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solv-int9807008.txt |@word represent:1 partial:1 consider:2 chain:4 funct:2 results:3 landen:1 proposition:11 grateful:2 follow:3 denotes:1 analiz:1 c0:10 paris:2 eα:14 tr:3 ego:1 quasi:2 tj:3 petersburg:2 elliptic:23 under:2 tr1:1 tr2:1 case:28 r14:1 r12:5 r13:3 r11:1 terminate:1 agnolo:1 choice:2 witten:2 δjk:1 matrices:4 condition:4 specify:1 frobenius:1 hamiltonian:1 did:1 sklyanin:8 list:2 solution:6 t0:8 solved:1 commute:3 quasiperiodicity:3 eigenvalues:6 div:8 degeneracy:1 zm:2 zn:18 sturm:1 computation:5 periodicity:1 takhtajan:1 consistent:1 za:1 imply:2 masson:1 further:2 odd:2 substitute:1 canonical:5 spectral:16 index:2 gl:1 appear:2 brackets:2 giving:1 sum:1 expressed:5 version:4 poles:6 above:3 kyoto:1 suppose:1 3a:1 method:2 lifshits:1 satisfy:6 ωmn:4 degree:3 respectively:6 even:1 here:10 following:19 inverse:2 leeds:1 ansatz:4 separation:15 berkeley:1 represented:1 standard:3 equations:12 z1:1 z2:1 z3:1 obtained:9 divisor:3 suitably:2 institute:1 shift:1 study:5 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solv-int9807009.txt |@word partial:2 consider:4 similarity:2 results:5 four:1 roy:2 follow:1 whose:1 ıs:1 γx:2 depend:2 kγ:2 finally:1 kη:2 present:1 under:2 cahn:4 te:1 worth:1 applied:2 conjecture:6 supported:1 springer:2 choice:1 summarized:1 condition:8 leads:2 presented:1 list:1 solution:6 vector:2 optics:1 painlev:17 further:2 ode:6 index:2 nonlinear:2 tabor:1 expressed:2 new:1 64z:1 method:33 exercise:1 satisfy:3 edited:1 2ks:2 respectively:2 here:3 reported:1 explore:1 consideration:1 equations:27 appears:1 obtained:7 search:1 study:1 studied:1 allows:5 contradiction:2 resulting:1 studies:1 sci:1 york:1 family:1 namely:1 apply:2 derivatives:3 use:2 takes:1 would:3 prove:1 contains:1 next:1 noting:1 therefore:1 type:7 theoretical:1 more:3 solitons:1 apparent:1 berlin:1 appendix:3 mansfield:2 normalized:2 particular:3 known:1 cases:5 must:4 ramani:1 account:1 equation:26 infinitesimal:4 following:5 merely:1 example:2 f2:1 stated:2 calculation:1 discussed:1 neglected:1 numbers:1 allowed:1 verlag:2 six:1 how:1 nontrivial:1 acta:1 ordinary:2 tried:1 algebra:1 max:2 advice:1 different:8 wrong:1 sx:1 clarkson:4 explicit:1 st:1 complexity:2 spain:1 order:3 restriction:2 holds:1 developed:2 satisfied:2 interpreted:1 paper:4 through:2 mentioned:1 satisfies:2 still:1 its:1 group:1 thank:1 singular:32 interesting:1 solving:2 choose:1 mail:1 them:5 good:1 salamanca:2 acklund:1 they:4 identically:1 2u:2 february:1 invariants:3 university:1 40k:1 identified:1 chowdhury:1 2f:1 found:2 pb95:1 arxiv:1 reduce:5 our:3 es:1 out:1 shown:6 furthermore:2 since:2 research:1 smm:16 kent:1 correct:1 math:5 shows:1 theory:1 ısica:2 possibility:2 8z:2 reason:1 advantages:1 term:1 βt:2 determining:2 could:3 similarly:1 correctness:1 levi:1 times:1 turn:1 universidad:1 initial:2 symmetry:9 bluman:1 relate:1 variables:1 xx:2 set:2 done:1 submit:1 precisely:3 affords:1 their:1 introduction:2 leading:3 carnevale:1 system:1 construct:1 hilliard:4 appl:2 listed:1 statement:2 whith:1 siam:2 recovered:1 gives:1 fz:4 relationship:1 tool:2 part:2 authors:8 x0:7 believe:1 was:6 require:1 zero:2 winternitz:3 determined:2 were:5 2z:1 result:2 symmetries:45 derivative:1 generality:2 seen:1 apparently:1 clearly:1 lie:2 latter:1 able:1 take:2 added:1 unless:1 shall:2 acknowledgements:1 why:1 nonlinearity:1 considered:3 professor:2 later:1 physica:2 segur:1 32z:2 physics:2 incomplete:1 particularly:1 show:3 reductions:4 12k:1 solutions:9 trivial:2 eliminated:1 q2:1 based:1 just:1 parameters:1 should:7 only:13 generators:3 do:3 his:1 means:3 de:3 cannot:1 applying:1 gen:1 qu:1 qt:2 fields:1 dgicyt:1 differential:5 expansions:1 remove:1 ut:7 choudhury:3 ars:1 reference:3 see:2 computer:1 usefulness:1 eliminating:1 fail:1 terms:6 cole:1 αu:1 αx:6 uη:1 written:4 correctly:2 between:1 invariant:11 champagne:1 conditions:2 counterexample:1 notice:1 2αu:1 recently:3 olver:3 hereman:1 comp:1 however:3 comm:1 solv:1 ames:1 both:5 last:2 many:1 equal:1 contract:1 pde:2 expression:1 relevant:1 facilities:1 continuation:1 corresponds:1 analyzed:1 simply:1 16z:1 respect:1 rep:1 pp:13 transformations:2 second:1 basis:1 computing:1 odes:3 been:9 int:1 reduction:2 6f:1 offered:1 6k:5 scrutiny:1 ours:1 careful:2 former:1 manifolds:2 case:10 look:1 pacs:1 engineering:1 evaluated:2 will:1 cast:1 while:1 applies:1 orica:1 property:8 procedure:1 non:42 surface:8 according:5 counterexamples:1 vx:1 nuov:1 confirmed:1 φt:3 combination:1 φx:10 seek:1 same:1 φj:2 several:1 difficult:1 independent:1 used:2 effect:1 v2:1 2u2:1 ablowitz:1 normalization:1 concordance:1 nevertheless:3 rosenau:2 well:3 analysis:2 obviously:1 academic:1 without:1 zhdanov:1 manifold:34 φtt:1 proposed:1 sentence:2 obtain:4 identify:6 integer:1 omissions:1 previous:2 conclusions:4 sattinger:1 weiss:3 lett:3 easy:1 5f:1 transformation:1 sonia:1 aspects:1 easily:1 spatial:2 possible:2 press:1 using:10 loss:2 like:1 identifying:1 separately:4 yields:1 reduced:3 because:3 methods:1 classical:38 truncated:2 conditional:7 some:6 examples:7 fushchych:1 est:4 ηx2:1 confirm:1 avoid:2 d49:1 does:2 provides:3 algorithmic:1 obey:1 usal:1 journal:1 d70:1 expansion:3 step:1 although:1 substitution:3 comparison:1 package:1 ηxx:3 dependence:1 o:4 discusses:1 consequently:1 φxx:1 presence:2 into:1 fz2:3 ηu:8 ηt:2 references:1 determine:3 ηx:3 fzz:6 area:1 there:2 u0:1 u3:1 u2:6 doubt:1 facultad:1 way:2 sections:1 form:6 singlevalued:2 jul:1 flawed:1 properly:1 removed:1 pdes:2 made:2 compute:1 ux:6 evident:1 whether:1 characteristic:7 us:5 par:1 those:6 uj:2 demonstrate:1 agree:1 detailed:1 associated:8 infinitesimals:4 defined:3 abstract:1 homographic:6 check:3 again:1 cim:1 no:3 mathematica:1 when:6 field:1 other:2 special:1 papers:1 mathematics:2 15f:1 variable:2 lead:1 established:1 pilar:1 4k:2 4f:1 requires:4 original:2 once:1
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solv-int9807010.txt |@word consider:4 equalities:3 uw0:2 results:1 leads:2 ge:1 commute:1 computation:2 go:1 research:1 gk:1 gh:1 21st:1 depend:1 aug:1 tu:2 finally:2 ev0:2 applied:1 abelian:1 zhang:2 far:1 rise:2 prof:2 difference:4 matrices:2 condition:1 four:1 evk:3 solves:2 notes:1 solution:4 large:1 discrete:37 vector:11 interchanging:1 science:1 relation:2 pbi:1 ρk:6 application:2 grateful:1 direct:2 zero:28 chen:1 further:4 linear:1 spectral:20 what:2 nonlinear:4 section:4 hereditary:5 fuchssteiner:6 above:2 scientists:1 new:4 method:2 satisfy:5 hasn:1 full:1 simultaneously:1 lee:1 degree:4 respectively:3 here:1 groups:1 concluding:2 const:1 equations:29 change:1 obtained:1 institute:1 shift:1 vbi:2 resulting:1 usually:2 hospitality:1 suitable:1 studies:1 φki:1 classification:1 apply:1 establish:2 virasoro:9 use:2 eω:3 takes:1 would:1 prove:2 eφ:6 uniqueness:4 next:1 process:2 call:1 therefore:9 associated:6 volterra:4 type:5 theoretical:1 more:2 ir:1 points:1 initial:4 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solv-int9808002.txt |@word fredenhagen:1 concept:2 consider:1 results:3 four:2 p00:1 francesco:4 expressions:3 whose:3 depend:2 aug:1 equivalence:13 young:2 γk:1 γj:1 γi:4 dijkgraaf:1 th:2 γf:1 kν:1 belonging:2 connects:2 coprime:1 entries:1 matrices:11 condition:2 nijk:11 level:5 irreducible:2 notes:1 indices:2 eigenvalues:10 degeneracy:1 zn:3 lecture:1 profs:1 second:1 odd:8 scientific:1 even:6 index:1 3y:2 appear:1 d2:2 section:3 expressed:2 proprieties:1 current:1 expresses:1 acknowledgments:1 satisfy:3 led:1 degree:2 respectively:2 here:2 modular:3 possibility:2 groups:1 z4:1 equations:7 appears:2 interpret:1 obtained:1 antisymmetric:1 cern:1 study:3 completely:1 accomplished:1 products:3 oberle:1 sjl:1 published:1 φkk:7 useful:1 classification:2 s00:1 p62:1 lima:1 p42:1 unit:1 p40:1 p31:1 proceed:1 would:1 commun:2 positive:1 charge:6 angela:1 next:2 ψk:1 nucl:4 call:1 therefore:4 themselves:1 tell:1 more:3 nkl:2 s0l:1 particular:1 cases:4 must:1 springer:1 frobenius:1 equation:9 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solv-int9808004.txt |@word consider:5 results:1 leads:1 eds:2 commute:1 mℓ:1 expressions:3 denotes:1 issues:1 inverse:1 const:1 λin:4 aug:1 superspace:1 concerned:1 tu:1 tr:1 ts:1 tn:1 tl:7 alvarez:2 tk:4 th:10 under:2 analogous:2 must:2 ta:5 zhang:1 negev:1 manin:4 gurion:1 brunelli:1 hamiltonian:1 turns:1 notes:2 t2:1 solution:1 t1:1 proposition:3 indices:2 relation:1 λi1:2 wronskian:3 consistent:2 l2l:5 l2n:10 integrability:1 b130:1 further:2 odd:6 even:5 index:1 what:1 nonlinear:1 chicago:2 transforms:1 expressed:2 henceforth:1 consistently:1 above:1 krivonos:3 new:2 method:2 satisfy:2 full:1 respectively:4 modify:1 here:3 sheva:1 xα:1 equations:2 box:1 remark:1 generalizing:1 institute:1 study:2 allows:1 contradiction:1 ibort:1 ramos:1 simply:1 mulase:1 fourier:1 studies:1 appropriately:1 via:1 ratios:1 f1:2 modifying:1 use:1 would:2 commun:6 positive:1 finally:1 next:1 ψj:4 comparing:1 nucl:3 therefore:2 m2:30 ψa:1 type:1 theoretical:1 more:1 israel:1 started:1 solitons:2 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solv-int9808005.txt |@word partial:1 consider:11 remarkable:2 rev:3 results:7 gy:1 gx:1 leads:1 generalize:3 follow:1 whose:1 inverse:2 pointing:2 concerned:1 γj:5 finally:4 those:3 under:2 analogous:2 worth:2 norm:1 chennai:1 g3:6 g2:6 g1:6 far:1 choice:2 every:1 matrices:1 condition:5 presented:1 irreducible:3 solution:4 solved:3 vector:3 section:4 indices:2 eigenvalues:9 noted:5 degeneracy:2 l2b:1 consistent:4 direct:1 cosh:1 second:7 further:8 eik2:1 linear:3 even:6 established:3 what:1 nonlinear:5 plays:1 sum:1 associate:1 expressed:2 en:1 establishes:2 new:7 net:1 principal:2 method:2 satisfy:4 turbiner:2 degree:16 respectively:7 realizations:1 here:12 explore:1 them:1 separation:4 address:4 equations:4 bhubaneswar:2 obtained:9 institute:3 study:1 vectors:1 vbn:1 contradiction:1 therein:1 gambardella:2 via:1 followed:1 family:2 extra:1 ground:2 hcd:3 highly:3 first:10 total:2 establish:2 use:4 would:4 positive:2 eφ:1 negative:1 next:2 comparing:2 going:1 taken:1 type:13 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solv-int9808006.txt |@word gu:9 partial:1 consider:5 chinese:2 global:1 gx:3 four:1 ferreira:1 ηi2:1 sattinger:1 expressions:2 gl:5 cases:4 whose:3 isometric:11 inverse:1 depend:1 calculate:1 aug:1 shanghai:1 kζ:2 th:1 under:1 tg:4 case:2 g1:4 g0:3 conditions:1 wave:5 entries:2 matrices:1 condition:3 harlow:1 dajczer:2 list:1 applicable:4 involution:2 vector:10 math:9 dealt:4 eigenvalues:2 anal:1 fok:1 ρk:1 a126:1 akns:1 zn:1 ρj:7 zi:10 zk:13 σhh:5 direct:2 second:3 surface:2 reine:1 odd:2 eigenspaces:1 theory:4 spectral:6 nonlinear:5 diag:4 kρi:5 axes:2 dzi:1 odes:1 above:3 2µc:3 new:3 method:6 satisfy:2 degree:4 respectively:1 here:11 bi:15 σh1:1 china:2 sinh:1 sine:8 equations:14 z1:2 change:2 obtained:1 remark:3 glk:1 antisymmetric:1 institute:1 study:1 studied:1 2µx:1 procedure:1 γkj:1 γijk:2 useful:2 apply:2 linearly:9 plot:1 ψx:4 would:1 prove:1 chk:1 bundles:1 δiα:2 ψt:1 ξl2:1 m1:1 therefore:7 those:1 m2:1 taken:1 ablowitz:1 vj:2 more:2 flat:8 µzi:3 µe1:1 immersion:15 becomes:2 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solv-int9808007.txt |@word alj:2 consider:9 four:4 gf:1 scalar:1 grateful:1 n31:43 expressions:6 q43:2 inverse:6 const:2 calculate:3 finally:1 infinitesimally:1 reissner:1 analogous:3 eiλx:4 very:1 wave:3 sons:1 formula:1 matrices:2 condition:4 riemann:3 immediately:1 transmission:1 solution:6 moldova:1 large:1 solved:2 vector:6 consultant:1 akns:3 upper:3 sign:6 astrophys:1 second:2 further:12 dψ2:1 zs:2 spectral:1 nonlinear:3 g22:1 g23:1 tetrad:1 deeply:1 section:3 analogously:5 expressed:7 d3:5 poles:1 above:1 nine:1 3a:2 equivalent:1 satisfy:1 κi:5 κj:5 respectively:2 component:2 here:5 dimensionality:1 tangent:1 sinh:8 q12:18 represented:2 consideration:1 along:1 marchenko:2 equations:43 obtained:6 great:1 antisymmetric:1 institute:1 vectors:5 akj:1 action:1 fourier:1 r010:3 via:8 useful:1 substitution:1 decrease:1 linearly:1 derivatives:3 eψ:52 analytic:1 covariant:4 tl:1 comparing:2 m1:9 therefore:4 ψm:1 ψa:3 type:1 more:1 nauka:1 solitons:2 nkj:1 odinger:10 curvature:14 eν:1 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solv-int9808008.txt |@word concept:1 partial:4 consider:5 remarkable:1 results:1 invent:1 eds:3 scalar:4 proposition:9 generalize:1 sci:2 nwo:1 gi:2 gr:9 devoted:2 whose:2 ihes:1 depend:1 calculate:2 aug:1 disposal:1 tn:19 finally:7 ajk:1 dijkgraaf:2 manifolds:22 th:4 under:2 eβ:1 γg:1 verdier:1 fax:1 string:1 advantage:1 orthogonal:5 very:2 cγαβ:1 pressley:1 ηii:1 geometrical:1 witten:9 bihamiltonian:1 lecture:3 ui:7 exact:1 condition:2 dim:1 dubrovin:10 immediately:1 hamiltonian:1 irreducible:2 notes:3 t2:2 solution:3 t1:10 viℓ:1 vector:13 progress:1 indices:1 peterson:1 ξnj:1 2k1:2 ten:1 sℓ:4 det:7 direct:1 matrices:2 zero:3 zx:2 tℓ:1 further:2 zv:1 odd:4 canonical:3 bilinear:4 aim:1 nonlinear:3 stands:6 invertible:2 a3p:2 section:3 zhang:2 expressed:1 version:1 en:1 subspaces:2 sup:1 suppose:2 aℓi:6 order:5 consisting:2 3d:1 satisfy:14 aik:2 degree:1 αij:4 deduces:3 respectively:4 never:1 component:7 here:6 b2p:1 desired:1 them:1 bj:2 groups:5 standard:1 equations:29 appears:1 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solv-int9808009.txt |@word partial:1 consider:4 φn1:17 funct:1 particular:1 four:13 ǫa2:3 proposition:6 consists:1 follow:1 disk:2 φn2:16 compact:5 inverse:2 const:2 quantenphysik:1 concerned:2 tu:1 riemannroch:1 finally:8 γh:1 those:2 elliptic:7 stable:2 u1i:1 belonging:1 fay:1 choice:3 every:1 lecture:1 discretizations:1 difference:3 matrices:4 prλ:1 leads:1 dubrovin:2 obvious:1 riemann:8 eds:2 bn:5 notes:3 enol:1 solution:2 pullback:2 discrete:19 vector:6 small:6 eigenvalues:2 anal:3 referred:1 linearizing:1 mn:12 force:1 ten:1 coefficient:3 sign:3 zero:18 me2:3 further:6 odd:4 situated:2 spectral:12 index:1 what:2 nonlinear:3 adds:1 appear:1 diag:2 section:1 m32:1 henceforth:1 version:2 poles:21 above:6 deift:1 new:6 method:1 lifshits:1 body:1 exchange:1 mem:1 respectively:4 component:2 here:7 behaviour:2 groups:1 others:2 path:3 along:2 strong:1 equations:2 change:1 differential:4 obtained:1 divisor:10 studied:3 reason:1 χa1:1 periodic:1 prym:8 loop:1 poisson:1 usually:1 mz:1 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solv-int9808010.txt |@word ψ1x:1 edc:1 gu:1 φ1i:7 φ1n:3 consider:1 chinese:1 focus:1 four:2 ψ1i:12 φ1x:1 ψ1l:3 ψ1n:28 edu:1 sci:1 inverse:4 aug:1 tu:1 tr:2 δhn:1 under:3 applied:2 proved:2 zhang:1 very:1 rise:1 matrices:7 condition:2 trm:3 hamiltonian:19 list:1 solution:1 large:1 involution:6 vector:1 independence:1 geng:2 solutions:1 grateful:1 takhtajan:1 direct:3 past:1 zero:4 further:1 odd:2 theory:4 spectral:9 will:2 what:1 nonlinear:3 diag:1 section:4 selected:1 wxxx:3 above:3 new:11 technology:1 increasing:1 method:4 satisfy:1 china:4 represented:1 equations:3 implicit:1 obtained:3 institute:1 vectors:2 allows:1 guide:1 resulting:2 poisson:3 usually:1 hospitality:1 uniquely:1 f3:9 2φn:4 derivatives:2 use:2 handled:1 would:1 prove:1 sake:1 positive:1 ψj:5 few:1 ψn:110 therefore:6 m2:8 taken:1 qci:1 more:1 introducing:3 becomes:3 operators:1 berlin:2 warm:1 cases:5 iii:3 must:1 springer:3 valued:1 ma:6 science:3 equation:1 work:1 det:7 cao:2 2ψn:15 following:9 making:2 example:3 proof:1 wojciechowski:1 f1:18 f2:8 ma2:1 f4:9 f5:4 f6:2 f7:1 calculation:3 organized:1 φij:3 chin:2 dxi:2 sense:2 yet:1 needs:2 verify:1 holds:3 how:2 acta:1 ψij:5 sin:1 konopelchenko:2 simplicity:1 may:3 φ2j:10 φ2i:10 after:1 φ2n:18 φ2l:3 lax:11 representations:5 fj:4 φ2x:1 fm:2 fn:40 λ2j:1 λ2n:5 dynamical:1 third:1 explicit:1 representation:1 order:7 commutator:2 hierarchy:3 indeed:3 satisfied:2 kong:6 paper:4 japan:1 still:2 its:2 till:1 chosen:4 interesting:1 2λn:3 coordinates:4 li:6 forms:1 lu:1 systems:14 constitutes:1 jacobi:4 main:1 them:2 greater:1 introduce:7 now:6 hierarchies:2 possess:1 easily:1 term:1 2w:2 equality:1 always:1 university:5 presented:2 each:3 2l:1 found:1 2n:11 2i:7 2j:1 constraints:13 another:2 r2n:1 idea:1 extended:3 1n:10 special:2 out:1 shown:1 matrix:6 nuovo:2 since:4 research:1 investigation:1 m2j:1 ref:4 math:14 ψ2x:1 given:4 standard:2 ψ2l:3 completely:2 ψ2n:26 ψ2i:10 york:1 ψ2j:13 put:4 checked:1 finite:4 pairs:6 r1:2 ministry:1 1v:1 m22:1 motion:18 turn:1 invitation:1 βn:1 βj:3 first:4 ding:1 λ3n:1 utilizes:1 symmetry:16 variables:13 l37:1 least:2 directly:1 fi:1 ψx:1 xu:4 city:4 ψ1j:15 fk:1 bracket:2 similarly:2 introduction:1 adjoint:1 system:14 adopted:1 their:2 xiu:1 1i:5 1j:3 structures:5 final:1 vxx:3 mining:1 2an:1 authors:2 vφ2:1 vxxx:3 18b:1 kind:3 cimento:2 integrability:3 aims:1 1l:1 project:1 determined:3 gives:1 ann:1 need:1 constrained:18 orders:2 note:1 take:2 even:3 established:2 regular:1 nothing:1 class:1 soliton:6 considered:3 physica:2 kp:2 li1:1 h2k:1 hietarinta:1 λln:6 physics:1 oevel:2 show:2 supported:1 relation:5 akns:7 find:2 aψ:3 than:1 only:2 explicitly:3 2bi:1 integrable:7 hope:1 do:3 cheng:1 notation:1 get:3 dependent:13 famous:1 dx:7 combinations:2 years:1 gen:3 babelon:1 qx:2 arxiv:1 consisting:3 ψji:1 set:1 constructing:2 reference:1 achieved:1 imposing:1 national:1 δjl:1 see:1 result:2 aroused:1 ostrogradsky:4 satisfying:1 tend:2 written:1 αi:3 c2k:2 boundary:1 email:2 αn:1 jx:4 extend:2 deliver:1 however:3 hefei:1 solv:2 wx:4 suggested:1 providing:1 viallet:1 mono:1 taking:1 b2k:2 expression:2 ck:3 cj:1 ci:3 cn:4 cl:4 reasons:1 dimensional:6 m12:1 2λj:1 kowloon:2 respect:2 throughout:1 px:2 been:7 int:2 interest:1 basic:1 ak:3 generating:1 describe:1 corresponding:6 m1i:1 residue:1 c3:2 c2:2 c1:4 c0:5 those:2 c4:1 case:18 aix:1 means:2 arnold:1 trick:1 aψ1:10 suppose:1 rbi:1 di:3 property:2 region:2 refs:3 thus:2 iv:1 ii:2 reads:2 il:2 vx:8 bargmann:2 φil:1 binary:11 hong:6 φx:1 acknowledgments:1 make:1 same:2 any:2 φj:5 several:1 φn:133 higher:6 independent:9 used:1 eds:1 upon:1 moment:1 uses:1 potentials:2 center:1 nevertheless:1 analysis:4 concrete:2 without:1 researchers:1 proposed:1 among:1 when:8 nonlinearization:14 obtain:2 using:2 λj:24 λi:19 λn:49 functionally:8 adv:1 preprint:1 point:1 had:1 wen:1 setting:1 transformed:2 lett:6 easy:1 remaining:2 2v:4 know:1 bix:1 integer:2 formal:1 like:2 δv:2 follows:6 δu:2 yields:1 integrals:19 δw:2 mathematical:2 because:2 methods:2 classical:2 successfully:3 some:3 b4:1 b0:5 b1:4 b2:2 b3:2 sidorenko:2 l17:1 defined:2 faddeev:1 scientific:1 bl:7 bn:2 bi:4 bj:1 constraint:15 commun:1 o:1 2ci:1 2k:15 soc:1 into:2 nsc:1 functional:1 pair:1 references:1 comparing:1 there:2 appl:1 resulted:1 m1:8 φji:1 form:1 but:3 hk:1 hn:1 true:1 us:3 liouville:6 problem:15 cix:1 similar:1 examples:1 mechanics:1 shandong:1 constant:2 ai:5 certain:1 abstract:1 aj:3 zeng:5 general:2 exist:1 rule:1 education:1 constructed:1 ni:1 functions:2 no:1 wxx:3 nx:3 field:1 valid:1 remarks:2 solitons:1 department:3 mathematics:3 conclusion:3 conclude:1 denote:2 φ1j:8 separate:1 problems:2 vw2:1 a0:5 generated:1 a2:6 structure:1 implies:1 assume:4 required:9 together:1 investigated:1 presenting:1 ustc:1 n0:1 n2:15
