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solv-int9608001.txt |@word represent:4 consider:1 similarity:1 rev:1 results:1 consists:1 gn:37 inverse:1 const:1 aug:1 bqn:1 finally:1 preserved:2 under:2 include:1 dramatically:1 divergent:2 case:3 very:3 account:1 wave:4 putting:1 affect:1 condition:2 school:2 presented:2 solution:15 discrete:5 wronskian:1 cosh:8 zero:2 dynamics:8 even:1 index:1 nonlinear:1 appear:2 section:4 henceforth:1 1fn:1 goes:3 new:2 method:2 avery:1 nimmo:1 conte:1 here:1 behaviour:1 sinh:11 nonsingular:8 directions:4 consideration:1 equations:3 box:1 institute:1 shift:4 study:1 studied:1 hospitality:1 plenum:1 brn:1 use:2 proceed:1 would:2 positive:1 century:1 suppl:2 choosen:1 m1:3 m0:2 m2:2 volterra:6 type:5 more:1 introducing:1 becomes:3 berlin:1 4ac:5 known:1 must:1 me:1 mg:1 thanks:1 integrating:1 science:1 equation:2 work:1 iα0:8 following:3 making:2 expanding:1 organized:1 purposes:1 collision:4 indicates:1 allowed:1 tan:4 occur:1 verlag:1 decaying:1 means:2 nontrivial:1 pure:1 significance:1 those:1 algebra:1 may:1 ζj:2 after:2 variant:2 lump:2 applications:1 shadwick:1 waves:3 summarize:1 fn:39 clarkson:1 so:10 order:4 developed:1 mainly:1 stability:1 paper:2 existence:2 its:2 solitary:3 derive:1 ll:15 systems:6 mail:1 main:1 pjl:1 them:3 pjk:1 collide:1 scaling:1 framework:1 they:1 multidimensional:1 now:2 developments:1 expresion:1 represents:3 february:1 ifa:1 2c:4 done:1 2i:2 arbitrariness:1 series:1 used:1 our:1 special:1 shown:2 network:1 factors:1 u2n:1 crucial:1 re:2 rational:24 rn:8 ro:1 math:5 theory:1 interactions:1 succesfully:1 little:1 clarify:1 completely:1 complicated:1 york:2 put:1 interaction:1 could:1 generalizations:1 indebted:1 romania:1 ono:2 number:1 philadelphia:1 simplified:1 given:6 introduction:2 interact:1 system:13 construct:2 their:5 constants:6 siam:1 progr:3 cope:1 exactly:2 segur:1 focusing:1 probably:1 july:1 sign:1 than:1 unfortunately:1 showed:2 painleve:1 limiting:1 manner:2 conjugate:2 recover:3 any:3 viewed:1 relatively:1 depending:1 lumps:1 self:1 k2:8 k1:8 take:2 finding:3 bilinear:6 continuous:3 elastically:2 opposite:3 plugging:1 multisoliton:2 significant:1 phase:7 class:3 soliton:16 don:2 rogers:1 kj:9 clear:1 later:1 exp:24 hietarinta:1 physics:1 drastically:1 labels:1 anyway:1 notations:1 iǫ:1 gauge:4 solutions:33 participate:1 find:6 only:2 factor:1 integrable:3 moser:1 dn:6 do:2 mckean:1 his:2 get:2 express:1 cannot:1 progress:1 during:1 dt:8 gen:1 evolution:1 continuum:2 arxiv:1 expansions:2 fixed:2 qn:8 constructing:1 exists:1 see:4 japan:1 discussions:1 phases:1 ladik:3 invariant:1 boundary:4 conditions:3 terms:9 comm:1 solv:1 both:5 many:2 taking:7 propagation:2 simple:1 dimensional:7 mkdv:2 cancel:4 respect:2 transformations:5 three:1 been:3 reduction:1 much:1 pj:12 choose:1 θj:1 obtained:1 direction:3 aknowledgements:1 2ǫj:2 p2:2 p1:8 unlike:1 ǫj:4 will:6 situation:2 property:1 procedure:5 vn2:1 kindness:1 changed:1 ve:4 coupled:2 sincere:1 thus:3 vn:9 dual:1 author:1 make:1 freeman:1 same:5 complex:10 cargese:1 φj:1 physical:1 development:1 investigated:2 infinity:3 again:1 hand:1 changing:1 ablowitz:12 expand:2 relies:1 mech:1 keeping:2 well:1 academic:1 firstly:2 posses:1 summer:2 proposed:3 less:2 being:3 obtain:4 valuable:1 atomic:1 scattering:1 adv:1 cut:1 bullough:1 conclusions:2 character:2 setting:1 lett:1 transformation:2 generalized:6 real:15 phenomenology:1 possible:1 know:2 press:1 using:6 like:1 follows:1 velocities:1 specific:1 steps:1 arbitrary:3 works:1 depend:2 bucharest:1 classical:1 some:1 springer:1 choosing:2 kdv:1 nonzero:4 dimensions:1 does:4 prof:3 propagating:3 power:2 step:1 although:1 properties:4 ηj0:2 about:1 discussed:4 o:21 nonvanishing:1 konopelchenko:1 soc:1 into:2 ηj:1 pair:1 appropriate:1 references:1 proportional:1 ψj:2 log:8 there:1 transform:1 long:3 why:1 accordingly:1 appl:2 way:1 ed:1 was:4 function:1 head:4 form:10 but:4 hu:1 construction:1 made:1 consist:1 up:5 un:13 limit:4 backlund:2 strongly:1 constant:1 b2:4 int:1 abstract:1 am:1 engineering:1 exist:1 formalism:5 constructed:1 satsuma:8 no:6 when:1 other:3 solitons:6 mathematics:1 theor:3 a12:6 hirota:6 wadati:4 structure:2 assume:1 4c:1 time:1 starting:1 having:2
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solv-int9608002.txt |@word partial:3 consider:7 coda:1 comparatively:1 results:6 leads:1 row:3 replacements:2 aug:1 alamos:1 funct:1 recurrence:1 charge:3 up2:1 up3:1 up1:1 straightforward:1 very:1 implicitly:1 removing:1 geometrical:1 every:1 entries:1 matrices:2 generalised:1 school:1 dubrovin:2 presented:2 t2:1 solution:4 large:1 solved:1 math:1 generalises:1 mulvey:2 anal:1 round:1 abstracted:1 direct:1 generalisations:1 second:1 further:5 dynamics:1 theory:1 established:2 nonlinear:4 brackets:1 sum:1 u34:1 u33:1 u32:1 u31:1 ˆj:2 method:2 satisfy:3 led:2 degree:3 respectively:1 here:2 inverse:2 equations:36 implicit:1 change:1 deduced:1 obtained:2 weinstein:1 involved:2 study:1 studied:2 accomplished:1 resulting:1 poisson:1 useful:1 elaborated:1 why:1 durham:2 unit:1 use:1 prove:1 positive:3 quasi:1 few:1 taken:1 3le:1 themselves:1 type:7 more:2 fractions:1 integers:2 becomes:1 particular:1 cases:1 equation:11 det:12 ms:1 following:7 drops:1 singularities:1 example:10 def:1 proof:2 give:2 dependence:2 lorentz:1 performed:1 arise:1 sought:2 guarantee:2 hodograph:1 purpose:2 s0:1 instead:1 parameter:1 mat:1 may:12 after:2 snj:5 applications:1 produce:1 multiplication:1 law:2 attempt:1 dynamical:2 sr:3 explicit:4 yielding:1 sk:1 so:1 sn:5 decreasing:1 order:7 superscript:1 holds:2 help:1 including:1 existence:4 its:2 roots:1 systems:5 hidden:1 easier:1 good:1 combination:2 regarding:1 introduce:2 scaling:1 devchand:1 now:2 possess:2 easily:1 february:1 university:1 hamiltonian:1 identified:2 each:4 side:2 homogeneous:1 arxiv:1 directly:1 series:3 related:1 out:1 furthermore:1 since:2 denotes:1 integrated:1 interchanging:1 linear:2 derived:2 diagonal:1 free:1 admits:3 nth:2 members:1 hand:2 definition:1 chiral:1 question:1 geometry:2 u24:1 u21:1 u22:1 assumed:1 consequence:3 guesswork:1 first:14 origin:1 xi:1 xn:2 symmetry:2 omitted:1 variables:20 number:8 relations:5 another:1 equating:3 given:5 introduction:1 unknown:2 vandermonde:1 system:5 construct:3 postulate:1 final:3 gives:1 asymmetric:1 reversed:1 exactly:1 x2:1 than:3 coefficients:5 wide:1 cyclic:2 integrability:1 individual:3 were:1 enables:1 powers:5 exhibit:1 symmetries:1 argument:1 manner:1 seen:3 clearly:3 note:1 sciences:1 take:2 ur2:1 explanation:1 doklady:1 index:1 most:1 ordinates:1 device:1 class:6 tsarev:1 observation:1 considered:1 clear:2 later:1 nuclear:1 typical:1 fact:3 quantity:2 discovered:1 relation:1 solutions:1 only:2 explicitly:1 factor:2 various:2 dependent:8 generalise:1 ones:1 dz:9 integrable:3 rˆoles:1 dv:6 du:6 boundary:1 evolution:3 determinants:3 densities:5 hinges:1 differential:11 expansions:1 yield:1 2πi:1 nauk:1 hydrodynamic:4 coefficient:5 set:6 observed:1 facts:1 computer:1 result:7 theoretic:1 contour:3 best:1 un1:1 un2:1 un3:1 runs:1 ways:1 pattern:1 symmetric:7 written:2 xvj:1 identification:1 simplest:1 invariant:1 geometric:1 terms:4 nature:1 reproduces:1 solv:1 article:2 multivariable:3 both:3 essentially:1 last:1 taking:1 admit:1 expression:5 generalisation:6 co:1 point:1 corresponds:2 dimensional:1 exploit:1 