order:6 hierarchy:2 indeed:2 kba:1 satisfied:3 whilst:1 paper:1 through:2 signs:1 mentioned:2 its:2 roots:1 laced:1 2λn:1 jij:2 boson:1 systems:5 jacobi:15 correspondence:1 non:1 ym:6 introduce:3 mention:1 they:2 now:4 discuss:1 ift:1 easily:1 2q:5 2r:7 january:1 university:1 hepth:1 possibilities:1 each:2 aratyn:3 differential:1 weight:1 ed:1 eα2:2 related:1 special:1 out:1 shown:2 matrix:3 since:5 particles:1 may:1 ra:8 rb:4 denoted:2 got:1 ref:3 ri:15 rj:7 rk:3 theory:2 ısica:1 zimerman:3 derivation:2 r2:20 times:2 motion:1 δim:2 δij:1 adjoint:1 first:6 xn:2 xl:1 number:1 set:1 relations:3 jji:1 given:5 necessarily:1 checked:2 introduction:1 leading:1 eqs:3 system:14 construct:1 their:1 structures:8 gives:1 part:1 x2:3 kulish:1 pamplona:1 see:3 determined:3 were:3 entries:2 argument:1 say:1 need:1 seen:1 any:1 lie:1 αn2:1 liu:2 take:3 subject:1 kab:1 play:1 scripta:1 magri:1 paid:1 algebraic:1 involving:7 letter:1 successive:1 acknowledgements:1 pages:1 soliton:1 parametrize:1 physica:1 proceedings:1 bracket:11 physics:1 fact:2 quantity:2 show:2 reductions:1 supported:2 relation:3 akns:15 substituting:2 q1:21 eboli:1 q2:19 just:2 aψ:1 should:1 jan:2 only:1 hamiltonians:1 dn:2 do:1 dl:1 dm:14 de:1 dx:2 combinations:1 differentiating:1 heaviside:4 fields:6 arxiv:1 qa:8 qb:4 qi:6 qk:3 qj:4 qm:7 ql:8 multiplying:1 exists:1 imposing:1 2c:1 argued:1 namely:1 result:1 terms:7 points:1 brazil:1 satisfying:2 αa:5 written:1 closed:1 consecutive:2 αn:5 greatful:1 notice:1 εij:2 recently:1 shabat:1 hereman:1 attention:1 however:3 solv:2 ker:3 prescription:2 taking:1 equal:1 admit:1 finds:1 otherwise:1 cm:30 conclude:1 simple:3 moreover:1 throughout:1 kp:1 considering:1 described:1 basis:1 addition:1 three:5 strategy:1 int:2 pg:1 algebras:2 choose:3 corresponding:1 quantities:2 representative:1 chevalley:1 last:1 careful:1 those:2 p2:8 p3:7 p1:3 p4:4 expanded:1 value:2 choices:2 will:2 orica:1 refs:1 ii:5 im:3 containing:1 verified:1 generic:1 recursion:8 make:1 kαa:2 same:5 paulo:1 verifies:1 pauli:1 hierarchies:1 gets:5 independent:2 used:3 flows:1 kij:1 infinite:2 identity:8 well:1 components:2 model:2 summer:1 λa0:1 unesp:1 being:1 obtain:1 λe:1 world:1 λn:1 zakharov:1 point:2 guaranteed:1 except:1 source:1 generalized:7 vii:1 decomposed:1 possible:1 press:1 using:5 yields:2 evolutions:1 gauge:1 because:1 some:3 choosing:1 2qa:1 kdv:1 fapesp:1 comments:1 does:1 scientific:1 derivatives:2 bm:7 rua:1 bi:3 fordy:4 integers:1 actual:1 discussed:1 o:2 compatible:6 2cm:3 r1:23 introduced:5 into:5 lies:1 gomes:3 references:1 determine:2 operator:8 schrodinger:1 hep:1 there:2 way:2 δlj:2 was:2 δlm:1 function:3 form:3 delta:2 hb:1 cnpq:1 ha:4 made:1 us:3 below:1 problem:2 constant:1 ad:6 defined:5 abstract:1 specified:1 ao:1 general:1 identities:9 check:2 constructed:1 functions:4 eα1:3 na:2 nb:1 mathematica:3 other:6 role:1 a17:1 denote:1 a0:11 important:1 structure:4 implies:2 proposed:1 4r:1 c2m:1 time:1
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solv-int9701013.txt |@word consider:8 remarkable:1 results:1 eds:2 ferreira:3 commute:1 grateful:1 types:1 gi:2 whose:1 paris:1 concerned:1 tn:12 tm:2 th:6 dressing:8 te:1 conjecture:3 g0:1 very:1 condition:2 turns:1 solution:13 large:1 aρn:2 direct:1 zero:2 evaluated:3 linear:5 section:1 expressed:1 cell:1 new:2 solitonic:1 method:2 satisfy:1 justification:1 respectively:2 underwood:2 here:2 luiz:1 reported:1 november:1 sine:1 equations:10 change:1 obtained:4 great:1 parameters:3 vectors:2 resulting:1 action:1 suitable:1 formulated:1 vii:1 univ:1 use:1 positive:2 coupled:1 negative:1 memorial:1 nucl:4 therefore:1 associated:4 type:4 theoretical:1 more:1 flat:1 solitons:1 operators:5 under:1 curvature:2 particular:1 known:2 cases:1 mk:4 theories:3 merida:1 following:1 trans:1 tau:2 high:1 numbers:1 sense:1 b401:1 feature:2 b409:1 leznov:1 symposium:1 map:1 product:1 algebra:5 may:1 orbits:1 lax:5 date:1 representations:2 fk:7 fm:1 constants:1 sp:1 explicit:1 correspond:3 element:5 so:1 sc:1 representation:2 order:1 talk:3 restriction:1 furnished:1 hierarchy:7 indeed:1 through:1 existence:2 its:2 write:1 group:10 ln:3 interesting:1 lm:1 actually:1 choose:1 non:5 now:3 developments:1 ift:2 term:1 finite:1 january:1 university:1 each:2 subset:1 differential:2 weight:1 energy:1 numeric:1 constitute:1 toda:3 eq:1 special:2 out:4 jimbo:1 matrix:3 gradation:3 research:1 gˆj:1 gˆ:6 gˆi:8 conjectured:1 ref:2 theory:2 ısica:2 possibility:1 quite:2 shansky:1 subalgebras:1 definition:1 anchez:3 times:3 american:1 gordon:1 consequence:1 βi:2 βj:3 first:1 sanchez:1 simplifies:1 features:1 relate:1 variables:2 number:2 construct:1 another:1 given:3 checked:1 adjoint:1 system:1 least:1 their:1 fn:6 fonctions:1 structures:2 exploring:1 kosmann:1 appearence:1 specify:1 pamplona:1 lying:1 guill:4 integrability:1 matter:1 kashiwara:1 generalization:1 say:1 seem:1 lie:4 wilson:2 responsible:1 εn:7 generalized:1 efn:1 latino:1 kac:5 collaboration:1 centro:1 gauss:1 acknowledgements:1 class:2 soliton:16 parametrize:1 considered:2 ef1:1 ef2:1 phil:1 physica:1 points:1 verdier:1 exp:2 physics:2 fact:2 supported:1 miwa:1 solutions:24 analogue:1 based:2 proposed:1 spite:1 jan:1 bernard:1 only:1 explicitly:1 generators:1 integrable:9 local:1 abelian:4 de:2 tranformations:1 babelon:2 fields:5 arxiv:1 common:3 set:3 exists:1 up:1 connections:3 see:1 japan:2 brazil:1 satisfying:1 ways:1 functionals:1 written:1 various:1 conditions:2 notice:1 latin:1 terms:7 shabat:1 rims:2 solv:2 both:1 according:1 zakharov:1 connection:3 argue:1 among:2 affine:3 author:1 point:1 dimensional:1 respect:1 schwarzbach:1 considering:1 described:2 transformations:4 been:1 basic:2 define:1 relations:1 corresponding:4 formed:1 subspace:1 instituto:1 general:2 those:4 case:1 multi:5 appearance:1 value:1 orica:1 property:1 procedure:2 miramontes:3 larger:2 mexico:1 them:5 systems:2 gervais:1 different:2 specialization:1 grant:1 journal:1 admit:1 same:1 paulo:1 turok:1 complex:1 emphasize:1 hierarchies:7 gets:1 subalgebra:3 used:1 upon:1 publ:2 birkhauser:1 potentials:1 infinite:2 subgroups:1 eigenvectors:3 variety:1 well:1 analysis:2 components:2 exponentials:1 unesp:1 being:1 underlying:1 using:1 bullough:1 nilpotent:1 efk:1 transformed:1 lett:1 mod:1 transformation:4 big:1 exponentiating:1 vacuum:12 integer:1 moreover:1 moody:5 follows:1 δj:1 b470:1 mathematical:1 because:1 methods:1 some:7 understood:1 acad:2 specified:1 kdv:1 olive:2 lead:1 decomposition:1 provides:1 proc:1 saveliev:3 conference:1 kyoto:2 equivalent:2 rua:1 bi:2 bj:1 bk:1 relating:1 properties:1 integers:1 central:2 dependence:1 o:2 compatible:1 cartier:1 ot:1 consequently:1 organizers:1 soc:2 into:1 integral:1 functional:2 appropriate:1 en:4 references:1 operator:1 hep:6 vac:6 support:1 there:1 lond:1 way:1 naturally:1 function:1 form:5 but:1 cnpq:1 highest:1 partially:1 made:1 cin:3 cim:1 ωn:2 problem:3 called:1 eigenvector:1 constant:2 int:3 certain:1 abstract:1 ao:1 denote:1 check:1 constructed:1 functions:6 ingredients:1 application:2 details:1 becomes:1 elements:6 vertex:1 important:1 a8:1 b311:1 implies:2 assume:1 required:2 orbit:2 presenting:2 hirota:3 original:2
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solv-int9701014.txt |@word consider:3 εq:1 results:2 known:2 london:1 solutions:2 using:1 satisfies:2 scattering:6 multidimensional:1 stewartson:8 row:3 q1:9 inverse:7 based:1 ψj2:1 zakharov:2 solving:3 royal:1 nonlocal:1 jan:1 conjugated:1 systems:2 theorem:3 mail:1 shabat:2 columns:1 above:1 g1:4 naukova:1 possible:1 wave:2 fokas:2 putting:1 background:2 qu:4 respectively:1 ds:5 condition:1 closure:1 dirac:3 riemann:1 course:1 follows:1 arxiv:1 solution:6 dumka:1 solved:1 investigate:1 n1:1 l2:2 math:3 l1:2 anal:1 works:1 reduced:1 because:1 g2:4 formulate:1 perturbation:1 related:1 second:2 elements:1 subject:1 nonzero:1 ru:1 nonlinear:2 dimensions:1 diag:1 shall:1 squared:1 eigenstates:1 pioneer:1 µi:1 causes:1 rb:1 between:1 formula:1 boundary:2 order:1 approach:2 method:7 kiselev:1 satisfy:4 linear:2 ufa:2 kaup:3 proc:1 expansion:2 q2:7 here:2 element:1 solv:1 ψj1:1 come:1 hilbert:1 obtained:1 generalizing:1 ok:1 institute:1 study:1 prove:1 o:1 ist:2 compatible:1 trivial:1 linearizes:1 philadelphia:1 fourier:9 2iπ:1 first:4 soc:1 formulated:1 ikη:5 kiev:1 h2:3 variables:2 h1:5 ikξ:4 transform:6 dimensional:2 represented:1 santini:1 references:1 operator:1 respect:4 pp:1 rows:2 may:1 introduction:1 equations:8 system:6 long:1 defined:1 perturbations:1 goursat:1 statement:2 basic:2 siam:2 was:1 define:1 function:1 form:5 academy:1 factor:1 interaction:1 integrable:4 russian:2 denote:4 coefficients:3 hyperbolic:1 equation:16 work:1 see:1 value:1 column:2 three:1 str:1 following:3 problem:5 gives:1 russia:1 theorems:1 give:1 int:1 packets:1 abstract:1 surface:3 general:1 dual:1 linearized:5 solitons:1 dk:1 functions:3 s2:1 make:1 when:1 sciences:1 conditions:4 details:1 spatial:1 mathematics:1 ordinary:1 out:2 bilinear:4 used:1 develope:1 dξdη:1 waves:1 investigations:1 models:1 i0:1 problems:1 v1:2 v2:2 plane:1 uses:1 formulae:1 linearization:1 uˆ:1 ablowitz:2 class:1 structure:1 matrix:3 realized:1 short:1 ig2:1 ig1:1 well:1 physica:1 χj:1 segur:1 χi:1 exp:10 time:1 appl:2 hˆ:2 s1:1 davey:9