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solv-int9808011.txt |@word gu:3 sci:2 consider:5 chinese:3 leads:1 proposition:8 computation:2 edu:1 sung:1 localized:7 gr:1 whose:3 inverse:4 aug:1 shanghai:1 jvn:1 th:1 under:1 include:1 applied:1 g1:3 wave:13 entries:2 li:2 matrices:8 iut:1 condition:5 solution:9 large:2 vector:3 math:4 zj0:2 permutability:3 solutions:15 zn:1 mn:4 zj:10 mi:2 direct:1 cosh:6 integrability:4 dynamics:1 theory:1 spectral:1 nonlinear:12 diag:4 section:1 slight:1 http:1 3i:2 bαβ:5 above:3 cao:1 method:6 satisfy:1 degree:2 exchange:1 respectively:5 never:1 component:2 here:9 desired:1 china:1 separation:1 directions:3 along:2 equations:8 appears:1 change:1 obtained:4 remark:2 institute:2 vectors:2 action:2 changes:1 via:2 lims:2 explained:1 limt:1 santini:2 apply:1 use:3 ψy:2 asymptotic:9 prove:1 ψt:1 next:1 m1:13 therefore:8 m2:8 boiti:2 more:2 separated:1 solitons:24 uxx:1 separates:2 cases:1 hold:5 springer:1 ulr:1 science:2 equation:29 work:1 det:3 mk:7 mj:12 iλα:11 ρr:5 values:3 following:1 example:3 proof:2 figure:1 give:2 high:2 numbers:2 uab:2 axis:2 darboux:18 get:1 write:2 acta:1 verlag:1 ft:2 replacing:1 fy:3 ζj:3 after:1 derived:4 different:10 applications:1 lax:3 verified:1 choice:1 constants:3 explicit:1 su:9 their:1 sh:1 lβ:22 φy:1 order:1 davey:3 multidimensions:2 holds:2 developed:1 move:6 satisfied:3 symbols:1 paper:2 including:1 mentioned:1 satisfies:1 still:3 its:3 sciences:1 ln:5 sα:5 lj:1 lk:1 actually:1 parts:2 lr:1 fig:6 mail:1 main:1 non:1 jη:4 acklund:1 multidimensional:1 now:6 discuss:1 ift:1 2u:1 always:1 university:2 each:3 2n:2 2i:3 characterized:1 constraints:3 lm1:1 lm2:1 owing:2 laboratory:1 special:2 shown:1 superscripts:1 matrix:13 ejk:1 iλj:1 iλi:1 since:4 rev:1 research:1 re:14 dsi:12 rn:1 limτ:2 shows:2 foundation:1 linear:4 localization:2 diagonal:14 reason:1 interaction:1 turn:1 u23:3 hence:7 vja:1 first:5 xj:10 xn:2 features:1 symmetry:1 reveals:1 variables:2 number:2 relations:1 sidorenko:1 given:3 hyperbolic:8 introduction:1 system:16 construct:5 hβ:4 bα1:1 structures:2 frame:1 vxs:1 gives:1 alonso:1 part:4 γjk:1 bαn:1 bαj:1 imply:2 youth:1 determined:1 were:3 treated:1 iωj:1 generality:1 generalization:1 need:1 any:6 jour:2 zero:2 lim:5 note:1 gφ:1 take:2 so:3 jxj:1 salle:1 unless:1 uyy:1 iwn:1 lα:27 iwj:1 algebraic:1 significant:1 phase:4 class:1 soliton:10 especially:2 physica:1 lλ:1 nondegenerate:1 zhou1:1 kp:1 exp:19 a145:1 pku:1 velocity:6 fact:1 show:1 reductions:1 supported:1 rth:1 gauge:1 akns:8 q1:4 q2:4 proposed:1 parameters:3 true:1 should:2 only:10 explicitly:1 integrable:2 constant:10 columns:1 do:3 cheng:1 means:2 2q1:1 aα:2 cannot:1 new:1 systems:3 evolution:2 kadomtsev:1 arxiv:1 fixed:1 coefficient:1 constructing:1 physically:1 national:2 hα:13 j1:1 see:1 techniques:1 project:1 phases:1 satisfying:1 interacting:1 ways:1 speed:1 fission:1 tend:3 enough:2 various:1 between:1 invariant:1 conditions:4 discovery:1 jy:2 vertical:1 numer:1 wn:2 matveev:1 however:4 wj:12 jn:1 comm:1 jj:3 jk:3 solv:1 useless:1 jf:1 pempinelli:3 limits:1 according:1 etc:3 connection:1 figures:3 vx2:1 σjk:1 cn:4 simple:1 corresponds:2 leon:1 dimensional:7 bα:1 polynomial:1 moreover:2 aαn:1 aαj:1 considering:1 most:13 transformations:8 been:1 int:1 κr:3 enlarging:1 u12:2 fudan:2 choose:1 hernandez:1 corresponding:2 coherent:2 c3:2 c2:2 c1:2 denote:4 c6:1 c5:1 c4:2 case:4 straight:1 heidelberg:1 will:3 suppose:12 behavior:3 procedure:1 changed:1 a29:1 vj:7 vk:3 vn:2 ii:2 ik:14 im:20 vv:3 vx:18 vy:15 vanish:2 vy2:1 binary:1 containing:1 φt:1 φx:1 recursion:1 same:5 complex:4 lux:1 proved:1 dα:5 higher:1 independent:1 infinity:2 peaks:19 numerical:1 hand:1 usually:1 identity:1 lower:1 off:2 petviashvili:1 without:1 components:2 ujk:9 coordinate:1 entry:1 elα:1 drawing:1 λr:3 just:2 generally:1 applicandae:1 solvability:1 rest:1 transforms:3 scattering:1 λn:2 stewartson:3 previous:1 conclusions:2 alternate:1 iω:6 other:3 5i:2 lett:8 theorem:12 transformation:8 generalized:1 real:11 fusion:1 using:2 loss:1 like:1 follows:2 velocities:9 html:1 specific:1 arbitrary:1 because:1 methods:1 mathematicae:1 some:4 nonzero:3 provided:1 describing:1 dimensions:4 does:4 tends:1 refer:1 uµν:1 2q2:1 aαβ:6 problems:4 bn:4 l1:1 nonlinearization:1 cβ:3 cα:5 properties:2 takes:1 pβ:1 pγ:1 pα:6 constraint:7 column:1 freedom:1 discussed:2 simulation:1 mutually:3 konopelchenko:2 mbn:1 h2:2 h1:2 martinez:1 pair:2 references:1 determine:1 ixj:5 rows:1 ixn:1 springerverlag:1 there:11 way:3 call:1 was:2 energy:1 function:1 form:3 hr:6 differences:5 but:1 construction:1 line:1 pdes:1 u13:2 uy:1 ux:5 ut:3 ωj:3 limit:4 ωn:1 problem:5 uf:3 a168:1 ordered:1 defined:1 certain:1 abstract:1 uij:2 general:2 globally:1 exist:1 interchanged:1 av:3 aα1:1 moves:1 constructed:3 qα:13 nj:1 qβ:2 when:12 valid:1 fokas:2 mathematics:3 zhou:5 separate:2 time:2 uniformly:1 medina:1 includes:1 peak:2 hietarinta:1 implies:14 space:2 together:1 gαβ:3 hirota:2 original:2
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solv-int9808012.txt |@word consider:2 four:1 computation:1 winds:1 expressions:2 als:1 compact:3 inverse:1 aug:1 charge:1 critical:7 under:1 orthogonal:1 every:1 entries:1 fǫ:3 continued:1 condition:11 leads:1 hamiltonian:1 irreducible:1 solution:2 interpolating:1 indices:1 eigenvalues:1 dealing:1 matrices:2 haag:2 diag:1 new:1 acknowledgments:1 satisfy:1 notions:1 exchange:6 respectively:1 tλλ:1 here:2 modular:8 free:1 equations:6 poisson:1 action:4 uniquely:1 examining:1 useful:1 inducing:1 lima:1 linearly:1 use:3 proceed:1 commun:2 suppl:1 next:1 nucl:4 therefore:2 reflects:1 introducing:2 operators:2 normalized:2 ward:1 sλλ:1 chiral:16 work:1 theories:2 bernard:1 values:1 following:3 compare:1 give:1 states:12 sense:1 verlinde:2 tan:1 robinson:1 verlag:1 goal:1 provide:1 acts:1 write:5 instead:1 iθ1:2 product:1 express:1 algebra:7 may:1 derived:2 different:1 representations:2 stress:1 short:1 natural:1 sectors:1 light:1 st:1 sh:1 pleasure:1 order:2 over:1 fλ:5 stability:1 through:1 statistical:1 b300:1 satisfies:2 buchholz:1 derive:1 group:4 thank:1 ln:3 interesting:2 solving:1 jacobi:2 imz:1 non:1 now:4 discuss:1 fσ:1 l0:9 2i:1 carlos:2 another:2 energy:2 related:2 operator:2 literature:1 quantum:1 our:1 eiht:1 matrix:7 rev:1 denotes:1 reader:1 formula:1 suffices:1 math:2 theory:5 singularities:1 ısica:1 diagonal:1 departamento:1 base:1 brasil:2 modularity:3 due:1 βh:3 symmetry:1 primary:3 iht:1 done:1 directly:1 takesaki:1 between:1 given:6 temperature:2 dedekind:1 system:1 their:2 fermions:1 holomorphic:1 continuous:1 part:1 occurence:1 translation:1 distance:1 kind:1 determines:1 cyclic:1 e2iπ:2 exhibit:1 say:1 seen:1 lim:1 note:1 instance:1 k1:4 indexed:1 rehren:3 trace:3 shall:1 algebraic:1 automorphism:3 pair:1 analytically:1 mack:1 class:1 tensor:1 laurent:1 considered:1 torus:2 partition:2 principle:2 exp:4 supported:1 relation:3 find:2 state:1 should:1 analytic:1 only:1 black:1 local:1 de:2 combinations:3 evolution:2 fields:3 arxiv:1 common:1 hλ:5 set:1 exists:1 achieved:1 see:1 japan:1 discussions:1 b303:1 satisfying:1 αt:7 federal:1 positivity:1 symmetric:1 written:1 simplest:2 theta:2 boundary:4 knowing:1 matricial:1 terms:2 vanishing:1 solv:1 context:1 sβ:1 hσ:1 hφ:1 profs:1 point:3 simple:2 considering:1 described:1 transformations:1 three:1 been:1 int:1 describes:1 combined:1 hawking:1 algebras:1 model1:1 field:14 direction:2 stems:1 present:1 k2:3 narnhofer:2 will:2 replaced:1 monodromy:4 property:2 conformal:11 unitary:1 reads:1 im:3 cone:1 santos:1 make:1 radiation:1 parts:1 used:1 effect:2 kubo:2 characters:4 reference:1 center:3 well:1 analysis:1 todorov:1 components:4 model:8 wagner:1 identify:2 eigenstates:1 density:1 easy:1 iπ:2 transformation:1 finitetemperature:1 around:1 stein:2 rules:2 iβ:3 possible:1 fusion:3 vacuum:1 using:2 like:1 tomita:1 exploiting:1 δn:1 yields:1 martin:2 terminology:1 classical:1 spring:1 some:1 b5:1 repeat:1 dimensions:2 does:1 kms:20 steps:1 proc:1 minimal:2 fφ:1 expansion:1 hǫ:1 properties:10 pγ:1 central:1 carried:1 pδ:1 column:1 pλ:12 o:1 introduced:1 projectors:1 2iπ:1 soc:1 letter:1 previously:1 functional:4 bath:1 tackle:1 references:1 strip:2 elementary:2 there:1 question:1 labelling:1 function:7 form:2 heat:1 cnpq:1 partially:1 compute:3 whether:1 us:2 below:1 limit:2 problem:1 similar:1 defined:4 certain:1 abstract:1 ao:2 examine:1 exist:1 periods:1 identities:1 universidade:1 functions:3 whereas:2 schroer:2 schwinger:2 application:1 other:2 details:1 picture:2 elements:1 models:1 generated:1 bounded:1 ising:7 variable:1 b312:1 factorized:1 holes:1 fλλ:7 time:3