simply:2 polynomial:8 considering:1 light:1 described:1 fairlie:3 three:3 been:1 appears:1 combined:1 define:1 field:2 generating:8 quantities:1 sufficient:1 general:4 case:6 subsets:1 conserved:5 will:5 suppose:2 a27:1 averaging:1 thus:1 cone:1 claimed:1 currents:1 make:1 connection:1 same:2 any:5 member:2 unity:2 φk:3 φm:3 φn:5 independent:14 used:1 ni:4 upon:1 nj:5 possible:2 arose:1 infinite:8 identity:1 recent:1 b258:1 without:1 uq1:1 uq2:1 soviet:1 possesses:1 dh1:1 just:2 infeld:4 summed:1 λk:2 λn:1 λm:1 previous:1 enters:1 preprint:1 density:1 quadratures:1 add:1 other:2 ur1:1 identical:1 differentiation:1 breaks:1 term:2 u23:1 using:2 formal:2 excluding:1 follows:4 serves:1 specific:1 steps:1 arbitrary:4 become:2 reduced:1 mathematical:1 right:3 often:1 some:2 born:4 examples:6 uspekhi:1 proofs:1 dimensions:4 recorded:1 conservative:1 linearly:4 power:2 equivalent:2 expansion:10 restrictive:1 ratios:1 stage:1 comparison:1 extension:3 novikov:2 numerator:1 correponding:1 zuk:5 zui:2 considerations:1 into:1 integral:2 references:1 determine:1 elementary:2 2dimensional:1 u4:22 there:3 u1:53 u3:43 u2:52 los:1 conservation:22 way:1 sections:1 function:11 form:4 but:4 construction:4 russian:1 flavour:1 evident:2 whether:1 characteristic:1 differentiable:1 ui:19 verification:1 uk:6 uj:14 demonstrate:2 stages:1 similar:1 motion:1 2πiz:6 strongly:1 proved:1 int:1 likewise:1 abstract:1 determinant:2 determinantal:1 single:1 constructed:1 again:1 functions:8 nk:9 no:2 when:1 application:1 setting:2 xfi:1 department:1 models:1 mineev:1 polynomials:4 variable:3 sides:3 n3:5 assume:1 together:2 n1:5 n2:5 laws:22 requires:1 once:1
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solv-int9608003.txt |@word φ1j:10 φ1k:1 allowed:1 consider:1 chinese:1 similarity:1 equalities:3 results:1 ds:2 leads:4 eds:1 ψ1j:9 commute:2 computation:2 gn:2 expressions:5 research:1 gh:6 whose:1 inverse:1 const:1 calculate:1 aug:1 shanghai:2 tr:7 including:1 finally:1 tm:23 present:1 under:7 p2:45 zhang:1 very:4 rise:7 wave:1 every:1 li:1 condition:5 obvious:1 hamiltonian:29 ref:5 guo:1 t1:1 large:2 involution:2 vector:3 phase:2 λnk:3 cmx:2 relation:1 anal:1 noted:1 trv:4 zn:1 ghm:4 grateful:1 zj:1 10b:1 10a:1 direct:4 suffices:1 painlev:1 further:8 q1x:1 spectral:9 what:3 nonlinear:9 stands:1 p1x:1 diag:1 section:5 11b:3 hereditary:1 annals:1 fuchssteiner:2 above:8 elucidate:1 new:5 technology:1 method:1 body:1 supporting:1 degree:1 respectively:3 here:5 china:5 bj:1 separation:1 represented:2 quite:1 equations:7 z1:1 dp2:1 obtained:1 search:1 institute:1 vectors:1 allows:2 amount:1 resulting:3 poisson:1 usually:1 geng:2 involves:1 control:2 named:1 technique:1 useful:1 ψ2j:8 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solv-int9608004.txt |@word miwa:1 sci:4 consider:9 pairing:3 global:10 brownian:1 results:16 bc:1 leads:1 roy:2 scalar:1 proposition:52 computation:1 follow:1 research:2 relationships:1 certainly:1 inverse:1 analytic:6 aug:1 reported:1 paris:4 tr:2 acting:3 tp:9 recurrence:5 matrix:5 finally:2 tm:4 tj:7 those:1 th:1 under:1 details:1 analogous:8 carried:1 p2:34 conjecture:2 iuj:1 proved:4 iul:4 straightforward:3 orthogonal:6 johansson:4 choice:4 implicit:1 corollary:9 4p2:2 jack:25 prof:1 difference:1 exact:5 condition:2 partitions:1 identity:5 exponential:3 bn:2 notes:4 integrating:1 list:1 solution:17 dib:2 t1:20 random:4 deformed:2 commute:2 small:1 eigenvalues:7 path:2 mκ:9 inspection:1 noted:6 application:1 zn:25 mn:1 zi:1 zj:21 zk:4 10b:3 lecture:1 10a:2 sin2:8 direct:2 13a:5 second:8 evaluated:2 zz:1 substituting:18 44b:2 44a:2 iyj:1 requiring:1 substitute:6 zs:2 even:5 established:7 what:2 developed:1 power:1 advantageous:1 giving:2 section:14 intimate:1 43b:2 brief:1 bdj:1 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solv-int9608008.txt |@word consider:1 similarity:1 rev:1 four:2 gˆateaux:1 consists:1 whose:6 simon:1 depend:1 aug:1 paris:1 extraneous:1 th:4 under:1 spec:2 case:2 erale:1 choice:2 every:2 difference:7 condition:7 leads:1 solution:15 discrete:17 indices:1 equation:52 painlev:15 ode:1 even:1 will:5 nonlinear:2 annali:1 version:5 en:1 sur:2 sup:1 method:4 degree:6 exchange:1 erieur:1 papageorgiou:1 les:1 possibility:1 consideration:1 equations:12 appears:1 conte:5 great:1 noticeable:1 study:1 changed:1 linearised:1 suitable:1 involves:1 family:1 extra:1 apply:1 linearly:1 derivatives:1 use:1 erentielles:1 remains:1 atze:1 france:1 examination:1 taken:2 more:1 formally:2 naive:5 particular:1 iii:3 must:2 ramani:1 originally:1 mv:1 values:2 following:2 making:1 example:1 numbers:1 process:1 involve:1 performed:1 sense:1 get:4 feature:1 how:1 pura:1 criterion:2 acta:1 ordinary:1 parameter:8 fr:1 may:2 singularities:2 movable:4 demanding:1 plane:2 representations:1 fordy:1 natural:1 imply:1 so:1 discretisation:13 representation:1 order:15 indeed:1 despite:1 satisfied:3 satisfies:2 its:8 dont:1 chosen:2 systems:1 mail:1 cea:2 they:2 half:2 singularity:4 possess:1 easily:1 term:4 possibilities:1 iff:1 each:1 side:5 arxiv:1 ej:1 series:1 hypergeometric:1 applicata:1 yvette:1 our:3 neighbourhood:2 etat:1 shown:1 robert:1 induces:1 denotes:1 acting:1 math:1 linear:2 free:4 admits:3 reason:2 proportionality:1 hand:6 obtention:1 dubbed:1 hence:4 think:1 first:5 origin:3 initial:1 features:2 variables:1 preservation:4 restrict:1 clear:1 open:1 given:4 perturbation:6 service:1 similarly:1 unknown:1 least:3 belongs:1 scheme:6 recovered:1 shifted:2 continuous:14 zeroth:1 x0:1 representing:1 coefficients:1 third:3 fuchs:3 iteration:1 namely:3 treated:1 perturbative:4 derivative:3 say:1 ans:1 seen:1 mappings:1 zero:2 depending:1 physique:1 instance:1 εn:2 shall:2 discretised:2 most:4 class:3 laurent:1 calculated:2 later:1 physica:1 ks:1 points:3 χj:2 fact:1 chances:1 notations:1 relation:3 solutions:2 analogue:2 parameters:1 explain:1 should:2 analytic:1 only:5 factor:3 equivalents:2 integrable:1 circle:1 do:4 ordre:2 means:1 dependent:1 de:8 invariant:3 du:1 eme:1 approach:1 differential:8 fixes:1 musette:3 set:1 ses:1 depends:1 radius:1 eliminating:2 best:1 satisfying:1 distinctive:1 bureau:2 between:8 probably:1 boundary:1 conditions:5 preserve:1 notice:1 terms:1 attention:1 transpose:2 efficiency:1 solv:1 article:1 both:1 essentially:1 last:2 solely:1 etc:1 expression:2 arbitrarily:1 point:1 whatever:1 simply:1 diff:1 second:2 three:3 int:2 faithfully:1 cauchy:1 corresponding:1 confinement:3 demand:2 c2:5 c1:5 general:7 applied:1 look:1 pacs:1 aim:1 while:1 suppose:1 leaves:1 di:1 property:11 noncritical:1 thus:4 k0:7 different:1 twoparameter:1 chazy:7 pay:1 discretise:1 same:3 complex:1 finite:7 independent:2 infinity:1 see:1 possible:1 infinite:1 center:1 analysis:1 possesses:3 left:6 being:1 grammaticos:2 obtain:1 λi:1 enters:1 preprint:1 seems:2 egrale:1 valid:1 lett:1 rules:3 february:1 world:2 formal:1 necessary:2 like:2 pickering:1 specific:1 yields:2 arbitrary:1 become:1 terminology:1 because:1 sequence:1 some:1 happens:1 provided:1 opposite:1 integration:3 ese:1 critical:3 minimal:1 refer:1 bf:1 obey:1 expansion:3 discretising:1 step:5 dictated:1 properties:1 getting:1 misleading:1 ensure:1 automatically:1 presence:1 into:2 right:2 references:1 utility:1 there:3 u3:3 u2:17 gif:1 way:1 ed:1 was:2 naturally:1 function:3 hard:1 hq:1 but:2 cedex:1 link:1 matematica:1 highest:1 versions:1 up:3 us:3 limit:8 uj:2 problem:2 similar:2 called:3 constant:1 defined:3 abstract:1 troisi:1 resultant:1 examine:2 check:2 faithful:6 index:2 when:1 priori:2 test:10 acceptable:1 arithmetic:1 conclusion:1 condens:1 critiques:1 polynomials:1 sides:1 implies:1 practically:1 saclay:2 time:1 having:2