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solv-int9701015.txt |@word ibid:1 partial:1 consider:2 similarity:1 alg:2 results:2 scalar:10 proposition:16 mp2:2 mp1:2 homomorphism:2 prop:2 whose:1 calculate:4 combinatorial:1 eigenbasis:4 technique:2 young:1 th:8 under:1 analogous:1 tb:1 tc:5 norm:4 ta:22 applied:1 tkm:1 straightforward:2 orthogonal:9 mpm:2 dokl:2 wave:3 corollary:1 valued:2 every:2 jack:16 summarized:1 difference:1 condition:1 partitions:3 entire:1 hamiltonian:6 irreducible:21 tion:2 pullback:2 commute:2 indices:1 gauge:2 lines:1 application:1 zn:5 submodules:7 ρm:4 coefficient:1 zero:1 spect:1 canonical:1 appear:1 giving:1 deeply:1 section:11 version:1 subspaces:1 bm:17 new:2 consisting:1 satisfy:5 degree:1 ranged:2 component:2 here:6 groups:1 zetlin:21 along:2 enveloping:1 appears:1 z2:1 obtained:2 remark:8 antisymmetric:1 gln:45 institute:1 vectors:3 p2:9 products:1 permutation:1 action:12 proof:5 changes:1 sci:1 uniquely:1 useful:1 apr:1 requiring:2 replace:1 weaker:1 sgn:1 total:1 establish:1 unit:2 use:3 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solv-int9701016.txt |@word represent:1 consider:3 results:1 scalar:1 commute:1 intricate:1 remarkably:1 whose:2 certainly:1 depend:1 those:6 elliptic:1 under:3 include:1 applied:1 belonging:1 amplitudes:4 string:4 primed:1 affect:1 little:1 exact:1 condition:4 turns:2 solution:1 vector:21 eigenvalues:2 neighborhood:1 direct:1 sergeev:2 zero:1 odd:1 even:2 aim:1 what:1 sum:3 selected:1 expressed:1 subspaces:2 new:5 consisting:1 degree:1 respectively:3 never:1 component:1 equals:1 here:5 objects:1 ansatz:3 directions:1 along:1 equations:2 change:1 obtained:3 great:2 shift:1 changed:1 allows:1 experience:1 action:4 makes:3 subtracts:1 coinciding:1 1st:1 select:1 use:1 links:1 chelyabinsk:2 commun:1 remains:2 give:1 explicitly:1 call:1 ψc:2 associated:2 ψf:2 bethe:3 ψd:8 ψe:8 formally:1 th:2 vacuums:1 operators:1 correspondingly:1 particular:1 known:1 cases:1 must:6 account:1 recall:2 equation:2 work:2 remain:1 values:2 following:3 making:2 root:1 compare:2 korepanov:3 figure:2 stated:1 arise:1 hexagons:1 states:4 numbers:1 want:1 sense:4 end:1 discussion:1 holds:2 write:2 how:2 consist:1 instead:1 parameter:5 sin:11 product:4 modest:1 plane:3 parallel:1 hedgehogs:1 transposed:2 physical:1 sectors:3 maybe:1 lines:3 so:3 enter:1 order:2 acts:3 indeed:1 over:3 move:1 paper:5 through:1 mentioned:1 still:1 its:3 roots:1 group:1 summands:1 matrices:1 fix:1 coordinates:2 fig:7 correspondence:1 non:1 combination:1 fragment:1 they:1 half:1 now:2 yu:2 discuss:1 eigenvalue:4 january:1 university:1 labeling:1 iff:1 each:11 side:1 baxter:2 schemes:1 successively:1 viniti:1 doing:1 oneparticle:1 our:3 beyond:1 event:1 out:10 shown:1 matrix:15 3rd:1 space:3 cubic:3 particles:2 acting:2 formula:2 math:1 shows:1 turning:2 linear:3 diagonal:1 free:1 surely:1 besides:1 put:1 beginning:1 pairs:2 could:1 success:1 isotropic:2 assumed:1 onto:3 first:2 already:1 variables:1 number:3 comprised:1 restrict:1 done:1 another:3 between:1 given:1 similarly:1 introduction:1 construct:1 indicate:1 calculations:1 structures:1 shifted:2 part:1 x2:1 representing:1 than:1 coefficients:1 was:3 require:1 see:3 determined:1 contrary:1 amplitude:2 russia:1 decompose:1 result:1 explicit:2 zamolodchikov:3 turned:2 say:1 need:1 seen:1 their:3 built:3 convenient:1 latter:3 note:2 extracted:1 take:4 analogy:1 finding:1 analogs:1 unless:1 trace:1 any:3 reach:1 algebraic:1 significant:1 formulae:3 consequences:1 considered:1 later:1 vertices:5 hints:1 points:4 hietarinta:2 section:6 fact:2 sector:3 show:1 text:1 discovered:3 spaces:3 solutions:2 trivial:4 find:1 parameters:1 kagome:8 enough:1 jan:1 only:2 going:4 formulation:1 factor:1 integrable:1 hope:1 do:3 triangle:13 goes:1 means:1 de:1 dc:1 ones:4 ϕe:13 ϕd:13 ϕg:1 ϕf:2 ϕa:3 ϕc:5 ϕb:2 stroganov:2 places:1 arxiv:1 method:1 including:1 constructing:1 namely:2 changes:3 said:1 tensor:3 state:1 simplest:2 probably:2 conditions:5 multiplied:1 triples:1 extend:1 importance:1 solv:1 both:3 cos:6 taking:2 according:4 families:2 faces:1 whole:2 comes:1 arbitrarily:1 relevant:1 point:2 simple:1 ce:1 2nd:1 dimensional:5 anti:1 moreover:1 considering:2 second:1 three:5 been:1 covectors:2 deposited:1 interest:1 algebras:1 direction:1 arises:1 corresponding:5 search:1 present:2 case:3 novel:1 tank:1 look:1 tetrahedron:4 will:11 while:1 situation:1 properly:1 vectors:11 a27:1 strait:1 thus:6 them:1 itself:1 triple:1 technology:1 attach:1 different:3 author:1 make:1 belong:2 connection:1 same:3 linked:1 unity:4 φc:2 φd:1 φf:4 finite:3 composition:1 extended:1 trivially:1 hand:1 parametrized:2 edges:1 moving:1 infinite:1 eigenvectors:7 expression:1 mangazeev:2 well:4 obviously:1 without:1 studying:1 model:11 usual:1 just:1 less:1 being:1 bazhanov:1 obtain:2 transforms:1 scattering:1 eigenstates:5 previous:1 cut:1 family:2 mix:2 lattice:24 add:1 belongs:1 transformed:4 easy:2 transformation:3 identical:1 sums:2 vacuum:8 using:1 bit:1 intersection:2 decomposes:1 like:8 particle:23 sizes:1 follows:3 separately:1 yields:2 essential:1 mathematical:1 lenin:1 because:1 old:5 classical:2 some:9 respect:1 proper:2 ourselves:1 slice:1 describing:1 lead:1 dce:6 perpendicular:2 step:1 ratios:1 periodically:1 bz:1 integers:1 would:1 extending:1 discussed:1 ensure:1 act:1 automatically:1 considerations:1 into:3 down:1 lies:2 dualities:1 references:1 operator:3 proportional:2 tetrahedral:1 hep:2 deal:1 transfer:11 there:3 φcd:1 way:4 sections:1 naturally:1 form:7 but:4 construction:1 russian:1 line:1 trying:1 themselves:1 applying:1 evident:1 type:8 inside:5 attached:1 ωt:1 us:8 ψg:1 planes:2 problem:1 more:2 similar:2 called:1 eigenvector:6 ordered:1 int:1 abstract:1 denote:1 images:1 av:1 ax:1 moves:1 triangles:7 constructed:5 functions:1 no:2 when:5 field:1 other:5 papers:1 picture:1 superposition:1 separate:1 models:4 vertex:4 studied:1 sides:1 assume:2 curve:1 bca:1 together:6 time:1 strings:1 once:1
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solv-int9701017.txt |@word represent:1 concept:1 partial:2 consider:5 remarkable:1 squared:12 equalities:1 bull:1 pseudodifferential:1 results:4 leads:1 eds:7 ferreira:1 proposition:11 generalize:1 edu:1 consists:1 particularly:1 expressions:7 gl:2 χa:13 issues:3 gr:4 compact:1 whose:6 inverse:5 depend:2 chain:1 aug:1 workshop:2 technique:1 tr:13 acting:18 containing:1 tn:11 leibniz:1 finally:2 according:11 tj:2 tk:19 th:25 under:3 grinevich:2 indicating:2 ingredient:2 applied:4 belonging:1 supported:2 g2:3 g1:3 zhang:3 very:2 trisecant:1 rise:2 negev:1 wave:9 rl:1 corollary:2 commute:2 entries:2 induction:1 li:1 associated:3 difference:3 exact:1 deformations:1 gurion:1 entire:1 school:1 usp:1 usa:1 riemann:1 hamiltonian:6 turns:3 notes:1 t2:9 solution:5 t1:13 large:2 discrete:8 vector:6 progress:1 science:1 indices:4 eigenvalues:1 anal:1 originally:1 reproduced:1 application:5 zn:4 wronskian:7 vertical:1 const:1 ψi:8 direct:2 zero:5 summer:1 zz:2 bilocal:3 further:8 panda:1 khesin:1 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solv-int9701020.txt |@word gs:12 consider:1 chain:2 gp:1 superfields:10 four:1 gf:6 ferreira:1 generalize:1 antichiral:1 expressions:3 gl:3 scr:1 ihep:1 superspace:2 investigation:1 tk:8 th:3 under:1 belonging:6 connects:1 every:1 difference:1 presented:1 t2:13 solution:1 discrete:20 indices:3 relation:6 consistent:2 sign:1 second:5 chen:1 subscripts:1 index:6 what:2 nonlinear:1 invertible:1 brackets:3 sum:1 above:1 krivonos:4 new:15 acknowledgments:1 exercise:1 dψj:3 respectively:3 here:3 represented:1 equations:20 obtained:4 reason:1 permutation:5 usually:1 useful:2 protvino:1 summation:3 apply:1 establish:2 derivatives:3 feb:1 takes:2 would:1 commun:1 covariant:3 positive:1 fordy:1 ψj:8 nucl:1 derivation:1 call:1 therefore:2 themselves:1 theoretical:1 more:5 introducing:2 operators:7 supergroup:2 odinger:1 pab:3 particular:3 cases:1 fermionic:8 equation:3 work:2 modified:5 reproduce:1 obvious:2 publications:1 following:8 making:1 ibs:2 example:1 decoupled:1 give:1 introduces:1 aratyn:2 information:2 boussinesq:1 goal:1 darboux:2 acts:3 leznov:7 nontrivial:1 zinovjev:1 gnls:29 may:1 after:1 derived:3 mapping:14 applications:1 fb:5 produce:2 lax:12 ff:1 fj:26 law:1 fl:7 short:1 remember:1 kulish:1 explicit:8 order:1 fα:1 hierarchy:23 developed:1 over:3 produced:2 its:3 lg:1 derive:4 group:3 thsun1:1 la:1 ln:11 interesting:1 lk:5 conjugation:3 actually:2 forms:2 systems:1 mail:1 main:1 supersymmetry:1 them:4 junction:3 combination:1 acklund:3 introduce:2 mention:1 they:4 bogoliubov:1 now:1 discuss:1 easily:2 term:1 hereafter:1 january:1 hepth:1 2d:1 form1:1 arrow:3 2j:5 mean:2 square:1 related:3 toda:3 entering:2 laboratory:1 operation:1 eq:3 ru:1 matrix:1 space:1 crucial:1 research:1 acting:3 equate:1 dutch:1 ref:2 math:2 foundation:1 completely:2 complicated:1 counterparts:1 simplifying:1 dubna:5 generate:3 e2:5 zimerman:1 chiral:1 fa:18 motion:2 fc:4 generalizations:1 first:5 origin:1 symmetry:11 number:1 done:1 relations:11 equating:1 given:2 rewritten:1 introduction:1 eqs:4 system:3 dfs:1 their:8 intermediate:1 superintegrable:1 dfj:2 scheme:2 dfa:3 gives:2 reversed:1 part:1 ivanov:2 kind:1 dff:8 zero:1 future:1 were:1 remembers:2 symmetries:5 rewrite:1 conjugate:1 need:1 mappings:18 convenient:1 lin:1 note:1 generalized:1 coincide:2 moscow:1 established:2 algebraic:1 letter:2 formulae:1 pair:1 considered:2 flow:6 physica:1 reflecting:1 exp:10 physics:1 nls:4 supported:1 purely:1 gauge:6 solutions:1 