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solv-int9808013.txt |@word fredenhagen:1 nψ:1 concept:2 consider:1 results:1 ginzburg:1 p00:1 computation:1 francesco:1 contributions:1 localized:1 row:2 depend:3 aug:1 equivalence:6 young:6 γk:1 γj:1 charge:9 dijkgraaf:1 γn:2 th:2 under:2 case:3 belonging:1 nσ:10 orthogonal:1 connects:2 every:1 matrices:17 condition:2 nijk:6 level:3 irreducible:8 notes:1 solution:2 b285:1 admissible:1 vector:5 indices:3 eigenvalues:2 3x5:1 enjoy:1 zn:3 consistent:1 direct:1 sign:1 further:1 4x3:1 scientific:1 spectral:1 established:1 3x:1 appear:1 d2:3 section:2 expressed:1 en:1 expresses:1 acknowledgments:1 satisfy:5 led:1 exchange:4 here:3 b246:1 modular:2 q2:1 ansatz:1 groups:2 δλn:1 equations:3 appears:1 δλi:1 obtained:3 antisymmetric:1 cern:1 lomi:1 study:2 vectors:1 allows:2 accomplished:1 products:3 oberle:1 sjl:1 published:1 φkk:4 useful:1 classification:2 s00:1 lima:1 b349:1 p40:2 standing:1 use:1 p31:2 takes:1 would:1 commun:3 positive:1 contains:2 γi:3 next:2 ψk:1 nucl:7 therefore:1 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solv-int9808014.txt |@word minors:3 consider:6 remarkable:1 froude:1 equalities:1 global:1 results:5 leads:8 computation:2 kato:2 consists:1 follow:1 expressions:1 denotes:2 once:1 gj:19 compact:1 inverse:8 aug:1 γr:7 tt:9 ℜz:3 ℜx:1 uω1:1 γj:10 uniqueness:3 tj:6 preserved:2 th:1 under:4 analogous:2 norm:10 applied:1 2γn:1 kπ:1 deforming:1 already:1 straightforward:3 orthogonal:2 far:1 pages:1 rise:1 differently:1 wave:33 rm:9 resonant:1 li:1 skew:1 exact:2 condition:2 essai:1 differentiated:1 hamiltonian:1 zeit:1 unscaled:1 t2:6 solution:53 t0:18 t1:12 large:3 solved:2 k6:1 spaces:11 minimal:1 recall:5 eigenvalues:1 anal:2 noted:1 related:1 dg1:2 upper:1 des:2 compensated:1 waveforms:2 8k:7 consistent:1 estimates:12 direct:2 cosh:13 approximation:7 imply:2 odd:2 substitute:1 linear:10 spectral:2 nonlinear:4 plays:1 appear:2 rate:1 d2:3 section:8 uniform:3 uj:10 poles:9 sur:1 above:8 toll:1 new:2 nonlinearly:1 change:1 method:4 ϕx:2 satisfy:6 full:6 led:1 degree:2 ebt:4 inviscid:1 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solv-int9808015.txt |@word rx:2 results:1 four:1 edu:1 follow:1 expressions:1 trickier:1 contributions:1 depend:1 aug:1 tu:1 tr:21 ts:8 under:1 analogous:2 sent:1 straightforward:2 very:1 affect:1 differentiated:1 did:1 solution:3 t1:1 convenience:1 differential:1 interchanging:1 still:1 smaller:1 occurrence:1 direct:1 cosh:1 painlev:5 concludes:1 odd:1 even:1 what:1 sum:1 expressed:2 above:3 exercise:1 equals:6 here:5 desired:2 free:1 sinh:12 address:1 sine:1 equations:1 change:4 obtained:2 products:4 complicated:1 changes:1 uniquely:1 divide:1 family:1 extra:1 prefer:1 replace:2 derivatives:4 use:6 usa:1 commun:1 remains:1 next:2 nucl:1 therefore:3 more:2 becomes:3 operators:2 known:1 iii:3 must:2 science:1 equation:8 det:12 norm:2 already:1 making:1 proof:2 f0:6 f1:5 give:2 caused:1 dxj:1 want:1 arise:1 end:1 awkward:1 s2:5 get:1 mccoy:2 parameter:1 product:5 fs:1 may:1 after:2 dx1:1 fi:8 fj:3 sy:1 sx:4 λ2n:1 third:1 computations:1 sk:1 so:7 correlation:1 representation:3 order:4 displayed:1 course:1 paper:2 satisfies:4 y2:1 its:1 before:3 derive:3 summands:1 conjugation:2 writing:2 mail:1 main:1 introduce:2 now:7 2t:4 eigenvalue:3 university:1 l2:4 each:1 2n:16 square:1 ei:8 ej:3 our:2 special:2 shown:6 rs:1 since:4 crucial:1 research:1 replacing:3 acting:2 formula:1 math:3 foundation:1 harold:1 little:1 undo:1 california:1 8t:1 determining:1 times:2 gordon:4 leading:1 hence:8 first:10 xj:15 simplifies:1 xy:12 given:2 likely:1 similarly:1 unknown:1 relations:2 dt2:1 gives:8 immediate:1 part:2 rsx:1 x2:5 coefficients:1 kind:1 approximations:1 second:7 were:1 unchanged:1 clearly:1 note:1 xi:1 formulas:5 begin:1 multiple:2 shall:1 quote:1 denominator:2 involving:1 preliminary:1 tracy:3 neighborhoods:1 clear:1 bracket:1 fact:4 show:5 supported:1 dy1:1 notations:1 relation:2 solutions:1 d2:4 find:6 subtracting:1 q0:9 parameters:2 bernard:1 only:2 going:2 factor:5 meant:1 do:1 establishes:1 notation:5 means:1 ϕs:5 ϕr:5 made:1 dx:4 dy:4 applying:2 dt:9 differentiating:1 determinants:5 widom:2 arxiv:1 qi:5 dx2n:1 kernel:5 set:2 national:1 see:4 satisfying:2 eigenfunctions:1 αy:1 symmetric:1 written:1 various:2 between:2 invariant:1 subscript:1 notice:1 terms:6 kei:1 tuj:1 solv:1 come:1 both:3 last:2 u02:5 taking:3 equal:1 etc:1 connection:2 among:1 point:1 appeared:1 had:1 ca:1 cf:1 mkdv:1 respect:2 kernels:3 duj:1 been:2 asymptotics:2 u12:5 b426:1 define:2 corresponding:1 quantities:3 observe:2 those:1 case:3 p0:8 will:4 replaced:1 error:2 cancelled:1 unitary:1 almost:1 vi:24 vj:4 thus:4 iv:1 ii:1 claimed:1 fermion:1 grant:1 recursion:1 make:3 same:2 any:1 hierarchies:1 literature:1 effect:1 v0:16 v1:7 purpose:1 identity:3 without:1 left:1 less:1 obtain:1 seems:1 wu:2 easy:1 eigenfunction:5 evaluate:1 showing:1 cruz:1 know:2 using:7 appearing:1 follows:4 integrals:1 reduced:1 replacement:3 because:1 some:1 play:1 deduce:4 proofs:1 everything:2 ucsc:1 summand:2 knew:1 equivalent:3 santa:1 would:2 o:2 fredholm:3 22n:1 integral:5 down:2 references:1 operator:7 substitutions:1 log:12 there:3 u1:17 u0:34 specifically:1 u2:2 inner:6 way:1 was:2 function:1 form:1 but:5 abused:1 pi:5 compute:6 ke:2 leclair:1 up:1 us:2 dms:1 ui:25 uj:13 problem:1 similar:1 constant:3 int:1 formulation:1 again:1 functions:3 when:9 setting:1 role:1 department:1 mathematics:1 expressible:1 variable:5 sides:1 4t:4 factors:1 time:2
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solv-int9808016.txt |@word secondly:1 since:3 partial:1 consider:9 remarkable:1 magnetic:2 leads:1 scalar:2 commute:2 computation:2 gn:13 seemed:1 particles:2 preserves:2 inverse:2 const:4 aug:1 subjected:1 equivalence:1 passage:1 tn:21 finally:1 tm:17 excluded:1 under:3 analogous:4 norm:1 case:16 conjecture:1 straightforward:2 very:1 wave:1 corollary:1 µp:2 discretizations:1 difference:6 matrices:2 condition:2 presented:2 integrating:1 list:1 solution:1 discrete:13 vector:4 inversions:2 zm:1 direct:1 second:3 further:3 theory:1 subscripts:1 aim:1 nonlinear:5 invertible:2 section:2 axes:4 analogously:2 expressed:1 above:7 fractional:1 new:6 rd:1 bn:2 contrast:1 satisfy:5 2ku:1 2kv:2 respectively:2 even:1 separation:1 others:1 directions:1 consideration:1 along:1 standard:1 equations:31 z1:3 change:1 obtained:8 parameters:1 institute:1 shift:9 study:3 allows:4 ourself:1 periodic:1 permutation:2 hexagon:1 makes:2 family:1 explained:1 brought:1 apply:1 total:1 unit:1 use:2 projector:2 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solv-int9808017.txt |@word consider:4 pointing:1 vasiliev:2 primed:6 ge:1 commute:4 grateful:1 consists:1 2r2:1 compact:1 whose:1 aug:1 lki:1 finally:3 present:3 th:1 under:4 include:1 worth:2 applied:1 belonging:1 straightforward:2 orthogonal:3 very:2 results:1 every:1 prof:1 exact:1 hamiltonian:9 solution:2 solved:1 cmw:11 noted:1 prevent:1 work:1 sukhatme:2 sin2:2 d6:11 integrability:5 further:5 odd:2 even:4 index:1 hansson:1 giving:1 expressed:3 3j:1 3i:2 above:1 new:5 net:1 avinash:1 3f:2 3d:8 body:18 outgoing:4 full:1 exchange:13 respectively:4 here:2 ulb:2 cos2:1 change:1 bhubaneswar:1 obtained:3 incoming:4 institute:1 study:1 p2:2 permutation:1 action:3 hospitality:1 y12:1 useful:1 projection:1 family:6 merely:1 replace:1 analyzing:1 apply:1 rψ:1 derivatives:6 dunkl:4 would:1 prove:3 remains:1 properties:1 few:1 nucl:1 noting:1 type:1 introducing:1 r5:1 rir:2 operators:17 x12:1 odinger:1 warm:1 particular:2 known:3 cases:4 marchioro:1 6d:3 equation:1 yjk:2 oscillator:6 modified:2 l123:3 itself:1 obvious:1 following:7 making:2 trans:1 example:1 proof:1 india:1 tan:2 motion:1 end:1 mutually:1 s3:4 s2:4 s1:4 get:1 recovers:1 write:1 far:1 enquire:1 pure:2 parameter:8 sin:19 r2j:4 algebra:2 may:8 oscillators:1 idi:1 k123:5 fd:1 natural:2 threebody:1 ss:1 yielding:1 sk:2 so:3 sn:1 operations:1 developed:1 years:2 through:3 still:1 its:2 before:1 group:10 la:1 interesting:4 erators:1 coordinates:16 brzezi:1 jacobi:1 mail:2 introduce:3 kki:2 they:1 rotation:4 now:7 discuss:2 easily:8 inversion:2 dj2:1 2r:2 2m:1 entirely:2 egusquiza:1 characterized:4 2k:1 differential:1 related:3 unprimed:2 literature:2 quantum:3 operation:1 eq:16 out:2 shown:5 matrix:5 space:2 furthermore:1 since:4 rev:1 denotes:1 particles:3 attracted:1 ref:6 ri:1 math:6 philosophy:1 panigrahi:1 free:2 cartesian:1 khare:5 hand:2 generate:1 r4:1 definition:1 derivation:1 r2:5 r3:1 counterpart:1 invitation:1 hence:11 xij:8 first:2 xj:7 xk:5 xi:15 symmetry:1 variables:2 another:3 xs:1 sutherland:2 angular:2 given:13 boulevard:1 checked:1 plaine:1 leading:1 eqs:6 relations:2 yij:12 their:3 way:2 relationship:3 exactly:3 proving:1 took:1 x2:2 x3:2 translation:1 