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solv-int9608009.txt |@word trigonometric:2 invent:1 scalar:9 commute:2 kato:1 whose:1 attracted:1 finally:1 those:2 include:1 orthogonal:7 choice:1 jack:12 difference:1 partitions:1 annihilated:1 hamiltonian:7 vector:3 math:6 eigenvalues:5 second:3 further:3 hansson:1 new:1 d1:1 method:1 satisfy:1 simultaneously:2 degree:1 exchange:5 respectively:1 here:1 understanding:1 obtained:7 remark:2 studied:1 sjk:5 products:1 poisson:1 action:1 suitable:1 uniquely:1 via:1 useful:1 family:2 masatoshi:1 brought:1 total:1 unit:1 b286:1 proceed:1 prove:1 distinct:2 positive:1 explicitly:1 call:2 type:3 operators:17 vasiliev:1 known:2 cases:1 isomorphism:5 tokyo:3 equation:2 fock:5 ms:1 following:4 trans:1 example:2 proof:2 beautiful:1 rodrigues:1 states:4 dxj:1 provide:1 acts:1 orthogonality:6 mµ:1 significance:1 sik:1 sij:10 dominance:1 product:8 fs:5 mat:1 algebra:2 may:1 oscillators:1 after:1 consequence:2 fc:7 iθj:1 third:1 element:2 so:2 sn:4 representation:2 acknowledges:3 informations:1 professors:2 already:1 japan:1 diagonalized:1 group:1 fruitful:1 stanley:2 jacobi:1 mail:1 them:2 introduce:6 they:6 instead:1 oxford:2 hall:1 yusuke:1 university:1 sin:1 each:2 2n:1 characterized:1 homogeneous:1 differential:1 directing:1 related:2 elementary:1 investigated:1 combining:1 quantum:1 our:3 special:1 space:3 res:4 since:6 rev:3 cww:1 particles:1 combinatorial:1 acting:1 rational:3 formula:3 mλ:2 monographs:1 interaction:2 impose:1 length:1 plane:1 δij:2 hence:1 first:5 xj:38 xk:17 xi:2 xn:5 manuscript:1 variables:2 construct:1 another:3 sutherland:14 xw:1 given:3 forrester:3 ordering:2 adjoint:3 relations:1 their:5 normalization:1 tool:1 exactly:2 part:1 norms:2 x1:5 coefficients:2 kind:2 showed:1 integrability:2 limiting:2 annihilation:1 determined:1 pairwise:2 were:2 pasquier:1 rewrite:1 reviewing:1 w0:2 conjugate:1 polychronakos:4 self:2 note:3 sciences:1 generalized:2 tokihiro:1 indexed:1 added:1 shall:1 algebraic:4 letter:2 commutation:1 calculated:1 partition:1 coincides:2 principle:1 exp:3 noumi:1 show:2 jµ:2 spaces:2 gauge:2 analogue:1 brink:1 ground:3 based:1 eigenspace:1 written:2 bernard:1 only:1 bases:2 integrable:1 circle:2 oct:1 hope:1 dn:1 his:2 dj:24 dk:2 notation:2 means:1 joint:2 meguro:1 dr:2 ds:2 arxiv:1 acknowledgments:1 investigate:1 paper:1 common:2 set:3 clarified:1 module:1 relative:1 edition:1 see:1 result:1 existence:1 discussions:1 terms:2 contour:1 interacting:2 symmetric:10 state:3 permutes:1 reading:1 preserve:1 attention:2 recently:2 extend:1 jw:1 jp:1 however:2 vanishing:1 solv:2 amer:1 come:1 comd:1 suggested:1 x2j:3 taking:1 expression:2 ci:1 conclude:1 2i2:1 harmonic:1 dimensional:1 polynomial:3 respect:6 ps:7 basis:5 due:2 been:3 quasihole:1 int:2 much:2 symmetrizing:1 interest:1 komaba:1 define:3 θj:3 θk:1 generating:2 deeper:1 quantities:4 ours:1 denote:2 present:1 case:4 tetsuji:1 evaluated:1 transformation:2 aim:1 di:3 property:1 procedure:2 vectors:3 a26:1 jpn:3 non:2 ii:3 ij:4 hideaki:1 different:1 author:3 perform:1 make:1 same:4 complex:1 arguments:2 diagonalize:6 proved:5 constructed:3 used:3 i1:3 lapointe:1 hand:1 expand:1 well:1 without:1 components:1 convenient:1 model:22 calogero:17 monomial:1 obtain:1 thanks:1 multiplet:1 λi:3 λn:4 adv:1 preprint:2 haldane:1 macdonald:1 belongs:1 transformed:2 lett:2 theorem:1 diagonalization:1 excited:4 momentum:3 real:1 acta:1 results:3 vacuum:3 press:1 using:7 uλµ:1 helpful:2 submission:1 follows:3 terminology:1 mathematical:3 because:1 classical:1 creation:1 some:4 gaudin:1 2xj:1 integration:1 comments:2 critical:1 provides:1 eigenfunctions:5 equivalent:1 wavefunctions:2 clarendon:1 properties:4 dunkl:4 commun:1 wadati:5 informing:1 range:2 introduced:1 soc:4 jλ:14 references:2 operator:11 pairing:1 long:2 start:1 describes:1 way:1 function:2 form:5 hs:7 but:1 hj:4 hc:8 he:1 annihilate:1 us:1 below:1 un:1 called:1 ac:4 associated:1 defined:3 abstract:1 aj:7 general:1 conserved:4 formalism:5 commuting:6 physical:2 satsuma:1 functions:4 wavefunction:2 other:5 department:1 conclusion:1 elements:4 kinds:1 ku:1 calculating:1 models:5 polynomials:20 includes:1 a1:1 generated:3 important:1 a5:1 a4:1 structure:5 opdam:1 constant:1 vinet:1 baker:3 cherednik:2 mimachi:1 restricted:1
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solv-int9608010.txt |@word partial:1 consider:4 results:1 four:1 scalar:1 commute:11 comments:1 ηi1:9 go:2 ηijk:1 compact:1 whose:3 const:3 aug:1 vs:1 kβ:1 kα:2 does:1 indicate:1 th:3 di2:3 subtleties:1 p2:41 choice:1 entries:2 condition:7 solves:2 hamiltonian:12 turns:1 try:1 involution:2 vector:17 ndimensional:1 noted:1 takhtajan:5 imply:2 further:1 dynamics:7 canonical:8 even:2 what:2 sub:4 brackets:5 giving:1 above:6 new:6 dtα:1 consisting:2 satisfy:3 here:1 canonically:1 quite:3 equations:3 change:1 obtained:1 generalizing:1 antisymmetric:4 changed:1 poisson:6 permutation:3 changes:2 via:1 useful:1 vij:1 summations:2 unit:1 derivatives:2 use:4 takes:4 would:3 prove:1 recalling:1 δiα:1 next:1 almost:1 approach:1 therefore:1 survive:1 decomposable:3 more:2 brings:1 operators:11 corrected:1 vi1:1 everywhere:1 vn:2 particular:2 cases:2 must:3 springer:1 recall:1 equation:2 work:1 det:2 δm:1 values:1 following:2 example:7 proof:1 f1:15 f2:5 f3:1 topic:1 sphere:2 simple:2 vanish:2 requirements:1 discussion:1 get:4 write:2 fourth:2 ordinary:1 explains:1 may:3 coming:1 fi:11 fj:2 fl:1 constants:5 natural:1 third:2 whenever:1 light:1 element:1 lβ:2 ǫijkl:1 fundamental:3 lα:2 subsequently:1 order:9 fα:2 produces:1 over:2 stays:4 satisfied:3 paper:2 motions:1 satisfies:1 still:3 its:3 before:1 x21:2 xl:1 coordinates:2 actually:2 systems:6 jacobi:2 derivative:1 main:2 fin:1 non:3 they:4 now:10 term:1 university:1 presented:1 iff:2 fσ:2 2n:3 subset:1 differential:17 directly:3 idea:2 related:1 contracting:1 toda:1 extended:1 our:3 eq:1 out:1 shown:1 matrix:13 space:1 restricted:1 furthermore:1 since:4 rev:3 chaos:1 conjectured:1 formula:1 math:4 commutation:2 linear:1 free:1 standard:16 might:1 log:1 r2:1 r3:1 could:3 finland:2 motion:23 place:5 generalizations:1 first:2 initial:1 xn:2 symmetry:1 xm:1 omitted:2 variables:4 number:2 rank:1 done:1 another:3 reached:1 open:1 angular:2 kfi:1 given:14 their:1 introduction:1 behaves:1 system:6 least:2 needed:1 v42:1 fn:22 dt3:1 dt2:1 dt1:1 commutativity:1 academy:1 assumption:1 part:6 x2:3 x3:3 x1:4 than:1 x4:22 eq1:6 eq3:6 eq2:6 integrability:2 project:1 matter:2 determined:2 were:1 p21:3 generalization:4 manuscript:1 conjugate:1 need:2 seen:2 any:4 generalizes:1 general:1 studying:2 note:3 take:2 jacobian:2 finding:1 so:3 gβ:3 gα:5 though:1 who:1 chart:1 algebraic:6 letter:3 nothing:3 appear:1 consequences:2 considered:1 clear:1 kl:1 bracket:18 hietarinta:2 usual:2 physics:1 fact:1 hyper:1 show:1 supported:1 bring:1 find:3 q1:33 q3:11 q2:41 just:1 should:2 only:3 explicitly:1 rich:1 factor:2 integrable:17 hamiltonians:8 ǫi1:3 columns:3 do:3 move:1 means:3 df:2 hopefully:1 overall:2 cannot:1 x24:2 combinations:1 dt:2 determinants:1 fields:15 