substituting:1 sorin:8 knowledge:1 parameters:2 explain:1 should:1 only:5 integrable:10 local:1 hope:1 do:3 dj:4 means:2 df:7 dd:5 db:1 da:6 dz:1 combinations:1 regarding:1 fields:4 arxiv:1 summary:1 contain:2 fixed:4 set:5 modulo:1 exists:1 see:2 result:1 discussions:1 recently:1 lee:1 invariant:1 boundary:1 conditions:1 ends:1 terms:2 however:1 labelle:1 analyzed:1 thank:1 region:1 equal:2 russia:1 admit:3 context:1 expression:2 simple:1 superfield:4 dimensional:1 solv:3 bα:14 bβ:11 respect:2 mathieu:2 transformations:12 basis:5 addition:4 due:2 been:4 interest:2 basic:1 define:2 direction:1 supersymmetric:27 concerning:2 covariance:1 pαβ:5 observe:2 understand:1 representative:1 derivative:4 present:3 case:5 splits:1 will:1 intas:1 property:1 taking:1 bonora:2 thus:2 according:1 reads:1 currents:1 different:7 stimulates:1 grant:3 connection:2 unity:1 complex:7 hierarchies:12 independent:1 flows:2 purpose:1 infinite:1 invariance:1 2gp:2 schr:1 nevertheless:1 no:5 well:3 without:1 components:4 coordinate:1 organization:1 subgroup:2 construct:1 proposed:1 obtain:5 valuable:1 using:1 facts:1 nissimov:1 enters:1 preprint:5 nwo:1 lett:8 easy:1 pjc:18 transformation:7 possible:1 cf:2 press:1 integer:1 psp:4 name:1 like:7 follows:2 integrals:1 arbitrary:7 become:2 because:2 some:5 understood:1 kdv:5 grading:1 toppan:1 integration:2 manipulations:1 does:1 connecting:3 provides:2 substitutes:1 bl:8 equivalent:3 bp:8 bs:2 imaginary:1 super:2 properties:1 comparison:1 about:2 extension:1 fairlie:1 discussed:3 range:2 extensions:1 act:3 idd:3 slightly:1 letters:1 into:3 appropriate:1 references:1 operator:9 bosonic:12 hep:3 additional:1 there:6 start:1 way:1 jinr:7 analyze:1 was:3 function:2 form:5 denoting:1 but:1 hk:1 repeated:3 russian:1 line:2 partially:1 applying:4 inside:2 up:1 us:8 limit:5 demonstrate:2 problem:1 similar:1 constant:2 ag:1 int:3 coincides:2 abstract:1 generating:1 proven:1 conserved:1 our:3 corresponding:8 constructed:3 integrability:2 variety:3 extract:1 other:2 jd:1 conclusion:1 briefly:1 important:2 structure:3 values:4 pacheva:1 time:2 4d:4
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solv-int9701021.txt |@word partial:1 remarkable:1 lagrangian:8 results:1 bc:1 four:4 eds:3 scalar:1 houches:1 edu:2 follow:1 mandelstam:1 coleman:1 inverse:2 aug:1 technique:1 recurrence:5 finally:1 does:1 manifolds:1 th:1 must:1 case:15 belonging:1 far:1 rise:1 choice:1 every:1 exact:2 condition:1 leads:1 school:1 level:1 bn:7 vertex:1 solution:2 indices:1 noted:1 concluded:1 zn:4 cap:1 tel:2 coefficient:2 mussardo:1 past:1 painlev:14 equal:1 further:1 dynamics:1 ode:4 linear:2 even:1 index:2 nonlinear:1 tsuchiya:1 appear:1 diag:1 section:3 slight:1 consistently:3 version:2 poles:1 above:6 fractional:1 new:9 method:2 body:1 full:2 led:2 christe:1 component:1 understanding:1 test:4 ansatz:3 address:1 along:1 sine:3 equations:13 z1:4 z2:4 obtained:1 tunneling:2 study:2 studied:2 allows:3 p2:8 decoupled:1 usually:1 resonance:1 studies:2 appropriately:1 via:4 useful:1 extra:1 apr:1 addressed:1 summation:1 apply:5 total:1 proceed:2 usa:2 bukhvostov:10 remains:1 positive:1 contains:1 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solv-int9701022.txt |@word partial:1 consider:8 remarkable:1 magnetic:1 results:3 zhedanov:1 devoted:1 chain:1 those:2 include:1 amplitudes:2 wave:1 govern:1 experimentally:1 difference:2 school:1 bn:45 tokyo:2 t2:11 solution:6 t1:13 discrete:13 vector:1 demonstrated:1 cmv:8 hasegawa:1 prediction:1 pulse:4 sign:1 integrability:5 meanings:1 nonlinear:12 section:3 version:2 new:12 waveguide:1 method:5 satisfy:1 respectively:1 component:4 here:3 concluding:2 equations:35 change:1 obtained:4 study:2 studied:3 studies:1 useful:1 apr:1 private:1 kharchev:1 use:1 waveguides:1 contains:3 next:1 call:2 relativistic:1 volterra:4 type:3 theoretical:1 possible:1 introducing:4 becomes:5 odinger:9 cases:2 must:2 springer:1 permits:1 equation:58 when:2 modified:4 mv:3 following:3 root:1 example:1 dnls:3 organized:1 information:1 pure:1 description:1 may:3 applications:1 lax:1 parallel:1 dynamical:1 ueno:1 lines:1 restriction:1 over:1 paper:3 through:1 japan:1 satisfies:1 still:1 sciences:1 interesting:1 systems:4 couplers:1 possessing:1 introduce:5 effects:1 hands:1 discuss:1 it1:2 february:1 several:5 hereafter:1 θij:1 mode:4 2i:1 differential:1 related:1 toda:26 wavelength:1 special:2 rev:1 iizuka:1 math:2 densities:4 fiber:2 interactions:1 completely:2 2dimensional:1 definition:1 takasaki:1 times:6 gordon:1 δij:1 βi:2 variables:7 number:2 1t:1 introduction:1 system:5 construct:1 their:1 2al:1 continuous:2 optical:4 x2:1 x3:1 amplitude:2 perturbative:1 jpn:5 7b:6 7a:6 rewrite:2 explicit:1 conjugate:3 seen:2 any:1 convenient:1 k3:1 k2:2 k1:2 gkl:2 k4:1 investigations:1 regular:1 remarks:2 soliton:12 considered:1 ki:1 ohta:1 ku:1 sum:3 laws:3 nls:11 show:4 bright:8 relation:3 solutions:2 find:1 parameters:4 situations:1 only:1 integrable:17 adequate:1 exchanged:1 envelopes:2 viewpoint:1 means:3 dependent:2 words:1 lossless:1 continuum:5 fields:1 arxiv:1 predicted:1 eiθn:1 view:4 ik3:1 set:3 ik4:1 physically:1 comparable:1 see:1 recently:1 phases:1 ladik:2 between:3 approach:1 notice:1 terms:1 shabat:1 however:1 key:1 jk:1 solv:1 jetp:1 both:1 last:1 propagation:5 faces:1 among:2 point:4 dimensional:6 moreover:1 masato:1 described:2 transformations:1 been:2 reduction:1 describes:1 define:1 6a:1 6b:1 arises:1 6d:1 quantities:1 narita:1 derivative:1 general:1 present:2 case:7 multi:4 stolen:1 conserved:7 cast:1 while:1 coupled:26 ii:2 reads:1 ij:6 dual:6 technology:1 fibers:1 lengths:1 media:1 same:7 complex:9 electro:1 φn:93 independent:1 numerical:1 hand:1 infinite:1 ablowitz:1 d1t:1 schr:9 modes:1 well:1 theses:1 components:2 quantitative:1 usual:1 being:1 reiθ:1 obtain:6 previous:2 adv:1 note:1 density:2 zakharov:1 except:1 lattice:10 lett:1 heidelberg:1 momentum:2 generalized:2 opt:1 iα:2 iβ:2 term:1 dark:11 picosecond:1 using:6 variants:2 follows:1 mironov:1 menyuk:1 communications:1 arbitrary:1 become:2 university:1 mathematical:1 methods:1 examples:1 b2:1 overlap:1 restoring:1 run:2 dch:3 equivalent:2 gji:1 although:1 about:1 discussed:1 meaning:1 reduced:1 2iφ:1 introduced:1 soc:6 maxwell:1 references:1 sov:1 operator:1 hep:1 additional:1 there:2 conservation:3 way:4 gij:7 medium:1 φjn:1 form:1 but:2 line:2 coupling:1 embedded:2 limit:6 agree:2 detailed:1 constant:1 int:1 abstract:1 am:1 denote:1 single:2 6c:1 corresponding:1 physical:1 no:3 hybrid:1 d2t:1 graduate:1 field:1 other:3 hirota:3 wadati:3 important:1 variable:1 independently:1 longer:1 assume:1 together:1 time:4 4d:1 4b:1 4c:1 4a:1
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solv-int9702001.txt |@word secondly:1 consider:4 yasuhiro:1 edn:3 proposition:10 row:3 whose:8 inverse:1 depend:1 analytic:1 young:1 finally:3 dz2:1 those:3 th:16 kokyuroku:1 applied:1 supported:1 putting:3 entries:9 difference:8 notes:1 solution:3 discrete:15 vector:3 anal:1 attracting:1 grantin:1 japanese:1 cosh:2 painlev:15 bilinear:8 what:1 nonlinear:2 appear:1 section:3 expressed:9 3n:13 above:1 scientists:1 ˆj:2 method:1 revealing:1 degree:1 respectively:3 here:3 papageorgiou:1 desired:1 sinh:3 equations:19 remark:1 shift:1 studied:2 hiroshima:2 suitable:1 studies:1 appropriately:1 useful:1 hermite:1 derivatives:1 use:1 feb:1 would:2 prove:4 sports:1 few:1 type:7 introducing:1 rich:1 fokas:1 appendix:2 encouragement:2 particular:2 known:2 cases:3 ramani:7 science:1 equation:9 klk:1 following:9 example:3 proof:6 2lk:1 give:3 means:1 how:2 parameter:1 replacing:1 after:1 derived:3 higashi:1 applications:1 lax:1 faculty:1 multiplication:1 natural:1 clarkson:1 explicit:1 so:4 fundamental:1 representation:3 existence:1 satisfies:7 its:2 τn:77 thank:1 kagamiyama:1 lj:4 lk:21 forms:1 systems:1 main:2 weber:1 them:3 good:1 combination:1 acklund:2 noticing:1 introduce:3 mention:1 they:4 identically:2 singularity:2 now:6 discuss:1 easily:2 2v:1 2w:1 xlk:1 university:2 l2:1 l3:1 l0:9 l1:19 2n:30 side:2 2j:7 mean:1 differential:1 ed:1 reduce:4 expect:2 combining:1 our:1 eq:31 special:7 shown:7 since:2 rev:1 denotes:2 may:1 adjust:1 rational:16 lecture:1 ref:2 math:5 linear:1 written:1 possibility:1 asi:1 derivation:1 ministry:1 hence:3 xun:1 first:5 suffix:1 laguerre:5 relate:1 variables:1 directly:1 size:2 passes:1 given:13 checked:1 rewritten:1 similarly:2 introduction:1 eqs:8 relations:5 their:1 statement:2 dt2:1 molecular:1 structures:1 1n:3 shifted:2 continuous:11 airy:2 l2n:46 unfortunately:1 kenji:1 piii:1 second:3 classes:1 gives:2 rewrite:1 ann:1 kajiwara:8 need:1 any:1 zero:2 convenient:1 εv:1 note:1 εn:1 εk:2 formulas:5 object:1 algebraic:3 2tw:1 pair:1 tη:1 sometimes:1 proceedings:1 ohta:6 exp:3 tanabe:1 hietarinta:2 show:3 authors:2 solutions:32 keywords:1 analogue:3 d2:2 find:3 subtracting:4 zη:1 based:1 parameters:2 state:1 should:1 lemma:6 only:1 transcendental:1 factor:1 integrable:1 columns:1 dn:6 do:1 notation:2 get:8 overall:1 ones:1 dz:2 determinants:8 arxiv:1 crm:1 ser:1 notice:1 culture:1 namely:3 result:4 eliminating:1 japan:4 discussions:1 terms:1 closer:1 behind:1 simplest:1 geometric:1 multiplied:2 ends:1 attention:1 recently:1 rims:1 confusion:1 p2n:2 however:3 jn:6 solv:1 article:2 xλ:2 many:2 taking:1 laplace:4 ln:14 admit:5 among:2 appeared:1 height:1 polynomial:6 moreover:6 pv:1 three:1 been:5 int:1 much:1 expected:1 pk:5 pn:4 pl:3 determinant:9 suppress:1 confinement:2 understand:1 present:2 case:2 p1:1 xτn:1 trick:1 aid:2 property:1 procedure:1 thus:3 contiguity:1 vn:12 ii:5 2τn:4 different:1 education:1 verified:1 make:1 same:4 strange:1 several:1 used:1 see:3 keys:1 effect:1 hand:2 identity:2 well:1 entry:1 profs:1 grammaticos:7 obtain:7 λk:2 yamamoto:1 ucker:3 adding:5 kluwer:1 regarded:2 parametrization:3 nato:1 lett:1 easy:2 theorem:6 transformation:2 analogy:1 read:1 test:1 know:1 using:10 ams:1 like:1 follows:4 reduces:4 yields:3 mathematical:1 right:2 methods:1 classical:2 sequence:1 some:2 okamoto:2 choosing:1 dz3:1 does:3 bessel:1 kyoto:1 equivalent:2 expansion:4 although:1 described:1 about:2 most:2 column:20 nijhoff:1 discussed:2 dzn:2 block:1 nothing:1 references:1 operator:1 next:1 rows:1 log:1 there:3 appl:1 was:1 function:17 2vn:1 but:2 representaion:1 applying:4 versions:1 us:1 un:5 limit:15 empty:1 demonstrate:1 problem:1 similar:1 called:1 pii:11 proved:1 defined:4 certain:1 abstract:1 general:1 engineering:2 formalism:1 identities:1 piv:1 constructed:4 satsuma:6 functions:5 nn:1 no:2 electrical:1 department:2 mathematics:1 2dn:1 conclusion:1 expressible:1 symbol:1 problems:1 polynomials:5 important:1 structure:1 hirota:1