x1:2 representing:1 wide:1 kind:1 showed:1 determined:2 projections:1 generalization:4 need:1 collapse:1 angle:3 latter:4 physique:2 lij:9 note:5 instance:1 potential:7 generalized:4 heisenberg:1 olshanetsky:1 shall:1 17c:1 eaire:1 letter:1 nothing:1 class:3 commutation:1 subspaces:3 ki:1 dimension:5 exp:4 physics:1 fact:3 iopb:1 show:12 ending:1 discovered:1 relation:5 keywords:1 brink:3 state:1 only:1 generators:1 libre:2 integrable:2 hamiltonians:2 his:1 dj:7 fnrs:1 di:10 de:4 famous:1 ones:1 words:1 during:1 du:1 dr:17 arxiv:1 she:1 satisfy:1 set:1 frame:1 j2:3 relative:2 see:5 result:1 terms:18 hilbert:1 inequalities:1 written:6 between:7 invariant:2 notice:1 recently:2 extend:1 attention:1 jk:1 solv:1 both:3 cos:11 last:1 cot:2 x2j:1 equal:1 point:1 simple:3 analyzed:1 boson:1 cq:2 marg:1 three:18 been:3 int:1 polychronakos:2 interest:1 expected:1 pi:11 abstract:1 define:1 direction:1 families:1 suppress:1 those:2 case:9 p3:3 p1:3 macfarlane:1 pacs:1 nski:1 will:1 while:5 irrespective:1 bhaduri:1 quesne:3 refs:2 ir:15 thus:4 tφ:1 ij:10 different:2 verified:1 author:1 belong:1 same:3 φl:3 extended:3 i1:2 i3:2 i2:2 effect:1 iop:1 kij:21 running:1 uses:1 purpose:1 brussels:1 recent:1 schr:1 k23:2 without:3 coordinate:1 model:8 calogero:8 left:1 obtain:2 transforms:1 momenta:5 scattering:4 renewed:1 regarded:1 except:1 iψ:2 add:1 valid:1 transformed:6 lett:7 easy:2 solvable:2 transformation:1 possible:1 eorique:1 belgium:1 using:8 mod:2 ljk:1 like:2 particle:3 follows:3 ai:3 steps:2 either:1 integrals:1 become:1 soft:1 mathematical:1 some:7 b2:3 ijk:2 provided:1 2xk:2 yki:2 centre:1 yields:1 eigenfunctions:1 rep:1 bl:1 equivalent:1 directeur:1 step:1 universit:2 takes:2 discussed:2 covariant:4 2j:4 act:1 introduced:1 perelomov:1 soc:1 into:1 integral:1 bound:1 bruxelles:2 references:1 determine:1 operator:16 k12:2 assumed:1 there:5 transform:1 start:1 lot:1 was:1 form:3 hr:8 but:6 ωx:2 2πk:2 us:5 below:1 problem:10 similar:3 called:1 ac:1 replacing:1 worthwhile:1 defined:7 ak:2 am:1 denote:1 conserved:1 corresponding:4 formalism:13 commuting:1 campus:1 again:2 functions:1 xki:2 ematique:1 when:3 detail:1 other:5 details:1 quantities:1 triomphe:1 polar:9 models:1 problems:15 2n:1 stay:1 generated:1 ago:1 independently:1 coulomb:1 dφ:8 values:4 mass:1 time:1 recherches:1 avoid:1
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solv-int9808018.txt |@word consider:6 mnr:1 global:1 trigonometric:14 eds:1 functionen:1 entropy:2 parameterization:2 gn:12 nested:1 mφ0:1 inverse:1 depend:1 aug:1 re:1 tr:2 finally:3 preserved:1 elliptic:24 under:6 magnetic:1 degeneration:1 case:31 conjecture:1 far:1 regional:1 geometrical:1 corollary:1 witten:5 contours:1 entries:2 affect:1 difference:1 matrices:3 din:2 riemann:4 hamiltonian:5 positions:1 notes:1 large:1 involution:7 small:1 eigenvalues:2 anal:1 equation:7 configurations:1 upper:2 work:1 periodicity:2 zk:3 seventies:1 direct:2 tex:1 imply:2 canonical:1 spectral:21 plays:1 rate:1 section:7 expressed:1 sheeted:2 ˆb:1 en:6 above:5 new:3 bn:1 ˆn:6 satisfy:1 degree:3 exchange:1 even:1 modular:2 ansatz:1 represented:1 equations:6 z1:1 change:4 remark:2 ℜp:2 shift:8 study:1 allows:1 glg:1 ekx:1 usually:1 hoker:10 fourier:4 changes:1 relation:1 kej:2 convolution:1 classification:1 namely:1 replace:2 decrease:1 oval:3 total:1 relating:2 use:2 eω:1 asymptotic:2 would:1 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solv-int9808019.txt |@word secondly:1 gt:15 partial:1 consider:15 results:4 gy:11 gx:5 four:21 scalar:6 proposition:2 generalize:2 subclass:4 gn:2 expressions:1 gl:3 assembled:1 compact:1 whose:2 certainly:1 calculate:1 aug:1 advantage:1 paris:1 tt:2 simplify:1 θtt:1 tn:2 γi:5 ie2:4 indicate:1 those:2 th:1 under:5 analogous:2 tc:6 norm:1 applied:3 ty:1 kφ:1 g1:5 g0:1 far:1 geometrical:5 invent:1 summarized:1 redefinition:1 deformations:1 condition:23 generalised:1 leads:1 presented:1 did:2 nucl:1 solution:12 twistors:1 convenience:1 vector:36 semidirect:1 strachan:4 mn:3 dealing:1 direct:3 integrability:6 htt:5 further:4 zw:3 canonical:2 will:23 what:1 nonlinear:2 appear:1 tetrad:1 brackets:1 giving:1 section:9 sigma:1 above:7 sup:1 abx:2 new:4 abz:1 acknowledgments:1 exercise:1 satisfy:5 edited:1 full:1 degree:1 lei:2 l1:6 component:1 b383:1 here:9 threads:1 ansatz:1 groups:1 directions:1 along:2 equations:50 appears:1 change:5 flaherty:1 obtained:4 chave:1 ctv:2 ultra:2 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solv-int9809001.txt |@word chain:14 results:3 commute:1 generalize:1 follow:1 research:1 contributions:2 row:1 whose:5 inverse:2 aug:1 b265:1 kα:3 γn:2 th:1 rαα:6 fan:1 entries:1 matrices:11 condition:1 presented:5 irreducible:1 sklyanin:1 michael:1 solution:4 t1:2 solved:2 convenience:2 vector:3 indices:2 eigenvalues:7 markov:1 qism:1 takhtajan:1 integrability:1 deutscher:1 writing:1 spectral:1 incompatible:1 section:7 sul:1 analogously:1 u33:1 u32:1 above:5 3l:2 new:1 method:5 satisfy:1 simultaneously:1 never:1 here:1 ansatz:12 berkeley:1 represented:1 equations:8 xη:1 obtained:6 remark:1 institute:1 study:2 vectors:8 allows:2 periodic:4 action:3 hospitality:1 makes:1 cancellation:1 useful:1 b215:1 family:1 jrl:1 a23:1 viz:1 apply:3 lima:1 b453:1 use:6 takes:1 working:2 prove:2 recalling:1 finally:2 angela:2 next:3 depicted:1 therefore:1 associated:1 type:2 bethe:20 postdoctoral:1 more:4 introducing:1 rk2:1 rk3:1 operators:2 berlin:3 known:2 hold:1 iii:1 account:1 rα:5 rβ:1 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solv-int9809002.txt |@word neighbors:4 partial:1 consider:5 chain:1 results:4 four:1 roy:1 commute:1 expressions:1 als:1 causes:1 whose:2 depend:2 aug:1 nonlocal:2 finally:1 under:3 include:2 p2:1 presently:1 straightforward:1 very:2 wave:1 every:1 govern:1 matrices:1 annihilated:2 solves:2 presented:4 positions:1 sklyanin:2 gun:3 large:1 solved:3 phase:3 eigenvalues:2 a123:1 direct:1 past:1 zero:5 substitute:2 will:4 sum:3 a231:1 suq:3 new:6 method:3 satisfy:1 respectively:2 proc:1 here:2 departamento:1 b385:1 equations:9 appears:1 shift:3 study:3 vectors:1 periodic:2 products:1 ξ2n:3 action:8 implement:1 via:3 projection:1 translational:2 apply:1 total:3 unit:1 use:1 would:2 ψr:1 suppl:1 angela:1 next:1 nucl:6 ξl2:1 call:1 therefore:2 type:3 bethe:12 more:1 separated:5 operators:1 particular:3 known:1 nepomechie:1 cases:2 iii:1 must:1 fan:1 account:1 recall:1 equation:9 work:1 vega:2 values:1 following:2 arrive:1 links:2 give:1 states:14 e2s:4 get:6 feature:1 b408:1 maps:1 nontrivial:1 hou:1 parameter:1 product:2 fs:1 mat:1 algebra:5 may:3 derived:1 different:1 plane:1 physik:1 representations:2 snz:1 caixa:1 sectors:2 computations:1 δi:1 element:1 so:1 sn:2 sl:6 pleasure:1 order:2 restriction:1 indeed:1 move:1 satisfied:1 produced:1 paper:1 including:1 statistical:1 satisfies:1 2sp:1 its:2 before:2 derive:1 group:11 thank:1 energies:1 interesting:5 fix:1 destri:1 gen:8 systems:1 kuniba:2 defining:1 non:1 combination:1 framework:1 mezincescu:1 ξin:1 they:2 cep:1 now:5 discuss:1 nor:1 eigenvalue:9 2p:6 name:1 temperley:12 2s:14 always:1 hamiltonian:5 toroidal:1 carlos:2 baxter:2 ei:1 weight:2 doing:1 energy:2 related:1 manifests:1 investigated:1 expect:1 quantum:16 ux2:1 ep:1 special:1 batchelor:3 shown:1 matrix:1 electronic:1 since:5 denotes:1 fellowship:1 acting:3 investigation:1 a132:1 math:8 involutive:1 linear:2 ısica:1 diagonal:1 possibility:1 solution:2 reason:1 e0:2 definition:2 hψ0:1 brasil:2 language:1 prester:1 consequence:1 yue:1 first:2 number:2 nested:1 exact:1 least:1 open:3 affords:1 interchange:2 given:4 salient:1 exists:1 similarly:1 introduction:1 relations:2 their:2 1b:1 potts:1 gives:2 free:2 b330:1 reflecting:1 x2:55 x3:3 x1:49 third:1 imply:1 were:3 providing:1 treated:1 stz:2 pasquier:1 spectrum:2 generalization:3 rittenberg:1 seek:3 any:2 built:1 depending:1 convenient:1 grosse:2 isolated:1 instance:1 generalized:1 alcaraz:1 heisenberg:1 play:1 multiple:1 impurities:2 algebraic:1 propagate:1 nothing:1 alez:2 karowski:3 measured:1 class:2 eigenfunctions:1 considered:1 neighboring:2 yang:1 principle:1 usual:2 fact:2 sector:10 12a:1 show:1 spaces:1 relation:1 substituting:3 ground:1 parameters:3 eigenspace:1 state:6 only:2 b462:1 integrable:1 hamiltonians:7 ruiz:2 do:2 notation:2 means:1 de:4 combinations:1 neither:1 quispel:1 densities:2 arxiv:1 acknowledgments:1 common:1 flanked:1 qn:2 set:3 computed:1 reference:2 operates:1 relative:1 see:1 discussions:1 terms:4 nonlocality:1 techniques:1 un2:1 satisfying:2 interacting:3 federal:1 sites:3 boundaries:5 written:1 closed:8 between:1 invariant:13 boundary:18 conditions:13 recently:1 hecke:1 extend:1 pseudoparticle:8 b419:1 solv:1 both:1 essentially:1 taking:1 equal:1 fiz:1 context:1 ansatz:10 mechanics:1 co:1 simple:1 dimensional:1 analyzed:1 2ns:1 respect:2 basis:3 simplification:1 due:1 been:1 a213:1 aijk:1 expected:1 algebras:2 b424:1 define:2 6a:1 supersymmetric:1 commutes:1 xxz:3 bulk:7 spin:18 present:1 case:3 u1n:1 pseudoparticles:14 single:1 ǫs:104 a21:4 thus:4 them:1 iv:1 ii:1 susy:1 santos:2 same:1 shifts:2 complex:1 roland:1 diagonalize:1 oberle:2 independent:1 used:2 infinity:1 singapore:1 zapletal:2 barber:1 purpose:1 invariance:4 eigenvectors:1 correspondent:1 reflection:1 nevertheless:1 solve:4 consistency:1 coordinate:6 position:2 model:3 arising:1 left:2 world:1 graded:1 being:2 obtain:1 using:5 momenta:1 scattering:1 eigenstates:5 parametrization:2 lattice:1 lett:2 diagonalization:1 role:1 solvable:1 eigenstate:2 momentum:1 take:2 eigenfunction:1 read:1 breaks:1 spanned:1 know:1 integer:4 postal:1 mod:2 lpthe:1 theor:1 particle:1 semi:2 manifest:1 collect:1 a321:1 steps:1 either:1 martin:3 become:1 right:2 methods:1 moreover:1 happens:1 provided:4 lima:2 eiθ:1 ξp:1 does:1 chains:9 δk:1 scientific:1 problems:1 wavefunctions:5 properties:1 extension:2 discussed:1 obeys:1 neighbor:1 introduced:1 projectors:3 lieb:12 soc:1 ξn:2 into:9 ξ1n:2 three:1 lies:1 references:1 operator:5 support:1 there:2 u1:4 u0:21 u2:2 start:1 cocommutativity:1 way:1 was:4 ψ2s:4 complete:2 form:1 restrictions:1 but:3 cnpq:1 highest:2 considerable:1 foerster:4 ux:2 uq:6 us:4 par:1 ul:1 un:26 uk:1 similar:1 strongly:1 associated:3 int:2 abstract:1 ao:2 general:1 conserved:1 together:1 a7:1 corresponding:3 universidade:1 gonz:2 physical:1 when:7 vanishes:2 application:1 other:2 compares:1 quantities:1 ns:3 conclusion:1 a12:4 models:6 vertex:2 important:1 ξl:8 additionally:1 ξa:6 ξb:6 impurity:3 correlated:1 l69:1 cherednik:2 having:1