arxiv:1 method:1 wish:1 qi:4 x22:2 set:4 constructing:1 j1:7 j2:14 j3:1 see:3 sec:1 result:2 p23:1 p22:4 discussions:1 recently:2 turku:2 tensor:19 symmetric:1 written:4 simplest:1 αi:1 invariant:2 αk:1 conditions:4 email:1 αn:14 choose:1 multiplied:1 nambu:44 terms:2 extend:1 missing:1 however:1 jn:20 chatterjee:2 solv:1 tensors:4 thank:1 suggested:1 essentially:1 last:3 vanishing:1 quantization:1 connection:1 kαn:3 otherwise:1 ci:3 point:1 invariances:1 dimensional:7 simply:1 respect:2 xα:9 lattice:1 skew:2 locally:2 due:1 been:5 int:1 interest:1 pi:3 define:7 determinant:2 corresponding:8 misprint:1 quantities:3 subspace:1 denote:1 present:1 case:8 p3:10 intriguing:1 p1:29 defining:2 appearance:2 arnold:1 will:2 while:1 property:1 studied:3 ki3:1 vi:1 vk:1 thus:2 surface:3 ki4:1 ii:2 itself:2 ni1:2 different:1 verified:1 acknowledgments:1 same:2 clearly:2 read:2 higher:3 independent:1 used:2 i1:12 i3:14 i2:23 i4:2 possible:1 vαk:1 changing:1 invariance:1 totally:1 identity:5 recent:1 off:1 well:2 analysis:1 solve:1 consistency:2 arising:1 dimension:6 left:1 manifold:10 proposed:1 numbering:1 tobe:1 underlying:2 immediately:1 alternative:2 functionally:1 conclusions:1 sahoo:1 leibnitz:2 lett:4 easy:3 theorem:3 guarantees:2 momentum:2 decomposability:2 iα:2 iβ:1 february:1 possibly:1 using:4 necessary:1 like:3 follows:3 reduces:2 continue:1 yields:1 works:1 reduced:1 ηjn:10 parity:1 because:1 methods:1 classical:2 some:3 q22:1 examples:3 nonzero:1 provided:3 scale:3 dimensions:2 lαβ:1 behave:1 equivalent:1 nj1:1 super:2 properties:1 ηj1:12 x32:2 most:1 column:2 commun:1 discussed:1 plying:1 remains:1 range:2 automatically:1 mathematical:1 equally:2 h2:4 into:1 h1:8 three:4 phase:1 references:1 determine:1 additional:1 there:4 question:1 ǫj1:1 way:1 was:4 function:2 complete:1 form:28 tally:1 but:13 hi:2 hn:4 whether:1 vkα:2 us:8 liouville:3 utu:1 problem:2 similar:1 mechanics:1 ab:1 constant:6 computing:1 defined:13 certain:1 abstract:1 direction:1 proven:1 determinantal:1 globally:2 conserved:2 formulation:2 commuting:9 defines:1 again:2 functions:4 no:1 when:3 field:2 other:5 department:1 elements:1 important:1 variable:1 structure:2 implies:3 assume:1 required:1 rule:2 correspondingly:2 starting:1 original:2
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solv-int9609001.txt |@word consider:6 pointing:1 alg:1 results:3 integration:2 leads:2 ρji:1 proposition:17 edu:2 consists:2 follow:3 gk:10 compact:2 whose:1 inverse:4 calculate:2 aug:1 λil:2 tm:1 present:2 th:1 under:3 connecting:2 suita:1 γe:1 string:1 orthogonal:4 very:1 ρj1:1 bilinear:1 connects:4 choice:1 suggesting:1 corollary:1 witten:1 every:3 orientations:1 entries:5 tridiagonal:13 associated:3 matrices:12 deformations:1 condition:1 look:1 four:6 βkn:1 hamiltonian:6 visits:1 solution:12 t0:29 large:5 solved:1 small:4 eigenvalues:8 λi1:2 rk:1 glued:6 ups:6 degeneracy:1 upper:2 work:1 neighborhood:5 orbifolds:1 eλt:3 sin2:1 direct:6 sign:6 zero:21 eλi:1 pass:1 linear:2 spectral:11 giving:2 diag:27 section:12 equivalent:1 brief:1 expressed:5 cell:5 3i:1 version:1 above:5 expresses:1 method:4 nakamura:1 publications:1 satisfy:1 λik:6 outgoing:6 full:4 αik:2 exchange:1 respectively:2 component:23 eλ2:3 here:5 b2k:2 cos2:1 groups:2 making:1 along:1 equations:5 z2:5 λin:4 obtained:7 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solv-int9609002.txt |@word represent:2 code:1 consider:2 lack:1 results:2 leads:1 eds:2 scalar:1 computation:1 consists:1 localized:3 inverse:3 finally:1 helps:1 th:2 case:4 jensen:1 advantage:1 very:2 wave:4 deformations:1 turns:1 solution:7 discrete:10 indices:1 3b:1 segre:2 grateful:1 dealing:1 direct:2 cosh:1 likely:1 dynamics:1 odd:1 spectral:16 nonlinear:26 appear:1 giving:1 nee:3 version:1 poles:1 reconstruction:1 roundoff:1 3c:1 values:2 3a:1 method:7 3d:1 coefficient:3 ibid:1 error:1 here:4 diagonal:1 water:1 les:1 sinh:1 others:1 standard:1 equations:3 change:1 deduced:1 obtained:2 remark:1 studied:1 allows:5 hospitality:1 conveniently:1 fourier:10 studies:1 useful:1 family:4 merely:1 plenum:1 sheppard:1 analyzing:1 1st:1 tools:1 unit:3 readily:1 standing:1 use:1 would:1 prove:2 intense:1 nucl:1 going:1 more:2 introducing:1 solitons:9 envelope:2 odinger:2 berlin:2 train:2 controlling:1 particular:2 discreteness:1 springer:4 valued:2 mb:1 equation:4 work:1 cai:1 obvious:2 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solv-int9609003.txt |@word supersymmetrical:2 darboux:1 partial:1 consider:5 rev:1 nauchn:1 results:3 leads:1 proposition:3 expressions:1 inverse:3 const:1 concerned:1 equivalence:1 γu:1 quasi:13 petersburg:2 th:1 under:4 include:1 applied:1 proved:1 orthogonal:1 very:1 condition:1 founded:1 hamiltonian:18 list:2 solution:7 solved:2 commute:1 science:2 concise:1 integrability:1 involution:3 further:3 dynamics:1 rectangular:2 4x2:2 substitute:2 canonical:9 even:1 3y:1 brackets:4 expressed:3 lifshitz:1 new:11 satisfy:1 respectively:1 here:4 canonically:1 ansatz:7 separation:11 address:1 equations:14 appears:1 change:1 search:1 institute:1 shift:1 study:1 completely:2 p2:1 resulting:1 poisson:5 suitable:1 heiles:6 formulated:1 substitution:1 linearization:1 apply:1 unit:1 use:1 takes:2 would:1 12x2:1 remains:1 whittaker:1 nonsymmetric:1 next:4 ψk:2 call:2 therefore:4 m2:1 means:3 type:1 theoretical:1 more:1 separated:8 becomes:3 holt:1 particular:3 known:5 ramani:2 account:2 quartic:7 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solv-int9609004.txt |@word represent:1 partial:13 gr:3 maximum:1 canonical:6 particular:2 desirable:1 results:2 2c1:4 four:5 scalar:1 expressions:2 consider:8 whose:2 inverse:6 calculate:3 iii:5 concerned:1 ξt:20 contained:1 removal:1 languages:1 program:2 elliptic:2 under:2 include:1 ǫc:1 lack:1 stud:1 straightforward:4 acoustic:1 far:2 implicitly:1 rise:1 wave:18 implicit:1 every:3 anonymous:1 nonlinearity:1 exact:9 condition:13 tri:1 entire:1 school:1 2κc:1 hamiltonian:3 u2x:2 notes:1 having:1 solution:23 large:1 solved:6 vector:2 science:1 12t:2 anal:1 noted:1 ten:1 direct:9 approximation:1 zero:13 design:1 further:2 implemented:3 ode:1 substitute:1 theory:1 nonlinear:10 appear:5 ct2:1 section:2 celebrated:1 3u:1 3t:2 current:1 fuchssteiner:7 above:3 new:8 method:40 contrast:2 satisfy:2 avoids:2 led:1 degree:2 respectively:4 commercial:1 here:3 water:3 cos2:2 groups:1 address:1 κt:2 κu:2 standard:1 equations:57 appears:1 twostep:1 obtained:6 remark:3 trans:2 division:1 institute:1 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solv-int9609005.txt |@word sector:16 concept:2 partial:1 gr:1 global:1 results:3 leads:5 follow:1 denotes:1 reasoning:1 consider:6 whose:2 certainly:7 depend:6 iii:2 concerned:3 technique:5 kapaev:5 finally:4 those:1 under:3 decomposition:1 adapt:1 applied:2 conjecture:2 kπ:7 rational:5 g1:3 returning:2 very:1 assuming:1 connects:2 dokl:1 choice:6 additional:1 affect:1 difference:1 matrices:2 deformations:4 condition:2 arrange:1 obvious:2 riemann:1 exits:1 wronskians:1 notes:1 having:1 t2:2 solution:23 large:34 convenience:1 dealt:1 small:5 eigenvalues:1 anal:3 coalescing:2 noted:2 assemblage:1 upper:1 smaller:1 11d:1 10b:1 ze:2 variables:1 10a:1 inconsequential:1 sign:2 approximation:19 painleve:1 evaluated:1 pass:3 iσ3:1 iσ2:1 iσ1:1 dψ2:4 dψ1:1 theory:2 even:3 aim:1 nonlinear:2 appear:2 ct2:1 giving:1 sun:1 section:9 near:4 