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solv-int9702002.txt |@word consider:4 remarkable:3 results:4 leads:3 proposition:4 computation:1 6y:1 follow:1 factorizing:1 inverse:1 dα0:1 dα1:4 γj:2 δhm:1 tm:2 spain:1 under:1 te:1 vxx:1 δw:1 wave:1 corollary:1 formula:1 manin:2 generalised:1 four:4 school:1 cvx:1 hamiltonian:12 differentiating:1 solution:10 leave:1 solved:1 convenience:1 harry:1 dαi:1 consistent:1 direct:1 zero:1 further:1 odd:1 spectral:3 aim:1 nonlinear:1 section:7 celebrated:1 birkhoff:1 above:11 new:3 ˆk:2 method:1 coefficient:1 κi:1 respectively:1 component:3 here:7 believed:1 xθ:1 china:1 du1:3 equations:4 supplying:1 obtained:1 remark:3 studied:2 pxx:1 beijing:2 modifying:1 linearization:1 derivatives:1 feb:1 proceed:1 prove:4 super:9 contains:1 γi:8 ψt:1 next:3 comparing:1 m1:1 m0:1 usp:1 associated:3 type:5 more:1 becomes:1 operators:8 odinger:3 validity:1 wi:3 corresponding:1 cases:3 iii:2 fermionic:3 keeping:1 ma:1 equation:20 mn:1 mi:1 modified:3 mk:3 following:9 example:3 proof:2 tau:1 give:1 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solv-int9702003.txt |@word footing:1 partial:2 consider:9 chain:1 particular:4 desirable:2 results:4 four:1 consists:1 follow:4 expressions:17 zhedanov:1 whose:2 certainly:1 careful:1 terms:13 tr:2 send:1 tn:5 must:1 unpleasant:1 indicate:1 under:4 analogous:3 characterised:1 presentation:1 2rk:2 2rj:1 advantage:1 assuming:1 springer:1 wave:1 hak:8 corollary:3 putting:1 updates:1 entries:9 discretizations:13 difference:28 matrices:4 condition:4 leads:1 cmk:2 immediately:3 hamiltonian:6 t2:12 solution:5 t1:1 large:1 discrete:9 vector:1 interpolating:2 shows:1 inspection:1 dealing:2 integrators:2 second:8 further:2 substitute:1 theory:3 spectral:1 λrk:1 what:1 nonlinear:7 stands:1 section:2 analogously:4 supplied:1 version:1 above:4 values:3 satisfy:1 full:2 respectively:1 never:1 here:8 bi:1 desired:3 objects:1 ansatz:1 represented:1 depend:2 along:1 equations:42 implicit:1 change:4 differential:2 obtained:4 sending:1 remark:2 hbk:3 shift:1 studied:1 allows:9 reason:1 amount:2 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solv-int9702004.txt |@word represent:1 consider:3 pointing:4 leads:1 scalar:1 commute:1 consists:1 reasoning:1 layers:1 whose:3 certainly:1 remarkable:1 finally:1 present:3 th:2 under:1 analogous:1 applied:1 belonging:1 amplitudes:6 string:1 very:2 choice:1 every:1 matrices:8 condition:7 turns:1 try:1 vector:23 permutability:1 possibility:1 sergeev:1 second:2 further:2 situated:3 subscripts:2 aim:1 adds:1 sum:2 above:2 new:2 outgoing:5 respectively:2 never:1 component:3 here:4 diagonal:1 desired:1 ansatz:1 directions:1 σab:7 along:3 equations:3 change:1 obtained:1 incoming:11 technical:2 vectors:8 contradiction:1 leaving:1 products:2 action:2 family:2 s01:4 s02:2 explained:6 marked:1 select:1 use:3 feb:1 superpositions:1 would:1 commun:1 remains:2 contains:1 next:1 depicted:3 call:1 taken:1 type:1 bethe:1 more:5 sort:1 operators:13 particular:1 cases:1 effort:1 must:4 deformed:1 recall:1 equation:10 work:12 remain:1 obvious:2 learn:1 following:2 korepanov:3 figure:13 give:2 states:12 species:1 simple:2 regularization:1 end:1 rather:3 discussion:1 holds:1 write:1 far:1 sij:1 parameter:3 product:13 description:1 transforming:1 after:2 collection:5 produce:1 waves:2 horizontal:2 hedgehogs:3 transposed:1 third:1 maybe:1 lines:7 summing:1 parameterized:1 so:4 definitions:1 order:1 hedgehog:2 acts:2 help:1 over:2 move:2 satisfied:1 interpreted:1 course:2 paper:11 through:3 mentioned:2 still:3 its:8 somewhere:1 exact:3 degrees:2 deformation:1 them:3 introduce:1 band:7 they:2 instead:3 now:3 yu:1 represents:1 february:1 always:1 university:1 labeling:1 each:5 found:1 baxter:2 domain:2 schemes:1 arbitrariness:1 doing:2 our:3 special:2 out:4 matrix:14 space:9 similarly:1 acting:1 reader:3 formula:1 math:1 linear:2 written:2 differ:1 free:1 reason:1 beginning:1 definition:1 could:2 impose:2 plane:10 onto:1 first:3 already:1 number:5 multiplying:1 construct:1 another:2 passes:1 given:5 interesting:2 their:2 introduction:3 relations:2 indicate:1 observations:3 calculations:1 shifted:1 statement:1 exactly:2 part:5 copy:1 than:2 coefficients:1 kind:2 require:3 zero:1 determined:2 were:1 providing:1 russia:1 symmetries:4 explicit:1 zamolodchikov:1 7p:1 any:8 viewed:1 lie:1 depict:1 convenient:1 latter:1 able:1 note:1 without:1 take:2 resembling:1 even:1 added:1 who:1 algebraic:2 connected:1 remarks:1 don:1 observation:2 considered:1 clear:2 sometimes:1 vertices:8 face:1 hietarinta:1 section:2 fact:3 text:1 ωcd:2 bring:1 spaces:7 relation:3 solutions:6 find:1 eigen:1 based:4 parameters:1 kagome:9 behind:1 should:2 only:3 going:2 subsection:4 factor:1 oblique:2 hope:1 do:1 cube:1 intersect:2 get:2 express:1 cannot:1 words:1 sorts:1 evolution:2 stroganov:1 arxiv:1 contain:1 including:1 fixed:1 set:3 exists:1 clarified:1 see:3 result:2 tensor:12 tend:1 state:3 correctly:1 between:3 probably:1 boundary:10 conditions:4 multiplied:2 vertical:1 confusion:1 however:1 jk:1 solv:4 many:1 taking:1 according:1 etc:1 faces:1 whole:1 reasons:1 continuation:1 corresponds:2 cd:6 dimensional:6 represented:1 simply:1 proved:1 throughout:1 withdrawn:1 considering:2 described:5 basis:1 three:2 been:3 int:4 much:2 algebras:1 define:5 covector:1 corresponding:10 commutes:1 concerning:1 σcd:3 those:15 case:1 multi:2 tanh:3 straight:4 tetrahedron:10 eigenstate:1 will:18 while:4 situation:1 procedure:1 a27:1 formulation:1 thus:4 ii:1 ik:1 itself:1 technology:1 different:2 perhaps:1 make:1 belong:1 same:6 intersecting:7 unity:1 complex:2 pauli:1 several:1 difficult:1 extended:1 infinity:3 cubic:2 hand:1 edges:24 infinite:3 off:1 mangazeev:1 well:2 edge:3 sets:1 model:7 left:5 just:4 twoparticle:1 obtain:2 rest:1 vanishes:1 identify:2 immediately:1 eigenstates:10 letting:1 cut:2 lattice:21 distinguish:1 remaining:1 build:1 possible:1 period:1 vacuum:12 using:3 bit:2 intersection:1 formal:1 imposed:1 like:5 particle:31 follows:3 remind:1 arbitrary:2 bazhanov:1 page:1 terminology:1 lenin:1 right:6 creation:6 some:16 choosing:1 proper:2 intact:1 permutable:1 lead:1 does:1 algebraization:3 assuming:2 intersections:1 s12:3 perpendicular:1 ratios:1 comparison:1 chelyabinsk:2 extension:1 meaning:2 act:1 introduced:4 own:1 statements:1 into:4 within:2 dualities:1 references:1 determine:1 operator:5 presupposes:1 tetrahedral:1 hep:2 formulate:1 transfer:13 there:6 transform:1 way:4 sections:1 naturally:1 form:3 but:5 repeated:1 construction:4 line:9 made:1 whether:1 attached:2 up:4 us:10 below:1 planes:1 problem:1 similar:2 ab:8 associated:2 links:1 defined:2 abstract:1 describe:3 general:1 periods:2 av:1 moves:1 constructed:3 again:1 no:2 dashed:1 when:3 detail:1 other:8 details:3 spatial:1 really:1 draw:2 elements:1 kinds:1 superposition:2 excitation:1 separate:1 models:1 vertex:4 generated:1 important:1 graphically:3 assume:4 required:1 curve:1 together:2 lying:5 time:1 starting:1 strings:4 once:1