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solv-int9809003.txt |@word consider:9 osp:28 global:1 results:10 invent:1 l11:2 scalar:4 lαβ:1 ga:20 intricate:1 expressions:2 gj:2 gi:2 compact:1 whose:5 inverse:7 depend:1 calculate:2 brzezinski:1 recurrence:1 finally:1 present:3 th:1 r12:7 r13:4 b184:1 very:3 b189:1 reader:1 wave:6 witten:1 entries:3 parameter:6 matrices:3 condition:3 dim:1 annihilated:1 presented:12 irreducible:1 sklyanin:3 solution:12 solved:3 vector:20 b286:1 eigenvalues:1 anal:1 superalgebras:1 lk1:1 zn:26 ρj:2 zi:4 zj:1 zk:1 takhtajan:1 za:54 zb:11 fold:1 second:5 b502:1 odd:6 theory:10 spectral:4 aαγ:1 diag:1 section:9 current:1 version:7 issues:1 new:1 method:14 satisfy:1 lkn:1 polyakov:1 degree:1 respectively:2 component:1 here:9 agreement:1 l21:2 l23:2 l22:2 κx:1 ansatz:29 represented:1 auxiliary:1 equations:22 z1:15 z2:1 obtained:5 remark:1 antisymmetric:2 lomi:1 study:1 vectors:7 allows:1 permutation:3 action:2 complicated:1 named:1 via:1 b229:1 apply:1 lima:2 semiclassical:23 planck:1 presents:1 use:2 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solv-int9809004.txt |@word homomorphism:1 systematic:2 consists:2 whose:4 aug:1 presents:1 up0:5 neue:1 summarized:2 dubrovin:11 induction:1 solution:9 convenience:1 vector:8 nullspace:1 direct:3 second:9 even:3 employ:2 sheeted:1 establishes:1 new:6 ˆj:11 simultaneously:3 never:1 here:6 pursuit:1 q13:2 q12:16 represented:1 path:2 logarithmic:1 obtained:4 suitably:1 study:1 sbornik:1 suitable:1 changes:1 appropriately:3 tu:1 projection:3 univ:2 unit:1 derivatives:6 would:2 e1:1 negative:1 vol:4 m1:7 therefore:1 type:19 gohberg:1 solitons:3 odinger:2 holo:1 berlin:3 hold:2 must:1 springer:4 permits:1 mo:2 mk:1 mj:4 concepts:1 root:1 example:2 indicated:1 mumford:2 boussinesq:38 provide:1 far:1 symposium:1 ordinary:4 preferable:1 description:1 replacing:1 oscillators:1 lax:8 summarize:1 meaningful:1 constants:11 gluing:1 third:8 summing:1 complexity:2 enter:1 first:10 order:32 restriction:1 over:3 london:3 satisfies:6 before:2 directional:2 hq0:1 fix:1 writing:1 them:2 gunning:1 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solv-int9809007.txt |@word eilbeck:1 set:1 consider:3 show:1 indeed:1 spectral:1 results:2 shape:3 paper:2 solutions:12 grateful:1 c2:1 japan:1 arctan:1 scattering:1 find:2 schmid:2 features:1 solitary:6 derive:3 maps:3 ln:2 interesting:1 philadelphia:1 lattice:3 only:1 ens:1 lett:3 easy:1 under:1 mail:1 travelling:3 transformation:15 real:1 applied:1 non:1 supported:1 above:1 straightforward:3 was:3 similar:2 heriot:1 acklund:7 wave:9 define:2 using:1 now:2 matrices:1 condition:2 2t:1 shaped:1 conditions:2 university:1 dijon:1 bright:1 chandre:1 discrete:9 differential:4 integrals:4 2c:2 become:1 universit:1 because:1 sep:1 some:3 cnrs:1 related:1 ωt:5 second:2 used:1 jupiter:1 result:1 kdv:2 homma:2 eq:2 takeno:5 out:1 closer:1 u3n:2 nonlinear:1 appear:1 dn:5 review:1 singular:1 rev:1 version:2 ladik:3 suggesting:1 boundary:2 approach:1 method:1 math:1 satisfy:1 sinh2:4 notice:1 theory:1 do:1 interactions:1 respectively:2 bn:5 bourgogne:2 spacing:1 here:1 solution:9 vanishing:1 inverse:1 bp:1 galilean:2 sinh:4 solv:1 consideration:1 equations:7 comparison:1 pairs:2 trans:1 carried:1 shift:1 could:1 studied:1 motion:4 calculations:1 watt:1 hospitality:1 first:2 soc:1 localised:1 see:3 cn:5 supply:1 simple:2 miura:6 into:3 transform:1 infinite:1 mkdv:5 ddimensional:1 operator:1 ct:1 given:4 much:1 transformations:6 introduction:1 transfer:1 there:1 visit:1 finally:1 been:1 france:1 sech2:3 their:1 difference:4 arxiv:1 therefore:4 way:2 siam:1 type:1 formation:2 gives:2 corresponding:2 complete:1 form:1 both:5 becomes:4 continuous:6 but:4 idea:1 neighbour:1 zero:1 link:2 integrable:1 known:4 x3:2 c1:1 than:1 those:1 dynamical:1 case:5 funds:1 applying:2 unfortunately:1 exponential:1 versions:4 recall:1 equation:16 mn:7 modified:1 besides:1 assume:1 un:27 limit:1 were:1 following:3 highlight:1 problem:2 more:1 obtain:2 nearest:1 associated:1 links:4 give:2 int:1 calculation:1 abstract:1 am:1 xiao:3 vn:31 conserved:1 proves:1 vn2:1 iφn:2 work:1 linked:2 solitons:1 yang:2 nh:1 completeness:1 integrability:2 no:1 1d:1 physique:1 same:3 bishop:2 instance:2 other:3 widely:1 quantities:1 department:1 mathematics:1 defines:4 parameter:1 φn:46 difficult:1 nonzero:2 fr:1 de:2 scripta:1 excitation:1 cubic:1 models:3 laboratoire:1 who:1 derived:1 φ2n:5 me:1 hand:1 a0:5 lax:5 waves:1 pair:3 acknowledgements:1 ablowitz:5 compatibility:1 recent:1 svn:2 scharf:2 nn:7 considered:1 sech:3 physica:1 segur:2 so:1 n0:5 n1:2 n2:2
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solv-int9809008.txt |@word represent:1 sci:1 heriot:1 remarkable:1 funct:1 equalities:3 results:2 nato:1 leads:1 scalar:2 proposition:7 grateful:2 constants:1 follow:1 gm:1 gk:1 issues:1 consider:8 whose:2 lkm:1 depend:4 paris:1 riemannian:1 equivalence:1 tr:4 editors:1 presents:1 list:1 must:1 petersburg:2 th:8 under:7 semenov:1 tr2:2 fay:1 g1:1 g0:2 2αn:3 pages:1 springer:2 geometrical:1 isomorphism:1 bihamiltonian:1 matrices:21 manyparticle:1 skii:3 dynamiques:1 riemann:4 dij:8 hamiltonian:9 bn:2 sklyanin:4 enol:4 solution:2 enon:10 magnet:3 solved:2 commute:1 shanskii:2 independence:1 anal:1 freidel:1 programme:3 upper:1 zn:1 work:1 houches:1 zk:1 oscillator:1 calculi:1 direct:3 valuable:1 fold:1 integrability:4 yangian:2 masson:1 involution:2 gn:3 iσ2:1 dynamics:1 zw:1 expressions:2 substitute:2 theory:2 spectral:8 what:1 nonlinear:2 const:1 euclidean:1 d2:1 section:4 celebrated:1 analogously:2 expressed:1 maillet:2 current:2 establishes:1 s12:3 new:5 method:2 satisfy:2 homology:1 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solv-int9809009.txt |@word partial:1 consider:7 pointing:1 funct:1 equalities:5 uw0:2 results:2 leads:2 eds:1 ge:1 commute:1 morosi:1 computation:3 edu:1 go:2 sci:1 expressions:2 research:2 gk:3 worked:1 gi:1 devoted:1 whose:1 21st:1 inverse:6 const:3 chinese:2 tma:1 paris:1 tu:3 nonlocal:3 γj:1 finally:4 δhk:3 th:2 ti:1 ev0:2 include:1 worth:2 case:12 belonging:2 izv:1 g1:2 g0:2 far:1 rise:2 conditions:3 focus:1 corollary:2 entries:2 discretizations:1 li:2 difference:6 exact:1 condition:1 tri:1 evk:6 solves:3 hamiltonian:7 did:1 notes:1 guo:1 solution:10 large:1 discrete:61 vector:15 gauthier:1 zhu:1 anal:1 ωij:3 ρk:6 application:1 grateful:1 direct:3 matrices:2 zero:33 pour:1 chen:1 further:4 mj:2 spectral:22 established:3 what:4 nonlinear:7 sub:7 invertible:1 saved:1 section:9 zhang:3 hereditary:6 experiment:1 fuchssteiner:9 above:6 scientists:1 international:1 method:7 satisfy:3 hasn:2 focuses:1 lee:1 degree:13 respectively:4 equals:1 here:5 papageorgiou:2 reported:1 china:1 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solv-int9809011.txt |@word consider:1 trigonometric:2 four:1 proposition:9 synthetic:2 whose:1 preserves:2 equivalence:1 passage:1 tn:15 manifolds:1 th:6 dressing:2 analogous:3 must:1 presentation:1 far:1 dokl:1 results:2 corollary:3 difference:1 generalised:23 dim:1 exits:1 level:5 bn:2 involution:2 vector:5 noted:4 takhtajan:1 direct:1 generalisations:1 zero:3 equal:1 canonical:2 bilinear:1 established:3 xψ:1 sub:4 brackets:24 sum:3 bc:1 find:1 above:2 new:1 d1:2 acknowledgments:1 compact:1 degree:7 here:8 groups:4 equations:33 deduced:1 obtained:2 identifiable:1 study:2 studied:8 poisson:23 action:25 ˇj:1 ˇi:2 quotient:15 uniquely:1 projection:1 family:2 3e0:1 2δx:2 linearly:1 presents:1 next:1 comparing:1 linear:1 m2:2 type:4 more:1 αvi:2 ecole:1 becomes:1 operators:13 appendix:1 hold:1 r1:1 springer:1 isomorphism:22 defines:2 feigin:2 equation:4 work:2 det:1 modified:2 theories:1 values:1 following:27 example:1 deg:7 f1:3 gallot:1 give:2 sokolov:4 cartan:2 sense:1 verlag:1 goal:1 