expressed:1 uniform:18 henceforth:1 version:2 poles:4 above:5 scientists:1 3b:2 3a:2 contributes:1 method:12 suppress:1 satisfy:3 full:1 modify:1 here:5 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solv-int9609006.txt |@word secondly:1 chinese:3 assembles:1 results:4 eds:1 scalar:2 expressions:1 gh:1 21st:1 inverse:1 calculate:1 shanghai:2 nonlocal:2 δhm:1 tm:1 those:1 include:1 equalities:1 case:3 advantage:1 g0:15 rise:1 2rc:2 2rb:2 prog:1 matrices:1 y1:5 presented:1 did:1 positions:1 solution:1 vector:8 frolov:1 anal:1 solutions:1 ρj:3 shatin:1 direct:2 zero:2 champagne:1 chen:3 further:2 dynamics:1 spectral:5 established:2 what:1 nonlinear:7 appear:1 hereditary:7 annals:1 fuchssteiner:5 above:4 international:1 acknowledgments:1 coefficient:1 simultaneously:1 lee:1 degree:10 here:3 china:4 galilean:2 equations:8 institute:1 reason:1 reports:1 resulting:1 usually:1 technique:2 analyzing:1 support:1 establish:1 2φm:1 virasoro:7 nonlinearization:2 would:3 prove:1 contains:1 therefore:2 hinton:2 until:1 more:2 sort:1 jpn:1 l191:1 becomes:1 operators:8 odinger:1 curvature:2 berlin:1 known:3 hold:2 springer:1 ma:8 science:4 equation:7 work:1 ρm:3 ρn:13 kamran:1 following:5 example:2 f0:17 repectively:1 give:1 calculation:1 ann:1 want:1 times:1 verlag:1 end:1 provide:1 verify:1 holds:1 rubin:1 acta:1 product:1 algebra:14 may:7 after:1 derived:1 hong:3 fb:1 lax:9 waves:1 representations:1 summarize:1 data:1 natural:1 third:1 correspond:1 mvm:1 martina:1 allow:1 recursion:1 ry2:1 order:1 ry1:3 help:1 hierarchy:29 developed:1 move:1 kong:3 paper:1 through:1 committee:1 differs:1 satisfies:1 y2:5 its:3 τn:3 derive:1 group:2 2λa:2 2λc:2 li:4 meantime:1 systems:3 olver:2 main:1 lx:3 introduce:1 they:3 now:1 yu:1 discuss:1 possess:2 easily:1 dirac:22 2q:8 2r:8 university:2 hamiltonian:3 2x:1 found:2 universit:1 referred:1 differential:1 financial:1 ed:2 related:1 constitute:2 isospectral:4 used:1 obtains:1 meth:1 special:1 out:2 shown:2 matrix:1 furthermore:1 since:1 rev:1 research:3 fellowship:1 stud:1 formula:1 induced:1 math:17 shows:1 foundation:2 theory:2 kaup:1 diagonal:2 completely:1 lf0:2 besides:1 shun:1 geometry:1 just:1 levi:1 ist:2 forms:1 lth:1 exhibited:1 first:13 initial:2 humboldt:1 symmetry:10 relate:1 variables:1 construct:1 directly:3 carry:1 precisely:1 interchange:1 given:4 1x:3 system:4 relations:4 their:1 master:4 xiu:1 scheme:1 exactly:3 newell:1 jordan:1 debnath:1 authors:2 x2:9 off:1 x1:9 kind:4 imply:1 winternitz:4 classes:1 were:2 result:1 symmetries:21 boston:1 topics:1 qy1:1 argument:2 qy2:3 need:2 sees:1 any:4 centerless:1 lie:4 depending:1 lin:2 xrx:1 φj:1 kac:1 towards:1 trace:1 kam:1 algebraic:2 involving:2 germany:1 letter:2 pair:2 why:1 soliton:18 ki:1 phil:1 kn:3 km:9 kl:2 proceedings:1 x1x:11 camb:1 physics:2 bulletin:1 fact:1 laws:1 oevel:2 show:4 timedependent:1 relation:3 akns:4 carefully:1 find:2 λu:3 elucidated:1 only:3 indeed:1 integrable:1 constant:2 local:2 means:1 dependent:9 de:1 famous:1 aσ1:1 ones:3 rt2:1 dr:1 gen:7 alexander:1 evolution:3 qr:1 fields:5 arxiv:1 common:2 shi:1 fixed:1 view:1 exists:1 sep:1 national:1 enjoyed:1 grosse:2 trick:2 see:2 utl:1 w1:1 w0:1 discussions:1 qt2:1 still:1 uλ:7 enough:1 determined:1 various:1 jf0:1 email:1 terms:2 wn:12 wm:4 attention:1 however:1 τm:2 key:2 solv:2 uφ:1 come:1 wx:1 informatik:1 kruskal:1 many:3 acknowledge:1 deduction:2 uni:1 whole:1 among:1 afterwards:1 conclude:1 simple:1 except:1 cx:2 polynomial:1 respect:3 lg0:1 writing:1 conference:1 λtm:2 λtn:3 due:1 been:4 int:2 b0x:1 algebras:2 fudan:1 choose:1 generating:1 corresponding:2 σi:1 systematic:1 derivative:3 present:2 applied:1 klaus:1 will:1 neat:1 theoretical:1 property:2 λt0:1 coupled:1 von:1 thus:4 vm:9 vn:3 reads:1 triple:1 vx:1 zhang:1 technology:1 binary:2 different:1 grant:1 φx:13 φy:2 acquire:1 same:2 pauli:1 hierarchies:2 φm:10 φn:7 difficult:1 independent:3 investigated:1 singapore:2 cubic:1 functions:2 flows:4 purpose:1 potentials:1 invariance:2 ablowitz:1 identity:1 schr:1 paderborn:3 analysis:1 solve:1 soviet:1 possesses:3 gelfand:1 proposed:3 obtain:3 valuable:1 using:1 scattering:2 λn:11 λm:2 infinitely:2 ease:1 wen:1 qx2:3 qx1:10 transformed:1 lett:4 easy:1 pitman:1 solvable:1 transformation:2 take:1 david:1 advances:1 rx1:3 equality:2 moreover:1 moody:1 theor:2 like:3 semi:1 follows:3 δu:1 schwarz:1 arbitrary:3 qxx:1 because:1 methods:1 some:5 b0:4 2qa:2 gateaux:1 provided:1 recently:2 dimensions:2 thank:2 defined:3 2xq:2 prof:1 2xr:2 proc:1 scientific:2 rep:1 equivalent:2 bi:1 bj:2 step:1 substitution:1 bx:2 injective:1 about:1 world:2 commutator:5 discussed:1 2x1:1 2x2:1 soc:2 into:2 right:1 references:1 operator:13 wλ:1 bjx:1 mkm:3 there:3 appl:2 way:1 lou:2 was:4 form:1 but:4 ωx:2 zhu:1 characteristic:3 utn:2 us:2 utm:1 2qb:2 problem:5 similar:4 detailed:1 associated:2 ai:1 abstract:1 describe:1 chan:3 doesn:1 general:1 associates:1 exist:2 ax:2 constructed:1 nj:2 mathematik:1 mathematica:1 generally:1 field:3 other:1 fokas:1 department:1 mathematics:2 rx2:10 nice:1 zheng:1 a0:2 variable:2 structure:7 scientia:1 ge:1 required:1 4r:8 4q:7 rxx:1 time:14 original:1
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solv-int9609007.txt |@word minors:1 consider:9 nauchn:2 results:2 commute:1 complication:1 computation:1 kowalewski:18 go:1 3a1:1 settlement:1 gk:2 gj:13 gi:4 row:1 inverse:7 tr:13 βc1:1 tn:2 γj:1 investigation:1 tj:1 petersburg:2 th:1 under:2 semenov:3 analogous:1 tr2:1 γe:1 case:2 r12:1 g2:10 g1:4 geometrical:1 δjk:2 entries:9 matrices:54 deformations:7 condition:1 common:1 groups:2 notations:3 presented:3 irreducible:2 notes:1 sklyanin:16 list:1 solution:1 t0:66 t1:13 try:3 involution:1 adjust:1 science:2 gauge:1 reyman:3 hospitality:1 iα1:2 direct:1 consists:1 second:1 pass:1 dynamics:1 expressions:1 substitute:3 obey:7 bilinear:1 aim:1 stands:1 brackets:16 t2a:1 deeply:1 section:2 expressed:1 above:1 3l:2 2u4:2 new:10 d1:2 method:9 contrast:1 satisfy:1 edited:3 additively:1 respectively:5 proc:1 here:12 following:13 l22:9 separation:1 consideration:2 enveloping:3 equations:6 obtained:6 shansky:3 search:1 property:3 institute:1 shift:2 larger:1 allows:1 experience:1 periodic:1 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solv-int9609008.txt |@word consider:14 funct:2 superfields:9 four:1 scalar:1 antichiral:6 expressions:2 devoted:1 depend:1 superspace:15 show:2 tr:19 finally:3 tk:5 th:2 under:1 semenov:1 analogous:1 presentation:1 straightforward:1 very:3 redefinition:1 manageable:1 condition:12 leads:3 trl:2 immediately:1 hamiltonian:11 turns:4 t2:1 t1:1 involution:1 vector:1 phase:14 small:3 drop:1 noted:1 freidel:1 zd:1 consistent:1 second:6 odd:10 panda:1 even:9 index:1 what:1 appear:1 invertible:2 brackets:11 section:9 analogously:1 d3:19 wxxx:1 version:2 subspaces:3 krivonos:6 method:1 groupe:1 led:1 respectively:1 modify:1 here:4 reported:1 tangent:1 dψx:1 quite:1 equations:15 deduced:3 obtained:9 shansky:1 antisymmetric:5 kanno:4 suitably:1 study:6 studied:4 poisson:27 action:2 suitable:3 involves:2 useful:1 classification:2 replace:1 put:1 2wx:1 apply:1 total:2 tools:1 unit:1 derivatives:2 use:5 ψy:2 would:1 commun:2 covariant:1 contains:1 suppl:1 france:1 few:1 those:2 a29:1 type:3 more:2 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solv-int9609009.txt |@word represent:4 logarithms:1 partial:2 consider:15 