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solv-int9702005.txt |@word represent:1 results:1 four:3 2r1:2 inverse:4 depend:3 tv:1 uniqueness:1 γn:2 elliptic:2 under:4 tc:1 norm:1 g3:1 g2:1 choice:1 difference:2 exact:2 condition:8 riemann:15 hamiltonian:1 notes:2 shock:1 solution:16 large:1 involution:2 vector:1 small:1 upper:2 wronskian:1 jump:3 integrability:1 further:1 dynamics:1 crystallography:1 substitute:1 theory:2 spectral:4 index:1 nonlinear:4 near:2 above:2 principal:1 method:3 coefficient:2 here:1 ansatz:3 const:1 equations:4 change:2 obtained:2 shift:2 inspired:1 studied:2 allows:1 makes:1 uniquely:1 via:5 modulated:4 decrease:1 use:2 feb:1 asymptotic:6 prove:1 contains:1 next:2 depicted:1 ψn:41 therefore:1 volterra:16 theoretical:2 more:1 zeroes:1 becomes:1 surface:6 known:2 ural:1 must:2 equation:10 averaged:1 modified:1 paragraph:4 values:4 following:8 example:1 proof:2 degenerate:1 r20:4 goal:1 provide:1 verify:1 holds:2 fourth:1 simplifies:1 parameter:5 algebra:1 modulation:2 derived:1 applications:2 studies:1 waves:1 wave:1 data:5 constants:4 dynamical:1 third:1 explicit:2 so:2 correlation:1 representation:1 conjugation:3 restriction:1 paper:7 mentioned:1 its:1 2λc:1 interesting:1 fix:1 solving:2 uniformization:1 complex:1 systems:4 main:3 non:1 they:1 now:3 easily:2 term:3 equality:1 invariants:1 2a:1 each:1 decreasing:1 side:1 domain:1 differential:4 formulate:1 series:1 obtains:2 eq:1 out:3 shown:1 matrix:8 discrete:1 induces:1 investigation:3 formula:9 rj:5 linear:4 completely:2 estimate:1 r4:27 definition:1 cycles:1 r1:26 r2:25 r3:31 determining:1 introduction:1 bidifferential:1 initial:5 variables:1 periodical:1 given:2 sheet:6 rewritten:1 manakov:3 unknown:1 eqs:1 πi:1 system:3 construct:1 indicate:1 statement:5 scheme:2 holomorphic:1 calculations:2 academy:1 whitham:4 determined:4 were:5 powers:1 spectrum:4 generalization:1 self:2 sciences:1 analogy:1 formulas:5 investigations:1 object:1 satisfy:1 regular:1 connected:3 sheets:1 phase:3 analytically:1 nonlinearity:1 ensues:1 mrp:7 points:1 exp:6 physics:3 quantity:2 akhiezer:1 analogously:1 solutions:15 analogue:1 d0:5 d1:2 parameters:2 written:3 should:1 analytic:6 only:1 explicitly:1 integrable:3 circle:1 local:1 get:2 de:2 dx:2 dw:1 dt:3 dq:2 heaviside:1 c2n:4 arxiv:1 investigate:1 fixed:3 kernel:2 computed:1 differentials:1 see:2 w3:2 w2:4 contour:2 tend:1 outside:1 ωj:2 various:1 between:1 boundary:1 conditions:5 meromorphic:1 terms:3 2πiω:1 wj:3 veselov:1 hypothesis:1 multiplier:1 solv:1 jetp:2 problem:22 4r2:1 last:2 equal:1 called:1 connection:2 σq:11 genus:2 temporal:1 cn:13 point:2 asymptotically:1 dimensional:1 pct:11 associated:1 zeta:1 described:1 piecewise:1 quickly:2 cauchy:10 combined:1 interest:1 basic:1 fig:2 describe:1 corresponding:1 quantities:7 gap:8 c1:1 weierstrass:1 spin:1 case:6 look:1 expanded:2 value:1 transformation:1 while:1 suppose:4 behavior:3 study:1 played:1 vol:1 thus:2 vn:6 according:1 author:1 same:1 stimulated:1 verifies:1 finite:2 φn:8 infinity:1 cubic:1 i0:5 lower:4 σp:23 reflection:1 changes:1 well:1 analysis:3 model:1 just:1 less:1 obtain:1 λc:2 formulated:3 scattering:4 cut:3 preprint:1 zakharov:2 bnt:1 iω:1 lattice:17 theorem:1 constant:2 plasma:1 remaining:1 real:2 couple:1 posed:1 using:1 unique:2 like:1 follows:1 velocities:1 korteweg:2 integrals:1 stationary:1 specifies:1 methods:1 deal:1 some:1 specified:2 kdv:2 integration:1 classical:1 does:2 tends:1 ufa:1 journal:2 expansion:1 step:1 quasilinear:1 dependence:1 o:5 whence:1 mathematical:4 into:1 integral:2 ηj:1 appropriate:1 en:13 references:1 zoology:1 abel:1 schrodinger:2 log:4 there:3 signifies:2 much:1 way:4 was:1 asymptotics:8 function:14 considerably:1 complete:2 form:4 2ηj:1 triangular:1 but:1 2πi:8 characteristic:1 liouville:1 un:3 4r1:1 4r3:1 define:5 similar:3 4r4:1 proved:1 int:1 abstract:1 paragraphs:1 general:2 examine:6 dν:1 dλ:5 dη:1 constructed:1 tedious:1 functions:2 no:2 whereas:2 interested:1 role:1 details:1 branch:4 np:1 models:1 searched:1 problems:2 variable:4 structure:1 implies:1 vries:2 baker:1 curve:5 together:1 time:1 restored:1
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solv-int9702006.txt |@word evidence:1 consider:4 pointing:1 four:6 eds:1 proposition:3 gj:2 gi:5 λij:4 c0:4 depend:1 dickey:1 quasi:11 manifolds:1 th:1 case:9 g1:2 p0:24 geometrical:1 putting:1 anonymous:1 matrices:1 nijenhuis:17 tri:1 presented:1 solution:8 enon:9 try:1 involution:3 vector:20 eigenvalues:4 neighborhood:1 integrability:4 canonical:4 invertible:2 diag:1 section:2 hereditary:1 3k:1 experiment:1 above:2 new:1 acknowledgments:1 satisfy:2 gravitation:1 lichnerowicz:1 q15:1 q14:3 tangent:1 q13:3 q12:7 equations:9 q4:10 obtained:2 scienze:2 remarks:1 studied:1 allows:1 p2:22 poisson:13 action:1 studi:2 heiles:9 useful:2 mail:2 classification:1 univ:2 linearly:1 derivatives:1 use:1 feb:1 takes:2 working:1 prove:2 distinct:1 contains:1 finally:1 next:1 few:1 taken:1 iteratively:1 type:4 entails:1 more:2 remark:1 equipped:1 known:2 iii:1 πni:1 account:3 integrating:3 ρi:3 recall:1 equation:10 work:1 concepts:1 following:3 example:3 proof:2 wojciechowski:1 weaker:1 give:1 assumptions:2 sense:1 np0:1 darboux:2 six:1 write:1 trieste:4 criterion:1 dwi:2 map:4 product:1 may:1 applications:1 levi:3 lax:1 italy:4 fk:2 constants:1 pau:1 λ2i:2 natural:1 dynamical:2 third:1 explicit:1 so:9 sect:2 definitions:1 order:2 terms:6 editrice:1 hierarchy:2 indeed:4 course:2 paper:2 mentioned:1 satisfies:2 its:4 le:2 thank:1 maps:1 interesting:1 fix:1 solving:1 coordinates:19 forms:3 degrees:14 systems:23 pays:1 jacobi:6 derivative:1 maximal:1 them:2 appliqu:1 introduce:1 number:3 hamilton:5 jβ:1 they:2 developments:1 easily:3 hamiltonian:21 iff:1 each:5 references:1 universit:1 difficult:1 referred:1 differential:1 ed:1 6q1:1 obtains:1 our:2 eq:13 out:1 shown:1 matrix:3 space:4 restricted:2 furthermore:1 since:4 mate:1 get:1 math:4 8h:2 linear:1 seventh:1 fisica:1 quite:2 ρii:1 york:1 members:1 ρij:4 put:1 dλi:2 motion:2 dipartimento:4 variabili:1 first:3 separable:9 xk:1 xi:3 peculiar:1 variables:1 primary:1 2p2:1 construct:3 directly:2 fi:10 open:1 given:8 bracket:2 ferrarese:1 similarly:1 πj:1 bologna:1 adjoint:1 system:11 relations:1 their:1 brevity:1 structures:2 final:1 authors:1 x2:1 separability:3 metodi:1 edition:1 second:2 aims:1 project:1 matter:1 w3:2 decompose:1 w2:2 este:1 w1:2 generality:1 murst:1 ann:1 recover:1 any:1 lie:1 mij:3 zero:1 depending:3 pursued:1 lij:4 take:1 polimi:1 3q1:1 magri:2 most:1 regular:1 eight:1 pair:3 soliton:3 iterating:1 considered:1 flow:2 playing:1 hi:3 qbh:12 rauch:1 vries:1 notion:1 fact:2 q44:1 q42:13 show:7 supported:1 notations:1 solutions:2 civita:3 q1:31 q3:20 q2:29 knowledge:1 than:2 only:4 factor:2 integrable:11 constant:1 preliminaries:1 dh:10 di:10 df:4 de:5 da:2 q32:8 q34:1 secondary:1 fields:2 arxiv:1 contain:1 qk:1 qn:1 2p1:2 set:6 reference:1 physically:1 morosi:7 p24:5 depends:4 w4:1 p21:2 result:5 p23:4 p22:4 recently:1 subject:1 said:3 tensor:16 symmetric:1 written:4 µn:4 µi:17 closed:1 between:2 αi:5 conditions:2 europa:2 wi:2 solv:1 tensors:2 faced:1 both:1 last:4 equazione:1 taking:1 according:1 fulfilled:1 assure:1 symplectic:3 passing:1 groups:1 point:1 simple:2 address:2 corresponds:1 2nd:1 dimensional:9 respect:3 pp:2 skew:1 three:6 been:1 int:1 reduction:4 pk:1 pn:1 abstract:1 generating:1 referee:1 corresponding:1 vinci:2 cotangent:1 sufficient:2 search:2 matematiche:2 observe:1 olver:1 c3:3 c2:5 c1:4 general:6 present:3 applied:2 p3:26 multi:1 p1:40 p4:13 choices:1 µj:5 property:2 procedure:3 della:1 non:1 equal:1 ii:1 reads:1 ij:1 exterior:1 verified:1 dhj:1 recursion:1 belong:1 member:2 verifies:4 gavrilov:1 finite:3 higher:1 nij:3 independent:2 extended:1 singapore:2 flows:4 hand:1 potentials:1 infinite:1 identity:1 electromagnetism:1 piazza:2 sets:1 model:1 arising:1 manifold:4 just:1 obtain:2 ninth:1 world:2 λj:7 λi:27 λn:2 previous:1 family:3 conclude:1 other:1 easy:1 doctorat:1 transformation:1 scientific:2 loss:1 using:2 insert:1 follows:1 ees:1 korteweg:1 arbitrary:9 stationary:5 italian:2 classical:1 some:4 springer:1 q22:6 q23:1 examples:1 moreover:4 kdv:3 cnr:1 dimensions:1 universita:1 per:1 prop:2 ese:1 2q2:4 2q3:2 2q1:6 bi:4 how:1 ple:1 2n:4 proceed:1 freedom:14 introduces:1 dependence:2 compatible:6 extensions:1 theory:1 introduced:3 h2:2 h3:3 into:4 h1:2 integral:3 jα:1 h4:2 phase:4 bihamiltonian:15 degli:2 there:4 λ3i:1 was:2 function:10 complete:2 form:4 denoting:2 but:2 construction:1 politecnico:2 matematica:3 partially:1 paires:1 smooth:4 us:8 liouville:4 iterated:1 proved:1 defined:6 milano:4 universal:1 condition:1 denote:1 single:1 proves:1 exist:3 gradients:1 constructed:2 functions:17 differentiable:1 no:2 pfaffian:8 field:19 setting:1 role:1 mathematics:1 bundle:1 sulla:1 structure:4 assume:1 physics:1 4i:1 starting:1
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solv-int9702007.txt |@word gt:2 partial:1 consider:1 results:2 four:1 scalar:2 edu:1 expressions:1 gk:28 compact:1 whose:1 certainly:1 replacements:1 concerned:1 tr:3 those:2 analogous:1 norm:3 entries:3 matrices:3 condition:2 bxy:4 solves:2 t2:2 solution:3 math:4 subscript:1 small:1 foundation:1 painlev:4 established:3 what:1 appear:2 invertible:5 trivial:1 expressed:1 version:2 above:4 replaced:2 satisfy:1 respectively:2 equals:2 here:5 cylindrical:1 sinh:6 address:1 path:1 sine:1 equations:19 logarithmic:1 obtained:2 remark:1 periodic:3 suitable:2 changes:1 followed:2 santa:1 family:1 sgs:1 replace:1 establish:1 derivatives:3 use:4 usa:1 bernard:1 remains:1 stated:1 next:1 comparing:2 nucl:1 examination:1 more:2 multiplying:1 becomes:1 operators:9 aware:1 appendix:1 particular:2 cases:1 hold:2 iii:4 valued:1 erratum:1 science:1 equation:10 work:4 det:25 modified:1 following:1 proof:3 indicated:1 give:5 cited:3 sense:2 occur:1 end:1 rather:1 verify:1 holds:4 write:2 how:1 mccoy:1 parameter:2 sato:2 product:2 fs:1 may:3 derived:2 multiplication:1 third:1 whenever:1 grant:1 explicit:1 so:6 correlation:1 representation:1 order:2 hierarchy:1 years:1 produced:1 paper:1 satisfies:4 still:1 its:2 before:1 derive:2 mail:1 eventually:2 them:1 they:1 now:11 yu:2 easily:2 finite:1 university:1 sufficiently:1 l2:3 each:2 found:2 traces:1 side:2 subset:2 differential:6 ei:2 toda:12 combining:2 quantum:1 our:5 special:6 ru:1 shown:3 jimbo:2 matrix:16 factors:1 since:7 rx:1 publish:1 combinatorial:1 formula:1 interchanging:2 shows:2 sinh2:2 harold:1 variant:1 diagonal:3 free:1 quite:1 california:1 publ:1 beginning:1 e0:2 