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solv-int9809012.txt |@word emile:2 homomorphism:2 consider:6 corps:4 similarity:1 alg:3 results:4 leads:2 eds:1 scalar:1 proposition:24 computation:6 follow:1 expressions:2 compact:11 whose:1 depend:3 skii:2 equivalence:2 containing:2 γj:1 γi:3 γh:43 preserved:1 elliptic:32 under:6 hermann:1 spinning:1 tc:5 p2:31 fay:1 g3:8 g2:8 straightforward:2 very:1 dλ1:5 springer:3 induce:1 geometrical:1 valued:1 commute:1 manifolds:2 ramified:5 zeitschrift:1 difference:1 exact:2 iut:3 condition:2 identity:6 four:11 dubrovin:4 riemann:4 level:15 turns:2 notes:1 enol:2 solution:12 d2:4 involution:26 convenience:1 vector:25 small:3 div:3 noted:1 context:1 unexpected:1 neighborhood:5 grateful:1 jacobians:1 estimates:3 direct:1 zero:10 a41:1 arnold:1 rigorous:1 further:9 dynamics:1 4x2:1 4x1:2 canonical:1 even:2 what:1 nonlinear:5 g23:2 diag:1 section:12 λdλ:7 brief:2 expressed:4 uniform:1 henceforth:1 version:1 poles:10 sur:4 above:15 new:3 construction:1 principal:1 acknowledgments:1 contrast:1 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solv-int9809013.txt |@word represent:1 partial:1 consider:1 illustrates:2 rx:1 desirable:1 four:10 scalar:3 generalize:1 customary:1 ruijsenaars:1 cases:1 certainly:1 depend:5 equivalence:7 tr:7 nonlocal:8 neighbours:1 preserved:2 elliptic:1 under:2 include:1 worth:1 straightforward:1 very:2 bilinear:1 emphasizes:1 choice:10 putting:1 entries:5 emphasized:1 difference:11 matrices:10 condition:6 leads:4 obvious:1 hamiltonian:3 turns:1 solution:2 fewer:1 deals:1 discrete:7 vector:5 small:1 relation:3 noted:1 dealing:1 consistent:3 direct:1 translating:1 zero:6 further:2 choices:2 theory:2 residue:2 what:3 nonlinear:6 invertible:2 euclidean:1 section:8 expressed:1 version:8 poles:7 above:2 lifshitz:1 new:2 unrestricted:1 subtracting:1 contrast:1 coefficient:2 condensed:1 degree:3 spacing:2 equals:2 here:5 met:1 them:1 free:1 making:1 directions:1 along:1 sine:5 equations:24 interpret:2 obtained:2 cλ:1 remark:1 remarks:2 involved:1 larger:1 allows:1 reason:1 eiη:1 resulting:2 poisson:2 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solv-int9809014.txt |@word consider:1 pointing:1 results:1 leads:2 gf:1 expressions:2 γx:1 paris:2 concerned:1 present:2 analogous:1 worth:1 threepoint:1 stud:2 straightforward:3 far:2 putting:3 difference:1 condition:1 immediately:1 presented:1 list:2 solution:1 discrete:11 relation:1 anal:1 upr:1 findings:1 zf:1 painlev:9 zx:2 zz:3 canonical:2 bilinear:6 established:1 what:1 nonlinear:6 appear:1 version:2 above:3 new:5 net:1 method:4 full:1 led:1 adressed:1 here:4 ǫxx:1 reported:1 inverse:1 ansatz:2 separation:2 ratio:1 standard:2 z0:1 logarithmic:2 obtained:6 remark:1 shift:1 study:1 studied:3 suggests:2 products:1 settled:1 involves:1 named:1 9a:1 vii:1 brought:1 apply:1 ψz:1 derivatives:2 use:2 proceed:1 nijhoff:1 france:2 call:1 therefore:1 australian:1 type:1 more:1 introducing:2 duality:1 ecole:1 becomes:1 constructs:1 particular:5 known:6 must:1 ramani:12 equation:35 work:1 modified:6 2yz:1 starts:1 following:2 example:2 calculation:1 indicates:1 council:1 occur:1 rather:1 how:2 pure:1 ordinary:1 parameter:2 description:1 singular:1 after:1 mapping:1 lax:1 fg:16 ζx:1 summarize:1 types:1 clarkson:2 explicit:1 correspond:1 so:1 definitions:1 order:2 indeed:2 major:1 through:4 argued:1 satisfies:1 its:2 perfect:1 derive:1 interesting:3 actually:1 forms:1 systems:1 miura:24 correspondence:1 them:2 good:1 auto:6 acklund:7 introduce:5 yy:5 they:4 half:2 singularity:7 now:2 easily:2 university:1 identified:2 2z:1 applied:1 universit:1 reproducing:1 homogeneous:2 domain:1 differential:1 series:1 related:2 obtains:1 entering:1 combining:1 our:9 eq:1 special:1 out:1 shown:3 jimbo:1 since:3 rev:1 research:2 contained:1 rational:1 suggesting:1 math:10 quite:1 york:1 put:1 pairs:1 derivation:4 determining:1 βx:1 first:3 intuition:1 already:1 relate:1 variables:1 number:2 will:4 xx:8 another:4 precisely:1 illustrate:1 xxxiv:1 given:5 publication:1 similarly:1 introduction:1 system:1 construct:4 interrelationships:1 calculations:2 aλ2:1 perfectly:1 exponents:1 recovered:1 shifted:1 asymmetric:1 continuous:2 zλ:1 x2:1 than:1 coefficients:1 18b:1 kind:1 18a:1 piii:1 namely:1 final:1 determined:1 retracing:1 usefulness:1 etage:1 generality:1 rewrite:2 kajiwara:2 need:1 cumbersome:1 their:3 jour:3 self:2 note:1 instance:1 analogy:1 schlesinger:7 play:1 towards:1 shall:2 riccati:1 simplify:1 involving:1 letter:4 observation:1 physica:2 ohta:2 hietarinta:2 fact:3 dover:1 probl:1 supported:1 cpt:1 joshi:1 solutions:3 find:5 based:6 parameters:2 only:5 explicitly:1 integrate:3 do:1 means:1 famous:1 ones:1 nearly:1 reveal:1 arxiv:1 activity:1 constructing:1 sep:1 trick:1 see:3 result:3 pvi:1 terms:5 subject:1 practice:1 satisfying:1 pattern:1 yet:2 enough:1 future:1 various:2 between:2 approach:8 αn:1 recently:2 ww:2 comm:2 solv:1 both:2 many:1 tour:1 expression:3 point:4 simple:1 corresponds:1 sakai:1 interrelations:1 moreover:1 transformations:20 second:1 equations:14 due:2 been:5 int:1 change:1 interest:1 inv:1 corresponding:2 25b:2 25a:1 systematic:4 those:1 case:4 appearance:1 aim:1 dept:1 monodromy:1 procedure:2 computed:1 thus:4 hicks:1 examined:1 dual:1 different:3 az:14 suggest:1 same:2 shifts:1 palaiseau:1 ince:1 resulting:2 several:1 used:2 satsuma:4 ablowitz:2 acknowledgement:1 changes:1 well:4 patterns:3 gambier:1 latter:1 proposed:1 being:1 λz:1 λx:1 grammaticos:12 obtain:8 homogeneity:1 λc:1 λa:4 integer:2 λn:1 previous:3 regarded:1 alternate:1 lett:4 5e:1 transformation:10 australia:1 using:6 appearing:1 systematically:1 follows:2 yields:1 polytechnique:1 works:3 because:3 often:1 deal:1 sequence:1 some:1 cnrs:1 examples:1 kdv:2 provided:1 eliminate:4 expressing:1 αxx:1 chains:1 obey:1 sixth:1 equivalent:1 step:1 relating:2 intense:1 p34:2 actual:1 most:2 a2:3 discretization:1 previously:2 into:1 integral:1 three:1 down:2 lies:1 references:1 next:2 ηx:1 hinted:1 there:2 question:1 long:1 start:5 appl:3 milne:1 way:3 was:7 form:6 but:1 construction:7 elimination:4 partially:1 made:1 compute:1 whether:1 up:3 us:2 below:1 problem:1 expect:1 pii:10 associated:1 defined:1 abstract:1 exist:1 postulating:1 relates:1 formalism:3 proceeds:1 adelaide:2 again:2 functions:13 when:1 detail:1 rewriting:1 other:1 role:1 fokas:4 mathematics:1 zhou:1 important:1 variable:1 needed:2 structure:3 auxiliary:1 4y:2 values:1 orbit:1 original:2 equivalently:1 remarked:1 starting:1 having:1 once:2
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solv-int9810001.txt |@word proposition:4 emile:1 homomorphism:6 consider:11 corps:1 funct:1 induces:2 enseignement:1 global:2 results:2 skii:1 hurtubise:3 commute:2 computation:2 parameterization:1 gl:1 compact:4 const:2 tx:1 paris:1 iii:1 equivalence:1 finally:1 does:1 manifolds:1 elliptic:5 under:2 semenov:4 td:1 aut:1 linearizes:1 p2:3 fay:1 neue:1 mpj:27 conditions:1 induce:1 choice:2 corollary:3 p1:3 every:2 formula:1 difference:1 matrices:5 condition:2 entire:1 riemann:12 hamiltonian:19 did:1 turns:2 notes:1 enol:1 z10:3 involution:1 vector:24 progress:1 fourier:1 eigenvalues:2 reyman:3 der:3 zn:7 neighborhood:2 jacobians:11 wirtinger:1 direct:1 b20:1 zero:5 further:3 fibres:2 eigenspaces:1 canonical:4 spectral:37 what:1 nonlinear:2 gβγ:1 invertible:7 gβα:1 d2:5 section:11 resume:2 xχ:1 expressed:2 find:1 symes:1 poles:1 above:10 new:1 gl2:1 d1:5 consisting:1 stabilizer:1 body:4 degree:16 respectively:4 never:1 here:1 tangent:5 ez2:3 groups:4 tz:1 baxter:1 equations:7 z1:10 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solv-int9810002.txt |@word consider:3 chain:11 similarity:3 alg:1 lack:3 results:2 commute:6 follow:1 expressions:2 gl:2 contributions:1 gi:3 row:3 whose:2 calculate:1 irrelevant:1 simple:2 finally:2 th:4 under:1 tr0:7 r12:6 straightforward:2 choice:1 every:1 matrices:12 condition:1 presented:1 sklyanin:1 solution:1 t1:2 large:2 convenience:1 indices:1 eigenvalues:2 superalgebras:1 noted:1 degeneracy:2 sin2:5 direct:2 integrability:7 concludes:1 addition:1 even:1 index:1 sub:1 invertible:1 factorizing:1 section:4 above:6 new:2 increasing:1 method:3 satisfy:2 here:5 bi:3 ansatz:3 groups:1 address:2 along:2 hl0:2 equations:6 obtained:2 studied:4 allows:1 periodic:2 permutation:1 usually:2 changes:1 br:2 yitp:1 apply:1 bra:1 use:2 would:1 prove:7 positive:1 next:1 comparing:1 m1:6 taken:2 type:2 bethe:3 more:1 introducing:1 vieux:2 operators:8 br2:2 particular:1 known:1 hold:1 recall:1 equation:1 work:3 modified:4 hopf:1 remain:1 values:2 following:2 cond:3 root:1 proof:6 links:2 give:1 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solv-int9810003.txt |@word represent:1 partial:6 consider:4 chain:8 nauchn:1 results:2 eds:1 scalar:4 contradict:1 follow:1 seemed:1 compact:1 whose:1 inverse:2 const:1 remarkable:1 bivector:1 bx1:1 assigning:1 bx2:1 manifolds:1 th:4 ti:1 include:2 friendly:1 ingredient:1 p2:1 r12:1 orthogonal:1 very:2 implicitly:2 quadruplet:3 trigonometric:2 got:1 difference:14 matrices:5 condition:4 groups:2 school:1 obvious:1 solves:2 did:1 chains:1 notes:1 sklyanin:1 itep:2 t3:3 t1:3 magnet:1 