springer:3 global:3 trisecant:1 fxxx:2 leads:3 eds:1 scalar:1 commute:1 grateful:1 consists:1 follow:1 disk:1 gi:1 devoted:2 inverse:1 calculate:1 paris:1 technique:1 nonlocal:2 finally:2 funk:1 th:1 dressing:11 analogous:1 include:1 applied:1 belonging:2 fay:1 string:1 g1:13 very:2 rise:8 dell:2 choice:1 difficult:2 difference:1 ǫf:4 riemann:1 solves:2 presented:4 tokyo:1 solution:10 discrete:3 vector:2 anal:1 neighborhood:1 za:4 zb:1 zero:5 bilocal:1 dynamics:1 theory:7 bilinear:15 established:1 what:2 nonlinear:4 plays:1 giving:1 section:9 analogously:1 expressed:1 maillet:1 poles:4 sur:1 above:1 new:1 method:12 contrast:1 compact:5 condensed:4 full:3 simultaneously:2 respectively:3 component:2 here:9 les:2 tangent:1 groups:1 address:1 consideration:1 equations:48 change:2 obtained:4 great:1 antisymmetric:1 institute:3 lomi:1 study:2 studied:1 allows:5 completely:3 action:4 hospitality:1 studies:1 exeter:1 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solv-int9609010.txt |@word proposition:14 partial:3 consider:6 similarity:1 rev:2 separates:7 results:4 four:1 scalar:1 commute:6 generalize:1 computation:1 kato:1 consists:3 sci:1 eη:62 devoted:1 inverse:1 sogo:2 analytic:2 integral:1 combinatorial:2 paris:1 description:1 according:4 tj:15 tk:3 ti:32 analogous:15 include:1 case:16 conjecture:8 proved:1 summand:1 straightforward:3 orthogonal:14 very:1 αh:1 wave:5 ed0:5 jack:34 difference:6 exact:2 partitions:4 awata:1 specify:1 accompanying:1 evaluation:1 permits:1 solution:3 try:1 ǫk:1 convenience:2 supplement:1 esi:1 eigenvalues:23 mκ:14 noted:4 zl:9 deformed:1 zn:9 says:1 zi:3 zj:100 zk:33 consistent:3 sin2:8 direct:4 integrability:1 further:3 ǫl:2 odd:2 substitute:1 theory:3 even:4 established:8 brackets:3 specification:2 version:1 en:1 establishes:2 new:5 ˆj:5 contributes:2 consisting:3 ˆn:2 body:4 κn:2 led:2 κi:1 κj:6 exchange:4 respectively:2 fock:1 component:1 eigenoperators:2 here:10 desired:1 them:1 cos2:2 groups:2 depend:1 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solv-int9610001.txt |@word represent:3 positions:2 darboux:1 consider:6 chain:1 similarity:2 depends:1 lack:1 desirable:1 results:8 four:2 scalar:8 proposition:29 consists:2 expressions:4 gl:4 gk:8 soc:1 whose:1 careful:2 nauchn:1 calculate:1 reformulate:1 funct:1 tr:5 ajj:3 nonlocal:5 tn:1 tm:3 tj:7 those:1 th:1 under:6 semenov:6 aux:4 analogous:6 include:1 presentation:2 g1:1 g0:5 very:5 springer:4 every:1 entries:4 tridiagonal:1 zeitschrift:1 difference:1 matrices:45 condition:14 dressing:1 dij:5 hamiltonian:25 turns:3 notes:1 sklyanin:5 solution:2 t0:1 involution:3 commute:1 math:6 subscript:2 indices:1 reyman:1 inspection:1 freidel:1 upper:1 mn:2 zj:3 zk:25 dealing:1 consistent:2 direct:13 b21:3 elegant:1 second:5 progress:1 further:4 dynamics:1 langmuir:1 odd:2 linear:13 subscripts:8 will:7 what:2 nonlinear:1 plays:1 stands:1 brackets:20 trivial:2 sum:11 analogously:1 expressed:1 maillet:1 nondegeneracy:2 zre:1 version:2 above:3 sixth:1 new:8 consisting:4 satisfy:4 full:2 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solv-int9610002.txt |@word gd:1 concept:2 consider:6 funct:2 results:2 four:3 eds:2 scalar:2 proposition:6 3a3:1 3a2:2 3a1:3 3a0:6 whose:3 inverse:1 clarification:1 iii:1 description:1 show:4 list:1 finally:4 tj:12 present:2 th:6 under:3 presently:1 takes:1 zhang:1 far:1 rise:3 geometrical:2 summarized:1 li:1 condition:1 3h1:5 3h2:5 3h3:2 hamiltonian:5 turns:1 t2:17 solution:2 discrete:3 vector:11 gauge:1 anal:2 inspection:1 solutions:2 discover:1 second:3 expressions:1 substitute:1 canonical:5 spectral:2 established:1 nonlinear:1 brackets:1 section:7 current:1 above:3 saldini:1 method:1 coefficient:2 full:1 respectively:2 realizations:1 here:2 behaviour:1 identifications:1 tangent:1 groups:1 based:2 equations:68 change:1 obtained:6 remark:4 oikawa:3 rests:2 study:1 studied:1 allows:1 resulting:1 action:1 implement:1 suitable:3 via:4 projection:4 family:2 bonora:2 merely:1 apply:1 select:1 h1x:2 use:5 asymptotic:2 double:1 positive:1 examined:1 negative:1 next:1 comparing:2 linear:4 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solv-int9610003.txt |@word darboux:1 consider:13 both:1 trigonometric:2 scalar:1 kowalewski:2 go:2 devoted:1 preserves:2 inverse:3 concerned:1 technique:1 tr:2 editors:1 recurrence:1 petersburg:2 th:3 under:1 semenov:1 γb:1 analogous:1 include:2 tc:3 ta:6 p2:1 g2:1 r12:13 r13:3 straightforward:1 returning:1 rise:1 choice:1 entries:4 matrices:36 deformations:1 notations:1 trl:1 hamiltonian:5 bn:1 sklyanin:3 list:1 solution:5 correct:1 large:2 involution:3 vector:1 indices:1 eigenvalues:1 reyman:1 shansky:1 mn:5 force:1 zk:4 direct:1 consists:2 integrability:4 fits:1 further:1 theory:6 spectral:17 aim:2 invertible:4 brackets:6 sum:1 3j:1 poles:3 subspaces:2 new:10 construction:2 method:7 contrast:2 simultaneously:1 degree:1 αij:5 multipole:1 respectively:2 realizations:2 here:7 canonically:2 fairly:1 possibility:1 separation:9 enveloping:2 equations:7 change:2 obtained:3 tian:1 divisor:1 institute:1 items:2 leaves:1 studied:1 allows:3 hbc:1 sjk:2 substituted:1 procedure:1 poisson:19 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solv-int9610004.txt |@word consider:2 chain:17 alg:1 splitting:1 leads:1 scalar:1 row:2 th:5 division:1 ˆji:1 g2:9 g1:9 returning:1 condition:2 hamiltonian:4 notes:1 involution:2 vector:1 severed:1 gromov:1 l2n:2 integrability:1 odd:1 even:1 nonlinear:1 invertible:1 section:1 contracted:11 new:1 method:3 ˆn:1 component:2 here:1 groups:1 sine:1 equations:14 z2:5 contraction:16 obtained:2 p2:1 resulting:1 poisson:5 contr:5 action:2 fourier:2 family:1 parma:1 virasoro:8 use:1 eψ:1 remains:1 ψp:3 ψj:2 ψi:2 call:3 therefore:1 diagrams:1 nauka:1 curvature:2 known:1 ural:1 eα:8 ρi:6 science:1 equation:10 ρj:2 ρl:2 klj:1 ρr:2 following:1 example:2 cartan:10 gˆ1:2 give:1 sokolov:1 something:1 arise:1 yang:1 leznov:1 product:1 algebra:19 may:3 after:5 par:1 diagram:2 lax:3 fi:6 fj:4 dynamical:1 lines:1 so:1 sect:1 sl:3 representation:3 hierarchy:2 roots:3 group:1 ln:4 affine:8 lj:1 coordinates:2 lect:1 degrees:1 systems:4 mail:1 deformation:1 they:1 das:1 2u:1 2v:1 2w:2 classified:1 orthonormal:1 applied:1 l0:1 2c:2 crossing:3 reproducing:1 subset:1 ei:5 2a0:1 ej:3 related:1 toda:15 quantum:1 transitions:2 ep:2 out:2 ru:1 shown:2 matrix:14 space:4 gradient:1 denotes:2 rc:8 denoted:1 ref:1 math:2 aˆn:1 linear:2 8c:1 free:1 limε:1 base:1 put:1 finite:4 language:2 gˆ2:1 transition:2 motion:6 gordon:1 δij:2 isl:1 initial:1 dynkin:2 rank:1 another:1 equating:1 given:2 bracket:8 introduction:1 system:7 least:1 1d:1 variational:2 academy:1 2ap:1 than:1 eρi:2 second:1 toward:1 russia:1 say:1 any:1 lie:4 zero:4 self:1 sciences:1 kac:2 formulas:1 centre:1 algebraic:1 phase:1 looked:5 points:1 exp:6 russian:2 akns:3 d4:4 d3:2 based:2 commutators:2 2bp:1 only:1 generators:4 equipped:1 integrable:7 oct:1 columns:1 made:1 dx:3 gen:1 αj:4 babelon:1 arxiv:1 investigate:1 qi:2 nα:2 qj:1 set:2 exists:1 hα:3 interacting:1 functionals:1 written:1 between:2 αi:6 invariant:1 irc:4 approach:3 nonsemisimple:2 terms:2 p2i:1 wt:1 ji:1 solv:1 configuration:1 last:3 many:1 kji:2 equal:2 admit:1 lm:2 simple:4 respect:1 considering:1 described:1 transformations:1 basis:1 three:2 int:1 pi:5 choose:3 corresponding:2 quantities:2 derivative:1 viallet:1 general:1 case:2 will:1 property:1 procedure:2 vol:1 thus:4 iw:2 vt:1 vw:1 different:1 split:2 φi:1 φj:2 several:1 subalgebra:3 used:1 i2:2 effect:1 kij:2 infinite:2 off:2 well:1 without:1 components:2 sets:1 position:1 usual:1 graded:3 drinfeld:1 λe:1 world:1 previous:1 easily:2 using:1 n2α:1 moody:3 loss:1 particle:1 ad1:1 δu:5 δp:2 δn:2 δh:2 δf:1 δg:1 reduced:4 because:2 some:4 examples:1 ˆij:3 kdv:7 2d:4 lead:1 grading:2 integration:1 connecting:1 saveliev:1 scientific:1 step:1 bp:3 bq:2 patera:1 column:3 freedom:1 o:1 baxter:1 contractions:7 into:1 obtaining:1 pair:2 references:1 sov:1 operator:2 algebras:6 there:8 u2:1 sociated:1 was:1 hu:1 hj:1 hi:20 elimination:1 october:1 ut:1 us:1 liouville:1 define:1 associated:2 ad:1 defined:1 abstract:1 denote:1 aq:1 ap:5 conserved:2 constructed:1 again:1 no:2 rewriting:1 field:1 other:1 department:1 mathematics:1 vanished:1 kinds:1 models:4 a1:4 commutator:2 a3:2 structure:1 eαi:1 n2:2