definition:1 derivation:2 could:1 times:1 gordon:3 think:1 first:3 already:1 symmetry:1 reveals:1 xy:7 another:2 open:2 xu:2 interchange:1 given:8 similarly:1 twenty:1 system:1 sech2:1 their:1 eqk:3 dt2:3 gives:8 somewhat:1 authors:1 than:2 connections:1 kind:1 roles:1 imply:1 classes:1 were:5 argument:2 generalization:2 say:1 seem:1 any:2 depending:2 note:3 k0:5 take:2 formulas:1 trace:3 shall:4 extending:1 plan:1 reducible:1 tracy:2 class:1 observation:1 surprising:1 clear:1 axy:6 stronger:1 usual:1 fact:4 show:1 supported:1 miwa:2 relation:2 solutions:10 substituting:1 d2:6 find:3 subtracting:1 q1:4 q0:3 parameters:2 explain:1 written:1 analytic:1 only:2 constant:1 interested:1 do:1 notation:2 means:1 dc:2 words:2 during:1 dt:10 interpreted:1 ds:2 differentiating:1 closure:1 qs:1 determinants:4 widom:4 fields:1 arxiv:1 twice:1 qe:1 qk:35 fixed:2 kernel:7 set:9 national:1 respect:1 observed:1 facts:1 see:5 result:7 eliminating:1 w0:4 uθ:1 away:1 rims:1 state:1 between:1 boundary:2 notice:3 terms:2 nature:1 transpose:1 wu:1 comm:1 solv:2 both:1 last:1 many:1 taking:3 equal:4 display:1 holonomic:1 relevant:1 point:2 simple:1 ca:1 whatever:1 mkdv:1 asserted:1 kernels:1 described:1 been:3 int:2 belongs:1 pe:7 empty:1 define:8 determinant:4 families:1 quantities:1 observe:2 derivative:1 c3:1 c2:2 denote:3 present:1 case:9 tanh:1 evaluated:2 will:5 while:1 suppose:1 error:1 unitary:2 thus:2 non:1 iv:3 ii:3 vanish:1 fermion:1 different:1 author:1 make:2 same:3 clearly:1 hierarchies:1 several:1 difficult:1 upon:2 effect:3 hand:1 running:1 purpose:1 identity:2 off:2 acknowledgement:1 well:2 left:3 less:1 being:1 generally:1 obtain:4 intervals:2 tilde:2 λk:5 previous:1 adding:2 carat:2 lattice:1 setting:2 cruz:1 confined:1 using:4 replacing:1 follows:4 yields:1 either:1 arbitrary:1 become:1 reduced:1 replacement:2 right:1 methods:1 some:2 deduce:6 moreover:2 proofs:1 univ:1 integration:1 everything:1 ucsc:1 bessel:1 kyoto:1 equivalent:1 qe0:4 negatives:1 although:1 bx:8 simpler:1 about:2 would:2 extension:1 commun:1 pe0:4 dependence:1 ensure:1 fredholm:2 introduced:1 into:1 integral:6 references:1 operator:11 successively:1 log:14 removing:1 there:2 question:1 inner:1 way:1 was:12 function:5 form:1 denoting:1 but:2 true:1 leclair:1 us:1 ωv:1 dms:1 ui:2 b426:1 called:1 aa:4 ab:1 proved:2 defined:2 abstract:1 general:3 ay:8 ax:10 identities:4 functions:11 when:3 application:1 other:5 department:1 mathematics:1 elements:2 expressible:1 bounded:1 sides:1 implies:1 assume:2 dτ:2 required:1 lying:1 dϕ:3 4a:2
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solv-int9702008.txt |@word limited:2 saves:1 desirable:1 four:2 consists:1 whose:1 u3:20 list:7 under:6 risc:2 handling:1 every:1 affect:1 school:2 solution:7 au3:1 vector:2 incremented:1 consistent:1 10f:4 direct:1 likely:1 rigorous:1 implemented:3 even:1 above:2 designing:1 new:9 consisting:1 coefficient:4 here:3 obtained:8 study:2 completely:5 tschantz:1 suitable:1 appropriately:2 classification:2 9g:2 replace:5 total:7 circumvent:1 linearly:1 derivatives:18 would:2 negative:6 m1:2 therefore:8 m2:2 type:8 until:1 solitons:2 odinger:2 berlin:2 hold:1 must:22 springer:3 mb:1 work:6 mk:1 example:15 wang:8 indicated:1 give:11 want:1 end:4 eng:1 provide:1 verify:2 how:2 nontrivial:1 ordinary:1 wolfram:3 after:6 connects:2 lax:21 law:7 constants:3 attempt:1 third:3 algorithms:1 enter:7 order:27 restriction:1 interpretation:1 satisfied:2 pascal:1 london:4 thesis:1 compelling:1 differently:2 olver:3 shear:1 eventually:2 them:5 combination:4 uspekhi:1 they:4 eigenvalue:1 netherlands:1 each:5 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solv-int9703001.txt |@word proposition:12 check:1 belong:1 they:3 dickey:1 leibniz:1 alg:1 entries:2 obtain:1 rest:1 integration:1 four:2 scalar:1 commute:1 relation:1 assigned:1 edu:1 satisfies:4 yet:1 help:3 whose:1 const:1 nevertheless:1 density:4 functions:2 acting:1 actually:1 lemma:12 quasi:2 other:3 generators:1 systems:2 easy:1 under:2 jacobi:11 integrable:2 local:1 into:1 fˆj:3 belonging:1 closed:2 notation:1 means:1 very:2 end:1 posed:1 possible:1 introduce:1 choice:1 corollary:1 cannot:1 every:1 difficult:1 dx:1 soloviev:2 using:5 thus:3 now:5 exact:10 enjoys:2 hereafter:1 articles:1 term:9 symplectic:1 equality:1 densities:8 hamiltonian:1 did:1 fields:5 university:1 arxiv:1 2z:2 collect:1 iff:1 vector:8 yields:2 integrals:2 always:3 δf:8 δg:6 fixed:2 side:3 differential:4 often:2 ξy:1 absolutely:1 series:1 some:2 back:1 transferred:2 zero:4 used:1 zx:3 examples:3 eliminating:1 zt:2 close:1 dynamics:1 eq:1 expressions:1 special:1 canonical:1 bilinear:5 what:5 said:2 matrix:9 brackets:1 since:4 lagrangian:1 functionals:6 its:1 symmetric:3 replacing:2 written:2 does:2 above:2 simplest:1 formula:3 boundary:4 arrive:1 consisting:1 notice:3 terms:14 theory:2 attention:1 divergence:8 use:1 here:2 particular:2 uz:1 no:1 solv:1 along:1 refers:1 remaining:1 obtained:1 definition:1 about:2 works:2 last:2 derivation:5 freedom:1 taking:1 bilinearity:1 f3:6 o:2 example:4 etc:1 important:1 derivations:1 poisson:14 permutation:1 hence:1 ou:1 ωf:24 expression:2 involves:1 first:4 origin:2 δh:2 xh:1 symmetry:1 follows:1 precisely:1 relate:1 variables:2 integral:2 functional:2 transform:1 dimensional:1 thankful:1 ii:1 xy:2 references:1 invariant:1 another:1 type:2 cancel:1 respect:2 arbitrary:4 δu:15 linearly:1 equating:1 given:1 necessarily:3 hep:2 rewritten:1 whom:1 skew:4 there:1 question:2 only:3 properties:1 tr:14 defined:6 fˆl:2 therefore:4 statement:3 time:1 taken:1 variational:3 was:3 xz:6 define:3 zy:2 uij:1 fˆi:3 form:22 scalars:1 becomes:2 exactly:1 further:1 but:3 direct:1 part:1 too:1 mail:1 eliminated:1 verified:1 must:1 case:2 pull:1 kind:2 word:1 cyclic:22 structures:1 equation:3 up:6 theories:3 will:2 ωh:1 suppose:2 assume:1 aij:1 following:1 problem:1 property:1 my:1 called:2 ωg:32 proof:10 control:1 f1:6 f2:6 required:3 f4:6 derivative:11 int:1 coincides:1 abstract:1 sense:1 am:1 argument:1 topic:1 ij:3 right:1 pdq:1 our:1 proclaimed:1 ξf:98 keep:1 their:2 elements:2 compute:1 lie:2 write:1 th:2 genuine:1 depending:1 perform:1 make:3 holds:5 vanishes:1 same:4 poincar:1 stasheff:1 field:7 parts:1 take:1 get:1 department:1 mathematics:1 gets:1 subalgebra:4 higher:4 ξx:5 even:1 calculation:1 mar:1 see:1 algebra:4 any:5 earlier:2 mapping:1 polynomials:1 hand:5 ξh:20 commutator:1 analogue:1 involving:2 multiplication:1 fi:8 fj:8 account:1 fl:3 identity:12 ξg:76 fk:5 implies:3 imply:1 dω:2 considered:1 values:1 space:1 well:1 trilinear:6 bracket:14 so:2 uji:1 ujk:1 obvious:2 hamilton:1 fact:3 left:2
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solv-int9703002.txt |@word partial:3 consider:3 september:1 formula:5 obtain:3 scalar:1 proposition:5 using:1 its:1 c0:1 depend:1 fvi:2 sciences:2 adx:2 li:3 book:1 lett:1 easy:3 theorem:1 derivative:1 sokolov:2 main:1 variables:2 above:1 notation:1 ya:3 express:2 dyi:2 dx:38 dy:29 report:1 applying:1 differentiating:1 mod:1 easily:1 necessary:2 densities:1 called:3 bdy:1 university:1 differential:5 solution:2 bdx:1 δn:2 ai:13 vector:1 asymptotics:1 invariants:7 ˆbi:5 qj:2 crm:1 mathematical:2 arxiv:1 some:1 modified:1 2hi:1 integrability:3 street:1 b0:1 fux:11 deduce:1 moreover:1 into:2 analog:1 canonical:3 ru:1 vol:2 nonlinear:2 subsequent:2 since:1 expressed:1 denotes:2 method:1 eliminate:1 rb:1 ufa:4 invariant:3 conditions:4 ri:4 rj:1 ξi:7 terms:3 pui:2 respectively:2 δi:5 bi:14 constructive:2 admits:1 solv:1 fvk:5 equations:10 2ki:1 definition:2 repeating:1 a0:1 institute:2 starts:1 taking:1 prove:4 allows:1 russia:1 yui:1 hence:1 slightly:1 xui:1 montreal:1 first:1 ci:3 symmetry:5 ηn:3 h0:15 ηi:9 ran:1 references:1 operator:6 respect:2 total:3 derivatives:4 additional:1 second:1 hyperbolic:8 adjoint:1 there:3 u1:1 system:2 substitutions:1 defined:5 anderson:2 conservation:5 therefore:3 preprint:1 variational:2 gives:1 function:2 field:1 corresponding:2 relationship:2 commutes:1 academy:2 hj:2 maps:1 hi:24 virtue:2 mail:1 russian:4 eliminated:1 denote:3 dynamical:1 account:1 uy:1 ux:1 equation:13 mi:1 zero:1 us:5 technical:1 kamran:1 ui:7 following:1 im:3 bicomplex:1 laplace:9 ab:2 symmetries:2 rewrite:2 int:1 vi:8 abstract:1 vk:3 thus:1 uxy:1 conserved:2 exist:3 dxi:2 integrable:2 formally:1 any:1 constructed:1 low:1 functions:3 no:1 darboux:3 verify:2 application:2 k0:3 generalized:2 algorithm:2 calculation:1 mar:1 fu:2 june:1 systems:1 flows:2 v1:1 plane:1 ξn:3 linearization:2 law:2 compatibility:1 induction:2 give:2 center:2 consequences:1 hk:2 assume:1 γvi:2 ki:8 γui:1 sj:1 si:4 phis:1 doklady:1 imply:1 order:2 laws:2