discrete:60 a120:1 vector:2 indices:1 gauge:1 noted:1 upper:1 zero:3 pass:1 further:1 theory:3 bilinear:22 what:4 nonlinear:4 stands:1 section:4 expressed:2 current:1 version:1 above:3 kyoto:1 new:2 method:4 3d:2 simultaneously:1 exchange:1 respectively:7 spacing:2 here:8 understanding:1 ihes:1 κz:2 directions:3 along:2 sine:7 equations:50 z1:4 change:3 z3:4 obtained:4 remark:2 weinstein:1 clarify:1 institute:1 shift:3 vectors:3 periodic:1 complicated:1 makes:1 via:3 besides:2 extra:1 pinkall:1 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solv-int9810005.txt |@word consider:2 results:1 existing:2 eds:1 consists:1 localized:4 inverse:1 pˆn:1 quasi:1 those:1 th:1 under:1 advantage:1 lri:1 wave:1 rotating:1 vibrational:1 hamiltonian:2 solution:2 biological:1 tognetti:1 equation:8 zh:1 sin2:1 cosh:8 approximation:5 further:1 tev:1 aim:2 nonlinear:2 trapping:1 giving:1 waals:1 new:1 solitonic:1 acknowledgments:1 ˆn:2 pioneering:1 full:1 nonlinearly:2 eksp:1 here:1 ρy:1 2ka:2 sinh:6 path:1 equations:2 institute:1 studied:1 resulting:1 usually:1 vib:2 plenum:1 vis:1 sgn:2 use:1 ψy:1 would:1 intensively:1 neighbours:3 memory:1 taken:1 type:3 more:1 introducing:1 becomes:2 transient:1 jmn:4 der:1 work:1 modified:1 vibronic:2 believed:1 nearest:5 neglected:1 axis:1 decaying:1 discussion:1 very:1 sin:11 express:1 attend:1 φ2n:2 acknowledged:1 so:1 sn:4 βk:2 over:1 course:1 paper:3 scott:1 committee:1 japan:1 excitations:2 its:1 thank:1 fiz:1 acoustical:3 systems:2 mail:1 investigated:1 scaling:1 now:1 term:1 2r:5 presented:1 davydov:3 ifa:1 2m:1 eighties:1 differential:1 energy:2 frequency:1 quantum:3 our:2 special:1 vibron:2 restricted:1 since:1 rev:2 looking:1 emerged:1 rc:1 ro:1 math:1 standard:1 reason:1 complicated:2 york:1 put:1 interaction:7 exponentially:1 corrections:1 first:1 romania:1 variables:1 approximate:2 done:2 given:1 ablowitz:1 system:5 relations:3 their:2 dt2:1 siam:1 molecular:1 academy:1 segur:1 authors:3 eliminated:1 variational:1 kindly:1 vibrons:2 spectrum:1 qˆ2:1 elsewhere:1 self:2 storage:1 generalized:1 kac:5 philadelphia:1 shall:1 kan:1 kas:2 qˆm:1 qˆn:1 soliton:3 ka:13 kj:1 principle:1 velocity:2 vries:1 notations:1 solutions:1 d2:2 find:1 φtt:1 aφ:1 romanian:1 only:2 going:1 integrate:1 oct:1 get:3 de:1 during:1 dt:2 following:2 continuum:4 arxiv:1 investigate:1 qm:1 qn:13 satisfy:1 reference:2 namely:2 discussions:1 takeno:6 subject:1 interacting:1 phonons:3 nuclear:1 state:3 µk:1 between:4 αk:6 horia:1 terms:1 nature:1 solv:1 2αk:1 cos:16 last:2 tractable:1 many:1 contract:1 called:1 connection:3 whole:1 cn:4 simple:1 harmonic:2 dimensional:1 mkdv:1 conference:2 described:2 helfand:1 due:1 workshop:2 interest:2 nato:1 quantities:2 neighbour:2 coherent:2 present:1 case:1 will:1 christiansen:1 revisited:1 procedure:1 coupled:1 vk:6 vn:3 middle:1 hulubei:1 conf:1 protein:1 containing:1 φt:2 φx:3 parts:1 φm:4 φn:10 used:2 effect:1 moving:2 robust:1 opportunity:1 modes:1 solidi:1 expression:2 well:1 valerio:1 model:4 λv:1 when:1 obtain:1 scattering:1 yet:1 transformed:2 easy:1 real:1 possible:1 dφn:1 press:1 helpful:1 like:1 korteweg:1 integrals:1 become:1 works:1 reduced:2 bucharest:1 classical:2 b4:1 organizing:1 transport:1 describing:1 pev:1 langevin:1 does:1 prog:1 prof:2 proc:1 2µk:1 obey:1 step:1 although:1 found:1 working:1 dependence:1 range:5 introduced:1 mathematical:1 soc:1 φxx:1 into:1 bath:2 references:1 determine:1 van:1 transform:2 long:5 systems1:1 rcn:1 way:2 forward:1 was:5 function:1 complete:1 form:5 2vn:1 but:1 krumhansl:3 ωt:1 un:2 limit:3 anca:1 continuously:1 problem:2 similar:1 laplace:1 ac:2 int:4 covers:1 separating:1 engineering:1 simplest:1 na:1 generally:1 field:1 other:1 role:1 details:1 solitons:2 nr:1 theor:2 stat:1 a2:1 variable:1 physics:1 baker:3 together:2 phonon:2 time:2 dipoledipole:1 sarker:3
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solv-int9810006.txt |@word sci:1 consider:6 trigonometric:1 leads:8 roy:1 spiridonov:1 grateful:1 kowalewski:1 expressions:2 differentialgleichungen:1 devoted:1 depend:2 technique:3 petersburg:2 elliptic:5 under:2 kλ:2 ences:1 analogous:4 p2:13 supported:2 g2:1 g1:20 very:1 b188:1 wave:4 novel:1 redefinition:1 condition:4 dim:11 hamiltonian:3 list:2 solution:13 solved:2 math:4 manifestly:1 10k:1 2k1:3 b202:1 8k:2 arccos:1 cosh:28 integrability:3 substituting:1 dedonder:1 dynamics:1 4x2:1 nonlinear:1 g22:1 appear:1 g21:3 diag:3 sum:1 analogously:1 expressed:6 3m:2 3l:1 3c:1 3b:2 3a:2 3g:2 3f:1 coefficient:1 respectively:2 here:1 behaviour:2 objects:1 separation:6 represented:2 const:1 equations:6 obtained:8 remark:2 shift:1 study:2 reports:1 sofar:1 poisson:1 action:1 hospitality:1 options:1 useful:6 apr:1 natural:1 replace:1 decrease:1 apply:1 unit:1 derivatives:6 use:1 x42:3 x41:9 prove:1 positive:1 give:1 next:1 few:1 nucl:2 m1:8 therefore:2 m3:2 m2:9 taken:2 type:1 dnx:2 more:2 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solv-int9810007.txt |@word consiste:27 veut:6 rˆ:6 travaux:4 limites:16 limiter:1 tenseurs:1 equent:1 paris:2 theorique:2 lors:8 parit:2 processus:2 fronti:2 aux:171 eories:24 marche:1 conjecture:4 voie:2 ecessaires:1 p1:10 tandis:15 voit:43 voir:31 quantit:21 supports:1 affirm:1 associe:4 solution:14 correct:1 red:8 venons:2 indices:12 markov:1 andrews:1 force:1 enti:14 consistent:1 directement:17 chez:1 direct:2 horn:1 second:32 slr:13 appartienne:1 elliptiques:3 sll:7 remplacer:4 notera:1 maillet:1 inversibles:1 familles:1 propri:18 propre:19 ner:1 coefficient:1 notions:1 sugg:12 aij:4 neveu:5 here:1 d2:5 met:7 china:1 mes:3 mer:8 cult:1 explicites:6 expliciter:1 identiquement:1 naturel:12 efinis:4 study:1 diagrammes:19 sjj:2 sjk:2 sji:2 fourier:9 ecrite:2 nulle:22 reste:18 appeler:1 szenes:1 projection:1 classification:1 explained:1 julia:1 a23:1 bri:7 b342:1 noyau:5 etries:18 total:5 unit:14 electrique:10 tels:12 leurs:14 exacte:4 ηlr:1 exposant:2 centr:2 erentiels:2 assez:6 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solv-int9810009.txt |@word represent:1 consider:2 chain:8 illustrates:1 global:1 expressions:2 research:1 ihep:1 dηα:4 depend:1 calculate:1 longstanding:1 superspace:3 b389:1 tr:1 tp:6 finally:1 alvarez:1 present:7 th:10 under:3 discovering:1 applied:1 belonging:1 abelian:1 very:4 account:1 choice:1 every:2 manin:1 condition:1 riemann:1 issue:1 sdet:5 solution:14 discrete:8 inspection:1 concluded:1 unexpected:1 consistent:2 direct:1 α2n:2 sign:2 α2p:12 second:1 subtle:1 further:1 tαk:4 odd:3 linear:1 even:1 established:1 what:1 nonlinear:4 section:4 expressed:5 consistently:1 suspect:1 above:2 values:4 acknowledgments:1 contrast:1 led:1 relates:1 respectively:2 component:1 here:5 understanding:1 xλ:1 illustration:2 represented:2 consideration:1 quite:1 equations:22 appears:1 change:1 obtained:2 remark:1 shift:1 elaborate:1 studied:1 reason:2 suggests:1 resulting:3 changes:1 involves:1 via:6 useful:1 addresses:1 d87:1 addressed:1 case3:1 linearly:1 virasoro:1 derivatives:1 reflected:1 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solv-int9810010.txt |@word casimirs:1 partial:2 consider:2 maximum:1 alg:1 global:1 results:8 four:4 6x:2 ptx:1 types:1 follow:1 expressions:1 devoted:2 whose:1 inverse:1 depend:2 rodrguez:6 quasi:2 does:1 present:6 elliptic:6 under:4 include:1 worth:1 applied:2 belonging:1 r12:1 orthogonal:2 very:2 p0:3 formula:1 matrices:6 partially:1 hamiltonian:42 did:3 list:1 solution:12 solved:4 vector:1 indices:1 provided:1 nine:1 shows:1 still:1 application:1 y0:13 specially:1 concise:1 miller:1 sin2:19 direct:1 b21:2 cosh:21 integrability:2 further:1 4x1:1 even:1 aim:1 3x:2 plays:2 appear:4 morse:5 diag:2 section:8 celebrated:1 mechanics:1 expressed:1 suspect:1 above:1 new:11 t2:6 method:6 satisfy:4 compact:21 gµ:1 respectively:1 modify:1 here:6 understanding:1 cos2:29 separation:6 xν:1 consideration:1 along:1 extrema:2 equations:12 change:4 differential:4 obtained:9 remark:2 weinstein:2 assures:2 involved:1 study:10 studied:5 allows:5 completely:1 approaches:1 p2:2 periodic:6 zassenhaus:1 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solv-int9810011.txt |@word partial:1 consider:3 results:5 existing:1 leads:1 expressions:3 row:1 referring:1 tr:12 editors:1 passage:1 finally:1 tj:2 preserved:2 under:1 analogous:1 3ai:1 advantage:2 very:1 geometrical:3 matrices:7 condition:9 four:2 hamiltonian:11 turns:1 large:1 vector:2 indices:5 eigenvalues:4 shows:1 der:1 employing:1 dealing:1 sign:1 generalisations:1 second:4 deutscher:1 perspective:1 2aα:3 further:2 canonical:3 index:1 stands:1 diag:1 section:1 consistently:1 above:4 new:2 method:4 3e:1 satisfy:2 simultaneously:1 degree:2 here:2 understanding:1 herlt:1 objects:3 address:3 along:1 quite:1 equations:7 interpret:1 box:1 vectors:2 accomplished:2 periodic:2 resulting:2 poisson:1 usually:1 complicated:1 spacetime:6 involves:1 via:1 namely:1 reparametrized:1 replace:1 lanczos:1 apply:3 diagonalising:1 linearly:1 9v:1 derivatives:2 use:1 covariant:3 positive:1 next:1 veb:1 type:7 theoretical:1 more:4 flat:2 becomes:2 berlin:1 interaction:1 particular:3 known:7 hold:4 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