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solv-int9610005.txt |@word secondly:1 partial:2 consider:7 caused:1 results:2 gn:9 gm:23 certainly:1 const:1 equivalence:2 young:2 finally:2 under:1 multilinear:2 applied:2 rise:1 difference:7 condition:5 fukuoka:2 solution:17 try:1 discrete:41 mn:1 consistent:1 painlev:2 q1s:2 substituting:2 manipulating:1 expressions:4 bilinear:19 nonlinear:6 section:1 expressed:1 above:3 method:5 satisfy:4 κk:5 respectively:1 here:4 papageorgiou:2 equations:17 obtained:5 institute:1 study:2 suggests:1 examining:1 schur:1 technique:1 useful:1 divide:1 apply:2 readily:3 use:3 takes:2 nijhoff:1 next:2 ψj:1 comparing:1 ψn:3 therefore:1 volterra:2 more:1 becomes:2 operators:1 kokyuroku:2 encouragement:1 particular:3 must:2 ramani:4 science:2 equation:38 work:1 labeled:1 following:4 example:2 f1:3 f2:3 give:2 information:1 criterion:2 ordinary:1 simplicity:1 after:1 derived:3 diagram:1 hence:1 multiplication:1 fj:11 constants:4 effective:1 whenever:2 explicit:1 trilinear:1 so:3 sc:6 order:4 indeed:1 satisfied:3 scientist:1 including:1 satisfies:2 τn:42 derive:1 chosen:1 forms:9 choose:1 mail:1 defining:2 them:2 noticing:1 introduce:1 they:1 singularity:29 now:3 easily:2 university:4 kyushu:3 τnm:8 reduce:2 related:2 τnt:2 toda:2 expect:1 combining:1 eq:12 solved:1 since:1 crucial:1 research:1 looking:1 ref:2 math:1 whereupon:1 put:2 ministry:1 just:1 impose:2 consequence:1 first:3 variables:1 powerful:1 done:1 relations:1 directly:1 given:8 perturbation:1 introduction:1 eqs:7 system:1 construct:5 fn:22 gives:2 relationship:2 kenichi:1 σkl:1 continuous:2 authors:1 kenji:1 integrability:1 lotka:2 perturbative:1 zero:2 convenient:1 able:2 potential:12 take:1 finding:1 even:1 vnm:14 denominator:2 most:1 multisoliton:1 awk:1 nothing:1 soliton:19 kj:2 hungry:2 kp:6 ohta:1 tanabe:1 fact:1 supported:1 miwa:1 relation:4 solutions:6 keywords:1 earth:1 analogue:1 find:11 q1:4 based:3 µfn:1 parameters:1 integrable:2 oct:1 get:3 dependent:3 express:2 aδ:1 gen:1 δwk:2 arxiv:1 contain:2 through:6 qj:20 κl:2 art:1 utn:2 culture:1 depends:1 result:1 terms:5 pattern:11 diverge:1 written:1 routine:1 invariant:1 approach:1 discovery:1 preserve:1 notice:2 recently:1 rims:2 wk:6 wm:1 p2n:6 jp:1 however:1 vanishing:2 solv:1 article:2 come:1 σk:11 received:1 fnm:12 expression:3 cj:1 point:1 simple:1 mkdv:17 respect:1 gn2:1 transformations:2 three:2 int:1 reduction:2 pj:31 pk:10 pn:12 abstract:1 systems:2 suggested:1 determinant:1 arises:2 corresponding:1 both:1 confinement:6 c3:1 c2:6 c1:1 those:1 case:9 p0:2 p1:9 look:1 value:2 will:1 p2:2 aid:1 property:1 procedure:1 a21:1 a22:1 a23:1 wkl:7 jpn:5 thus:6 non:1 vn:9 im:1 vanish:2 technology:1 verified:2 grant:1 suggest:1 same:3 φj:1 finite:1 φn:3 difficult:1 independent:1 again:2 i1:2 i2:2 qjs:4 seta:1 tsujimoto:5 patterns:6 λa3:3 λa2:3 λa1:3 proposed:2 generally:1 grammaticos:4 obtain:11 intervals:1 integer:1 λk:2 ps1:2 previous:1 transformed:1 lett:3 transformation:5 psj:7 department:3 know:1 confined:7 using:4 formal:1 systematically:1 reduces:2 either:2 arbitrary:10 otsu:1 acad:1 methods:1 some:4 examples:1 moreover:2 proper:4 kdv:3 happens:2 proc:1 kyoto:1 equivalent:1 step:1 shifting:2 informatics:1 dictated:1 between:1 integers:1 concretely:1 constraint:1 numerator:1 introduced:1 automatically:1 soc:4 rev:1 into:4 δut:1 references:1 masayuki:1 sports:1 there:1 kasuga:2 dispersion:2 start:2 way:1 was:2 function:14 form:13 but:4 october:1 versions:1 ut:5 casorati:1 us:6 um:11 discretized:1 un:19 define:1 similar:1 mechanics:1 ac:1 constant:3 pin:3 defined:1 ak:3 generating:1 inm:17 engineering:1 exist:1 imai:1 education:1 simplest:1 constructed:2 satsuma:3 functions:3 nk:6 nm:1 no:1 when:2 vanishes:2 other:1 electrical:1 test:1 mathematics:1 conclusion:1 polynomials:2 µin:1 a1:50 a3:42 a2:47 dvt:5 variable:6 pi1:3 pi2:3 structure:1 algebraic:6 n3:104 implies:1 assume:5 required:1 observe:1 hirota:11 n1:102 n2:103 backward:1 requires:1 once:1
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solv-int9610006.txt |@word concept:1 partial:3 consider:11 equalities:1 global:1 leads:10 scalar:21 computation:1 gn:2 relationships:13 const:10 april:1 γi:1 manifolds:3 th:1 under:1 analogous:2 g1:1 orthogonal:3 very:1 geometrical:4 difference:1 matrices:1 rn:1 condition:6 list:2 solution:19 solved:1 vector:17 indices:1 gauge:3 ruslan:9 mn:7 force:20 specially:1 sin2:2 direct:1 sign:1 tex:1 second:9 further:2 recalculate:1 substitute:9 what:1 plays:1 section:1 3v:3 expressed:2 above:5 new:6 ˆk:1 told:1 satisfy:2 component:1 here:4 bi:8 refinement:1 tangent:6 groups:1 address:1 depend:11 along:2 equations:77 change:6 contraction:1 obtained:9 search:2 shift:22 vectors:1 reason:2 contradiction:1 spheres:4 proportionality:1 implement:1 makes:2 cancellation:1 via:4 spatially:1 projection:1 family:6 problematic:1 replace:1 brought:2 apply:5 unit:5 9v:1 derivatives:17 use:1 projector:3 prove:1 covariant:15 contains:10 closedness:1 m1:5 therefore:15 m2:2 taken:1 conservation:1 type:3 more:6 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solv-int9610007.txt |@word represent:1 partial:2 consider:4 remarkable:1 global:3 results:3 four:2 roy:1 kh:3 excludes:1 paris:6 equivalence:1 nonlocal:2 finally:1 does:4 excluded:1 stable:2 hermann:1 analogous:1 include:1 presentation:1 pickering:1 p2:10 conjecture:1 lack:1 very:1 pages:1 bulletin:1 choice:1 every:4 discretizations:1 affect:1 linearizability:1 exact:4 condition:4 school:1 eds:1 proc:1 notes:1 t2:1 applicable:3 discrete:48 indices:1 noted:1 12u:1 work:2 neighborhood:3 dealing:1 guidelines:1 second:9 ode:2 canonical:1 even:1 established:2 what:2 nonlinear:1 annali:1 section:3 celebrated:1 3u:1 version:1 en:1 sur:3 above:4 new:6 method:23 coefficient:1 degree:10 whose:2 respectively:2 never:2 here:5 papageorgiou:3 behaviour:1 les:1 groups:1 address:1 multivaluedness:1 shortness:1 equations:23 appears:1 change:1 conte:6 remark:1 algebra:1 amp:2 16t2:1 allows:1 adopt:1 situations:2 verhulst:2 studies:1 l58:1 useful:3 4a1:1 classification:2 search:3 manage:1 extraneous:1 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solv-int9610010.txt |@word invent:1 scalar:3 commute:1 whose:4 tj:22 tk:6 th:1 under:2 orthogonal:8 choice:2 jack:10 partitions:1 hamiltonian:5 vector:3 gauge:2 noted:2 zn:1 zi:1 zj:5 zk:3 sin2:1 direct:1 sign:1 second:1 even:2 tsuchiya:1 appear:2 section:1 expressed:1 version:1 fractional:1 bn:13 