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solv-int9703003.txt |@word partial:1 consider:5 results:1 four:2 scalar:5 grateful:2 foundations:1 expressions:1 compact:1 inverse:3 const:4 calculate:6 equivalence:11 finally:1 under:9 analogous:2 g3:1 g2:4 g1:2 g0:2 very:2 geometrical:5 matrices:1 fomenko:1 condition:4 leads:2 dubrovin:1 obvious:1 dij:8 trn:2 list:1 solution:11 moldova:2 solved:2 vector:9 phase:1 math:6 indices:6 3b:1 prevent:1 des:1 direct:2 sign:1 tex:1 painleve:7 street:1 further:1 substitute:1 canonical:10 even:1 index:1 what:1 nonlinear:2 appear:2 d2:1 3q:1 expressed:3 lexicographic:1 poles:1 sur:4 above:1 new:3 method:5 contrast:1 satisfy:2 relationships:8 simultaneously:3 respectively:1 modify:1 here:7 shouldn:1 dimensionality:1 address:1 consideration:1 along:3 quite:3 equations:52 appears:2 change:7 contraction:4 obtained:2 institute:1 study:2 vectors:1 sbornik:1 yˆ:7 generale:1 published:1 complicated:1 implement:1 γijk:2 via:2 mail:1 substitution:1 compare:1 ek:3 austria:1 apply:1 derivatives:6 use:4 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solv-int9703004.txt |@word represent:1 partial:1 consider:3 results:8 four:4 scalar:1 tl:13 analogous:1 include:2 far:1 updates:1 discretizations:5 difference:3 matrices:5 presented:7 chains:1 list:1 large:2 discrete:18 small:4 relation:3 takhtajan:1 direct:1 second:5 canonical:7 spectral:2 what:1 nonlinear:3 appear:2 brackets:2 section:11 version:1 above:5 international:1 respectively:1 even:1 here:2 delivering:1 b2k:1 ansatz:10 standard:4 equations:84 remark:1 property:1 hbk:3 allows:1 g2e:4 resulting:3 poisson:7 makes:1 uniquely:1 classification:1 deconinck:2 conventional:1 additive:1 commun:1 contains:2 call:2 therefore:1 themselves:1 type:2 tell:1 more:2 becomes:2 particular:2 known:2 iii:1 springer:2 recall:2 equation:4 work:1 modified:5 mk:13 reproduce:1 following:13 give:2 relativistic:19 cited:2 performed:1 bibliographical:1 feature:1 maps:1 nontrivial:1 parameter:9 map:31 product:1 mar:1 tried:1 may:10 earlier:1 derived:1 collection:2 lax:72 representations:23 fk:1 introduced:3 dynamical:1 explicit:7 correspond:1 so:1 sect:12 allow:3 representation:32 first:9 order:2 hierarchy:10 soc:2 paper:7 japan:2 satisfies:9 still:1 its:2 before:1 style:2 how:1 interesting:2 lj:4 lk:31 coordinates:1 systems:36 mail:1 deformation:6 them:1 combination:1 material:1 hamilton:15 they:6 now:1 yu:7 transparent:1 hereafter:7 university:1 hamiltonian:36 2x:1 2e:1 theory:2 each:1 found:2 universit:1 side:4 2k:1 significantly:2 related:6 toda:49 our:1 special:6 matrix:40 matriz:2 lagrangian:28 semi:1 denoted:5 hck:3 math:6 qd:1 turning:1 linear:6 given:7 quite:1 assures:1 reparametrizations:2 yuri:1 put:2 ruijsenaars:2 transition:2 motion:76 generalizations:1 βk:8 xj:2 xk:500 simplifies:5 omitted:2 variables:4 number:2 relations:3 another:2 story:1 perturbation:2 introduction:1 leading:2 generalities:1 system:12 least:1 their:4 1e:1 time:25 gives:1 exactly:1 serve:1 authors:1 translation:1 than:1 dtl:12 approximations:1 imply:2 kth:1 historical:1 were:2 providing:1 already:1 seem:2 recover:1 form:40 note:1 generalized:2 new:4 analogs:1 formulas:1 continuous:7 centre:1 denominator:1 most:1 connected:1 remarks:2 yamilov:2 workshop:1 considered:3 sometimes:1 coincides:2 exk:276 bracket:18 principle:1 physics:1 rtl:27 discovered:1 russian:2 gauge:3 trivial:1 find:3 leningrad:1 enough:1 only:4 integrable:9 hope:1 legendre:1 dk:54 simplest:3 cannot:1 closely:1 suris:9 lattices:6 dt:1 gen:4 evolution:1 arxiv:1 common:1 contain:1 hλ2:1 hλ:25 set:3 depends:2 close:1 analog:2 satisfying:4 ways:2 written:1 between:2 invariant:3 approach:1 terms:3 wk:8 however:5 p2k:2 vanishing:1 solv:1 both:6 last:3 many:2 equal:3 uni:1 comment:2 co:1 simple:1 corresponds:3 lagrange:5 appeared:2 speak:1 pp:1 invented:1 publishing:1 int:1 much:2 pj:1 pk:82 abstract:1 generating:2 corresponding:5 stepsize:3 estabrook:1 present:5 case:12 ǫe:4 will:5 replaced:1 ǫx:3 hdk:14 constructive:1 almost:1 vk:17 non:2 ii:1 reads:2 different:6 author:1 formulations:2 reminded:1 same:5 complex:1 several:1 fairly:1 acklund:1 see:3 flows:5 hand:5 identity:1 task:1 well:7 obviously:1 de:1 epk:42 very:1 ck:49 being:1 obtain:1 λg:3 λe:1 world:1 momenta:2 λh:1 previous:2 visualization:1 preprint:1 infinitely:1 seems:2 parametrization:20 exclusively:1 lattice:27 belongs:1 lett:2 euler:2 real:1 read:3 big:3 immediately:1 unique:3 formal:1 like:1 particle:2 follows:2 serves:2 collect:1 arbitrary:1 multiplicative:1 δg:3 because:2 parametrizations:1 interrelations:1 some:2 understood:1 proofs:2 2xk:3 proc:1 faddeev:2 scientific:1 equivalent:3 bi:5 bk:16 hǫ:5 transformations:1 simplify:1 dependence:1 o:8 plus:1 greatly:1 mixed:3 germany:1 ǫpk:10 slightly:1 discretization:13 letters:1 h2:36 into:1 h1:8 down:1 right:5 operator:1 methods:1 log:4 transform:1 quadratic:4 was:4 function:11 complete:3 newtonian:33 δkj:4 but:4 representaion:2 level:1 hg:11 he:12 algorithm:1 consist:1 limit:3 verification:1 problem:2 called:2 defined:5 flow:33 ak:32 formulation:4 functions:7 integrability:2 no:2 bremen:3 hpk:19 details:1 solitons:1 test:1 nice:6 hirota:3 sides:1 structure:11 using:1 required:1 together:1 resembles:1 8th:1 having:1 once:1
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solv-int9703005.txt |@word customary:1 consider:8 similarity:47 induces:1 pleasure:1 results:6 leads:1 proposition:2 generalize:1 follow:1 1p1:1 causes:1 devoted:1 b288:1 inverse:15 calculate:1 technique:1 trivial:1 tn:10 dz2:2 preserved:2 elliptic:1 under:3 kλ:3 worth:1 case:24 conjecture:1 supported:1 proved:1 string:1 straightforward:2 very:2 wave:1 putting:2 govern:1 difference:2 matrices:2 deformations:2 condition:1 school:1 hamiltonian:44 t2:1 solution:24 enon:16 t1:1 involution:1 harry:1 rev:1 equation:39 inconsistent:1 correct:1 wronskian:1 y0:6 concise:1 consistent:3 nonautonomous:1 direct:4 sign:1 second:9 plenum:1 zy:7 equal:1 further:2 zw:1 ode:10 linear:1 even:1 3z:2 what:1 nonlinear:2 appear:1 invertible:1 giving:3 fact:2 section:15 tabor:1 3w:1 expressed:1 3t:4 henceforth:2 3j:4 version:2 above:4 values:13 method:3 satisfy:4 8a:2 simultaneously:1 respectively:5 here:5 behaviour:1 canonically:1 xθ:2 2q22:1 z8:1 q13:2 sawada:2 concluding:1 equations:50 appears:2 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solv-int9703006.txt |@word represent:1 partial:1 consider:8 dynamic:3 results:2 leads:2 consists:1 follow:1 whose:1 inverse:1 producing:12 presents:1 finally:1 restriction:1 present:2 th:1 include:1 applied:2 string:1 returning:1 very:2 rise:2 wave:52 resonant:3 difference:1 exact:5 condition:4 did:1 dodd:2 solution:47 large:1 au0:1 phase:1 fourier:2 small:4 second:5 nonhomogeneous:2 further:1 dynamics:1 situated:2 substitute:1 linear:14 subscripts:1 nonlinear:6 stands:1 giving:2 sum:1 celebrated:1 uniform:1 version:1 above:2 u30:2 new:2 method:5 funtion:1 full:1 respectively:5 modify:1 here:1 water:2 free:8 groups:1 strong:1 equations:31 appears:2 obtained:6 study:7 studied:1 allows:1 resulting:3 suitable:1 makes:1 via:1 useful:2 montpellier:2 manna:3 vii:3 ai:1 establish:1 derivatives:5 use:6 asymptotic:3 uniformity:1 prove:1 contains:1 suppl:1 next:1 few:1 therefore:1 reductive:4 associated:14 selects:1 introducing:1 clearly:2 becomes:1 operators:1 merle:2 normalized:2 particular:3 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solv-int9703007.txt |@word consider:2 particular:4 datum:1 results:2 fluids:1 leads:1 ge:1 cooperative:1 suspected:1 consists:1 devoted:1 amplification:2 zone:1 providence:1 tr:5 ts:3 passage:2 finally:2 tm:6 th:2 under:1 case:8 straightforward:1 evolves:1 very:2 induce:2 wave:3 every:1 condition:3 harlow:1 entire:1 riemann:2 solves:1 level:3 transmission:1 unsuspected:1 solution:17 t0:9 occurs:1 large:4 discrete:2 vector:1 anal:1 optics:3 upper:8 grateful:1 pulse:11 cosh:3 approximation:1 go:1 zero:1 iσ2:1 linear:1 spectral:8 nonlinear:5 stands:1 poles:9 wenzel:2 reconstruction:1 new:1 method:2 coefficient:4 full:1 modify:1 here:4 believed:1 inverse:1 leeds:2 sinh:4 represented:1 19d:1 quite:1 equations:10 change:1 obtained:4 search:2 trans:1 institute:1 leaves:1 studied:2 allows:2 contradiction:1 suggests:1 resonance:2 fourier:1 montpellier:1 discontinuous:1 merely:1 explicitely:1 scaled:2 readily:1 asymptotic:1 would:5 intensively:1 remains:2 positive:2 france:1 therefore:1 spike:6 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solv-int9703008.txt |@word lakshmanan:1 consider:1 particular:1 focus:1 gg:1 eds:2 follow:1 expressions:2 devoted:1 inverse:1 finally:1 helps:1 ti:1 tg:1 dramatically:1 t11:1 supported:1 g3:1 g1:4 orthogonal:1 far:1 wave:2 electron:2 putting:1 ηir:5 exact:1 leads:1 presented:1 transmission:1 turns:1 solution:22 large:1 vector:3 math:1 ueda:1 optics:2 noted:1 hasegawa:2 work:3 zh:2 regained:1 pulse:1 cosh:1 zero:1 chen:1 further:2 dynamics:1 subscripts:1 established:1 nonlinear:8 trapping:1 cˆi:1 expressed:1 reminiscent:1 above:3 new:1 method:5 contrast:1 fiz:2 respectively:1 even:2 component:6 here:4 ansatz:1 quite:2 equations:4 change:10 obtained:5 eδ0:1 eδ1:2 daughter:1 suitably:1 shift:2 study:2 studied:3 allows:2 radhakrishnan:2 resulting:2 usually:1 complicated:1 birefringent:1 studies:1 cˆ1:5 via:1 coordinatized:1 santini:1 total:1 unit:4 readily:1 conventional:1 er1:1 er2:1 er3:1 positive:3 comparing:1 therefore:1 type:4 more:4 solitons:14 odinger:2 berlin:1 correspondingly:1 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solv-int9703009.txt |@word partial:1 consider:1 remarkable:1 primed:1 fluids:1 leads:1 expressions:1 whose:2 calculate:1 equivalence:3 finally:1 does:2 those:1 under:1 te:1 indicating:2 springer:2 results:2 linearizability:9 condition:12 exits:1 u2x:3 tanh:2 solution:4 small:3 still:1 approximation:1 integrability:4 2aγ:1 further:2 dynamics:5 theory:3 subscripts:1 what:2 nonlinear:4 appear:2 sum:2 3w:2 wxxx:4 version:1 above:3 new:4 respectively:1 here:1 free:1 address:1 consideration:1 equations:11 appears:2 obtained:1 instituto:1 ref:2 study:1 resulting:1 implement:1 makes:3 useful:1 manna:2 put:2 2wx:2 apply:1 asymptotic:2 would:1 call:1 therefore:1 taken:1 more:4 introducing:1 becomes:2 odinger:1 berlin:2 surface:1 cases:1 iii:1 must:2 account:1 dodd:1 equation:26 modified:1 itself:1 ρu:2 ρt:1 following:5 example:1 fapesp:1 compare:2 f3:6 µνi:1 calculation:1 allowed:2 νx:1 want:2 sense:1 νi:3 end:2 get:1 write:1 answer:2 instead:1 allowable:1 parameter:1 mar:1 description:1 may:4 after:1 corrections:1 waves:2 wave:7 compatibility:1 constants:6 natural:1 so:2 fundamental:1 paulista:1 order:14 neto:1 hierarchy:2 satisfied:5 nondimensional:2 through:3 existence:1 cole:2 its:1 thank:1 encompasses:1 systems:4 main:1 defining:1 alter:1 universality:1 solubility:1 they:1 now:4 ordinary:1 term:4 40b:1 always:3 morris:1 academic:1 each:1 found:1 mean:1 mikhailov:1 differential:1 financial:1 ed:2 idea:1 applicable:1 extended:1 our:2 eq:36 out:2 shown:2 rey:1 gibbon:1 space:1 furthermore:1 rev:3 dominated:1 issue:2 wiley:1 linear:2 ısica:1 governing:4 admits:1 completely:2 kodama:2 proportionality:1 ask:1 generate:1 βw:2 linearized:3 motion:1 turn:1 int:1 linearizes:1 first:4 already:3 variables:4 precisely:1 illustrate:1 dispersive:1 given:5 perturbation:3 introduction:1 eqs:1 system:1 cµ:1 final:1 gives:1 eliminates:1 whitham:1 part:2 authors:1 representing:1 specify:1 kind:2 pamplona:1 require:1 zero:1 determined:1 amplitude:3 perturbative:1 rewrite:1 correction:3 say:1 clearly:1 uξξ:2 depending:1 latter:1 ideas:2 uuxx:3 note:1 liu:1 take:2 normal:5 object:1 viscosity:1 birkh:1 simplify:1 uξ:7 letter:5 remarks:1 why:1 kf:1 velocity:2 kraenkel:3 vries:1 fact:1 show:4 notations:1 relation:2 substituting:1 find:2 orica:1 slow:1 ratio:1 parameters:2 pdes:1 basel:1 only:2 explicitly:2 coefficients:2 integrable:3 hopf:2 do:1 means:2 de:3 joint:1 aγ:5 ones:1 words:1 evolution:1 fields:1 arxiv:1 remove:1 london:1 set:1 exists:1 namely:1 result:2 brazil:3 satisfying:2 written:1 µi:1 αi:1 conditions:2 notice:1 terms:10 however:3 wt:6 key:1 solv:1 uτ:5 come:1 wx:8 undetermined:1 both:1 taking:1 according:2 fulfilled:1 context:1 passing:1 dimensional:4 simply:1 moreover:1 cp:1 cv:1 ct:1 described:2 transformations:1 second:1 uρ:4 been:3 ai:1 much:1 linearizable:8 define:1 traveling:1 corresponding:1 gas:6 remark:2 ensuring:1 c2:1 denote:1 present:2 case:7 look:1 pacs:1 arnold:1 will:5 near:4 suppose:2 ǫu:1 ǫz:1 2k:2 characteristics:1 thus:5 uxx:3 iv:1 ii:1 reads:3 obstacle:3 aspects:1 uxxx:3 verified:1 make:3 same:4 any:1 paulo:1 widely:1 higher:3 used:1 estadual:1 cρ0:1 ρu2:2 introduce:3 identity:4 task:1 schr:1 acknowledgement:1 changes:1 obstacles:4 analysis:3 burgers:12 coordinate:1 calogero:2 left:1 eilbeck:1 gelfand:1 alluded:1 when:2 obtain:2 differentiation:1 fokas:2 density:2 zakharov:1 auser:1 valid:1 transformed:5 lett:2 easy:1 solvable:1 transformation:11 ought:1 real:1 nuov:1 alternatively:1 possible:2 know:1 using:1 insert:1 appearing:2 like:1 δw:2 performing:1 discarded:1 korteweg:1 arbitrary:1 pereira:3 δb:1 reduced:1 methods:1 exposed:1 some:1 back:1 b4:1 b2:1 kdv:2 specific:1 scale:2 lead:1 integration:2 2c2:1 equal:1 yields:1 inserting:1 equivalent:5 rua:1 bi:1 illustration:1 pressure:1 montero:1 comparison:1 about:3 algebraic:1 discussed:1 meaning:1 o:25 plus:1 discard:1 introduced:1 perturbed:3 into:4 references:1 determine:1 heated:1 proportional:1 support:1 there:2 question:3 long:5 u2:5 dispersion:2 accordingly:1 way:2 lowest:2 form:15 but:3 cnpq:1 true:1 ux:3 whether:1 ut:3 up:7 us:2 limit:3 constant:2 defined:1 certain:2 abstract:1 influence:1 ao:1 general:6 exist:1 universidade:1 tedious:1 functions:1 cim:1 no:1 wxx:2 ny:1 setting:1 solitons:1 commutator:1 a3:1 important:1 a5:1 dissipation:1 kx:2 geometrical:1 wx2:5 heats:1 time:1 original:1
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solv-int9703010.txt |@word consider:2 results:1 four:2 expressions:1 particles:1 depend:1 present:1 th:2 under:2 worth:1 belonging:3 r12:1 r13:1 straightforward:1 very:1 continues:1 translations:1 matrices:1 condition:2 illustrated:1 obvious:1 large:2 vector:5 indices:1 eigenvalues:2 petersburg:1 configurations:5 upper:1 says:1 dealing:1 consistent:1 direct:1 sergeev:1 further:1 situated:1 even:2 index:1 what:1 abc:1 appear:1 sum:4 above:2 new:1 method:1 contrast:1 outgoing:1 leg:1 here:6 others:1 path:1 along:1 equations:1 z3:2 search:1 incoming:1 study:1 vectors:12 amount:1 periodic:1 products:1 action:4 makes:1 uniquely:1 family:2 marked:1 apply:2 use:2 chelyabinsk:2 commun:1 remains:1 depicted:2 call:1 taken:2 themselves:1 selects:2 more:3 flat:1 operators:10 particular:2 known:1 hold:1 iii:1 ii:1 equation:10 work:6 modified:1 anywhere:1 values:1 following:2 making:1 dropped:1 control:1 korepanov:6 figure:11 calculation:1 sense:2 states:4 numbers:2 arise:1 string:2 huge:1 rays:4 rather:2 verify:1 discussion:1 acts:2 conserve:1 how:2 nontrivial:1 instead:1 parameter:3 classify:1 product:8 mar:1 intended:1 algebra:4 coming:1 horizontal:1 constants:1 maybe:1 explicit:1 correspond:1 element:1 so:3 hedgehog:2 six:4 over:2 move:2 course:2 paper:6 statistical:1 mentioned:1 y2:2 its:2 roots:1 exact:1 fix:1 forms:1 defining:1 them:3 fragment:1 they:4 bazhanov:1 now:3 yu:1 eigenvalue:1 finite:4 university:1 hepth:1 possibilities:1 reasonable:1 each:5 found:1 redraw:1 side:1 baxter:2 schemes:1 directly:1 series:1 idea:1 begun:2 special:2 out:1 leave:1 superscripts:2 matrix:11 space:4 rd:1 acting:1 investigation:1 reader:1 denoted:1 formula:2 get:1 math:1 linear:1 free:1 quite:1 usual:3 8p:1 geometry:1 s123:4 thing:1 first:2 trigonometrical:4 already:1 number:6 linking:1 restrict:1 construct:1 another:1 interchange:1 given:4 attach:1 introduction:1 unknown:1 relations:1 paint:1 white:2 speaking:2 gives:1 numbered:1 discovered:1 exactly:2 seminarov:1 x1:3 pomi:1 see:3 determined:1 powers:1 declare:1 mangazeev:1 symmetries:1 lines:4 zamolodchikov:11 generalization:1 say:1 manner:1 7p:1 seem:2 paths:1 built:2 homological:1 polarization:2 take:3 trace:1 object:3 most:1 involving:1 connected:2 pair:4 class:2 clear:2 sometimes:5 dualities:1 countable:1 hietarinta:1 superscript:1 fact:1 show:2 notations:1 spaces:3 relation:2 solutions:7 trivial:1 fifth:1 homology:1 based:3 parameters:2 noninvertible:1 kagome:4 only:4 going:3 black:10 subsection:1 oblique:1 do:1 triangle:1 means:3 between:2 bear:1 yielded:1 ones:2 evolution:1 stroganov:1 arxiv:1 fixed:2 view:1 multiplying:1 constructing:1 exists:2 connections:1 namely:3 w3:1 result:1 triples:1 analog:1 said:1 tensor:7 pictures:1 f23:1 enough:1 simplest:2 probably:5 boundary:7 conditions:6 ends:1 terms:1 vertical:1 however:3 solv:5 configuration:3 c23:1 taking:1 russia:1 etc:1 connection:1 interesting:1 zapiski:1 arbitrarily:1 unclear:1 point:2 simple:1 corresponds:1 dimensional:3 consideration:1 proved:1 throughout:1 described:3 three:2 mark:2 much:1 algebras:7 define:1 dots:1 corresponding:6 both:1 painted:1 algebraization:1 external:1 careful:1 those:6 case:2 look:1 straight:2 tetrahedron:10 single:1 will:12 suppose:1 layer:2 a27:1 formulation:1 obeying:1 itself:1 technology:1 fermion:1 different:2 make:1 belong:1 same:3 unity:1 modification:1 several:1 events:1 used:1 upon:3 v2:1 edges:13 moving:2 infinite:5 cycle:1 eigenvectors:1 least:1 whose:2 no:1 well:2 roughly:1 edge:2 model:11 arising:1 possesses:1 left:3 just:1 being:1 obtain:1 torus:2 sdef:1 transforms:1 eigenstates:9 enters:1 conclusions:1 lattice:14 transformed:1 lett:1 easy:1 theorem:1 mod:1 march:1 easily:1 sums:1 possible:1 five:2 vacuum:4 using:3 bit:1 formal:3 r45:3 necessary:1 like:3 particle:1 follows:2 serves:1 continue:2 yields:4 become:1 works:1 lenin:1 because:1 some:18 labeling:1 sight:1 ourselves:1 describing:1 dimensions:1 does:1 provides:2 refer:1 slight:1 broken:2 references:1 permitted:4 algebraic:1 stand:1 act:2 introduced:1 perturbed:2 own:1 into:2 within:2 legged:4 due:1 lies:1 right:3 wherefrom:1 operator:7 tetrahedral:9 hep:2 additional:1 transfer:8 there:4 u1:2 conservation:1 way:2 was:1 complete:1 form:1 something:1 forming:1 but:6 construction:2 r56:2 made:1 up:1 us:7 placed:1 below:2 similar:1 called:4 mechanics:1 associated:3 int:5 abstract:1 general:2 intimately:1 conserved:2 invertibility:1 av:1 families:1 constructed:1 variety:1 generally:2 papers:2 really:1 draw:1 elements:2 kinds:1 12p:1 separate:1 models:2 vertex:5 sides:1 having:1 implied:1 strings:8
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solv-int9703011.txt |@word partial:2 consider:7 scratch:1 lack:1 results:4 cmpc:1 rebbi:1 grateful:1 consists:1 hole:1 devoted:1 particles:1 dimensionality:1 depend:2 fellowship:1 technique:1 editors:1 ıa:2 program:1 under:2 maryland:1 include:1 worth:1 applied:1 charles:1 straightforward:3 far:1 every:1 matrices:8 deformations:1 3h1:2 presented:2 proc:1 companies:1 solution:3 δh1:2 vector:11 harry:2 design:1 equal:1 dynamics:1 folk:1 canonical:3 even:1 appear:2 brackets:1 deeply:1 section:5 brief:2 3t:2 version:1 above:1 kyoto:1 international:1 increasing:1 method:6 nakamura:1 satisfy:2 edited:2 simultaneously:1 respectively:6 canonically:1 situation:1 directions:1 consideration:2 along:11 equations:12 appears:1 obtained:1 derivable:1 remark:1 antisymmetric:3 geophys:1 inspired:1 allows:1 periodic:3 poisson:24 usually:1 honor:1 family:3 vii:1 private:1 marcel:1 derivatives:3 use:2 would:1 prove:2 remains:1 contains:1 physics:1 ψt:1 few:1 linear:4 noting:1 call:1 therefore:3 vi:1 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