coefficient:2 confluent:1 simultaneously:1 exchange:2 respectively:1 here:1 groups:3 z1:1 change:3 differential:2 obtained:6 remark:2 studied:1 sjk:18 products:1 poisson:1 action:4 suitable:1 studies:1 named:1 via:1 apply:1 use:2 dunkl:6 distinct:2 humphreys:1 comparing:3 call:2 associated:3 type:18 more:1 operators:21 ti:1 appendix:2 isomorphism:4 tokyo:3 equation:4 work:1 labeled:1 fock:3 ms:1 following:6 making:1 trans:1 example:1 proof:2 give:1 calculation:1 states:3 dxj:1 turn:1 acts:3 orthogonality:4 sij:14 dominance:1 product:4 fs:4 algebra:2 may:1 after:1 fc:1 types:1 stress:1 element:3 sn:4 restriction:1 paper:1 japan:1 diagonalized:1 group:6 ln:2 2λn:2 tˆf:1 jacobi:1 mail:1 correspondence:1 non:5 introduce:6 they:3 acta:1 oxford:1 now:1 hall:1 eigenvalue:1 tonian:1 university:2 2x:3 2y:2 each:1 2n:2 characterized:1 homogeneous:1 weyl:5 hypergeometric:1 related:4 owing:1 quantum:2 our:2 shown:1 space:2 res:10 rep:1 since:4 rev:3 cww:1 rational:1 formula:1 get:1 math:5 clarify:1 ψ2n:9 eigenvalues:5 definition:2 interaction:1 omit:1 times:1 counterpart:2 ordering:4 δij:2 hence:1 first:1 xj:37 xk:12 xn:6 symmetry:3 laguerre:9 variables:1 relations:4 another:1 sutherland:5 xw:1 given:1 forrester:5 introduction:1 adjoint:3 system:1 construct:2 interests:1 relationship:1 part:1 x2:11 x1:6 kind:1 limiting:2 annihilation:4 determined:1 pasquier:1 self:2 note:3 sciences:1 potential:1 generalized:7 olshanetsky:1 shall:1 qalg:1 algebraic:2 but:1 nothing:1 eigenfunctions:5 partition:1 coincides:1 dimension:1 yang:2 exp:4 hamil:1 show:4 spaces:1 relation:2 analogue:2 d2:7 find:2 ground:4 based:1 state:4 should:2 bernard:1 bases:1 factor:1 integrable:1 γn:1 dn:1 dj:29 dk:4 notation:2 means:2 joint:2 dx:11 dy:6 meguro:1 arxiv:1 investigate:3 available:1 set:3 module:1 edition:1 see:1 commutation:3 review:1 λn:3 symmetric:14 written:2 permutes:1 between:1 invariant:3 subscript:1 x21:3 preserve:3 restricting:1 jp:1 however:1 solv:3 amer:1 diejen:2 x2k:5 x2j:8 f2n:6 context:1 expression:1 among:1 ci:3 coxeter:1 cn:1 conclude:2 harmonic:2 2nd:1 polynomial:5 respect:4 transformations:1 basis:8 create:1 been:3 int:3 symmetrizing:1 komaba:1 define:6 generating:1 subspace:1 x2n:4 catch:1 those:1 case:6 replaces:1 ǫj:3 value:1 aim:1 di:3 procedure:2 vectors:1 a26:1 a29:2 tions:1 ii:2 ic:3 generic:1 recursion:2 make:3 same:3 parts:2 arguments:4 constructed:3 used:1 hand:2 normalization:1 prescribed:1 reflection:2 components:1 coordinate:1 model:13 calogero:13 obtain:3 facts:1 multiplet:1 yamamoto:2 eigenstates:2 previous:1 renewed:1 preprint:3 haldane:1 macdonald:1 other:4 transformed:2 lett:1 excited:2 know:1 vacuum:3 press:2 using:7 advanced:1 follows:5 become:1 2dj:1 reduced:3 mathematical:1 classical:1 creation:5 some:3 gaudin:1 does:2 provides:2 obey:1 equivalent:3 wavefunctions:6 clarendon:1 bruhat:1 properties:2 generated:3 o:1 act:1 introduced:4 perelomov:3 soc:1 cambridge:2 jλ:8 references:1 operator:13 statistics:1 van:2 there:1 signifies:1 way:1 rela:1 function:1 form:4 extended:1 hj:5 hb:8 ha:1 applying:1 annihilate:2 up:1 below:1 called:1 aa:1 ac:5 constant:3 defined:1 abstract:1 aj:7 denote:3 tˆ:5 exist:1 formulation:1 formalism:2 commuting:2 physical:1 functions:5 wavefunction:4 detail:1 rewriting:2 setting:1 department:1 mathematics:1 theor:1 naive:1 conclusion:1 briefly:1 elements:6 ku:1 models:4 polynomials:30 a1:2 a3:2 a2:4 a5:3 a4:3 variable:2 structure:1 opdam:1 baker:5 cherednik:3 4n:1 equivalently:1 confinement:1 restricted:2
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solv-int9610011.txt |@word go:2 expressions:6 compact:1 whose:5 depend:2 finally:1 tm:419 present:4 th:7 under:15 tg:1 tb:4 itly:1 ta:10 g2:2 far:1 implicitly:1 difference:1 matrices:5 condition:8 solves:7 list:2 solution:4 t0:2 t1:36 discrete:3 small:1 biological:1 noted:1 cond:1 zero:2 further:1 dynamics:1 gm:7 index:1 what:1 nonlinear:1 suc:1 section:3 remain:1 expressed:1 version:1 goes:3 new:3 bn:6 nakamura:1 monodromy:1 coefficient:1 respectively:3 component:1 here:5 expansion:1 directions:1 equations:35 obtained:1 institute:1 shift:4 published:1 york:1 useful:1 although:1 family:4 plenum:1 modifying:1 scaled:1 asi:1 unit:1 use:1 yangian:3 prove:1 ψb:1 associated:3 ψa:2 type:3 bethe:3 diagrams:2 formally:2 initial:1 ti:1 appendix:1 known:1 ward:1 hold:1 iij:1 ma:1 tokyo:2 equation:26 work:3 det:16 labeled:1 values:1 indicating:1 following:20 cab:5 dec:1 root:2 example:4 beautiful:1 dedicated:1 f4:2 solved:1 sense:2 cartan:7 tab:1 arise:1 dress:3 lemma:4 rather:1 discussion:2 holds:1 leznov:1 answer:1 sij:5 parameter:2 mat:1 algebra:11 may:4 max:1 earlier:2 derived:1 diagram:3 date:5 representations:1 fm:12 types:1 natural:1 outline:1 lemmas:2 so:3 sm:11 representation:1 wiegmann:2 origin:4 parmentier:1 pointed:3 satisfied:1 paper:4 mentioned:1 ttb:1 its:2 thank:1 fix:1 affine:19 actually:2 systems:1 jacobi:3 kuniba:11 yi:4 non:2 yj:4 introduce:3 framework:1 pfaffians:3 they:4 now:2 yu:3 february:1 2r:3 university:1 2z:12 each:1 2m:11 2i:4 2j:6 mikhailov:1 series:1 reduce:9 related:1 toda:12 ex:1 combining:1 quantum:3 our:7 eq:7 out:3 jimbo:5 matrix:24 space:3 denotes:2 2δab:1 stud:2 rm:3 ref:5 math:6 theory:2 quite:3 e8:2 e7:2 e6:5 definition:1 phy:9 int:4 xj:5 xi:5 xn:3 peculiar:1 dynkin:5 twisted:1 construct:3 enumerate:1 xr:2 open:1 given:8 introduction:1 eqs:9 system:25 least:1 iab:4 their:1 convention:1 structures:1 interests:1 recursively:3 reflecting:1 than:2 kind:2 t3m:29 richer:1 determined:1 were:1 result:1 symmetries:1 argument:1 generalization:2 manuscript:1 any:3 viewed:4 lie:15 note:2 kac:2 fundamental:3 trace:1 shall:2 neatly:1 most:2 connected:2 formulae:3 nothing:2 t2m:146 future:1 class:2 soliton:3 considered:2 looked:2 ohta:1 ku:1 physics:1 fact:1 miwa:6 relation:5 solutions:23 keywords:1 substituting:1 d4:3 resemblance:1 knowledge:2 spite:1 should:2 analytic:3 only:2 explicitly:2 tsuboi:3 columns:1 dn:12 do:3 notation:2 express:1 ones:1 longest:1 suris:2 combinations:1 meguro:1 hij:5 zabrodin:3 dr:7 determinants:3 continuum:3 transposition:1 arxiv:1 summary:2 bab:2 ut:1 view:1 satisfy:2 set:3 constructing:1 j1:1 namely:1 w2:1 discussions:1 αa:11 written:3 αb:2 ladik:2 between:1 boundary:8 conditions:1 terms:5 sparsely:1 however:2 jl:1 densely:1 jk:1 solv:2 jetp:1 christiansen:1 f2m:5 expression:2 ansatz:3 solving:4 cn:6 cm:11 point:1 simple:7 had:1 corresponds:1 dimensional:1 polynomial:4 moreover:1 transformations:1 been:1 defined:1 pf:10 nato:1 algebras:7 komaba:2 determinant:6 relations:13 trices:1 fij:5 understand:1 those:2 case:8 disconnected:1 unlike:1 appearance:1 value:1 will:2 pressed:1 aij:2 jpn:10 a28:1 a29:2 refs:1 thus:3 them:3 ik:1 rij:4 il:1 rid:1 different:7 author:3 journal:1 acknowledgments:1 same:1 contents:1 proved:2 a2r:4 used:2 time:2 i1:1 upon:2 counterparts:2 v2:1 purpose:1 ablowitz:2 identity:3 tsujimoto:2 solve:1 components:1 firstly:4 model:2 eilbeck:1 proposed:2 resp:8 distribute:2 obtain:4 underlying:1 yet:1 trudi:1 character:1 except:1 lattice:3 analogue:1 valid:1 transformed:3 lett:4 theorem:7 tija:2 mod:2 solvable:3 transformation:3 bij:2 press:1 using:1 replace:2 moody:2 reshetikhin:1 nakanishi:2 necessary:3 like:1 sizes:1 follows:3 δr:1 δj:5 δi:2 δa:2 often:1 deal:1 back:4 cr:2 proofs:4 tmr:3 dense:1 olshanetsky:1 comments:1 tma:7 does:1 prof:2 saveliev:1 problems:1 equivalent:1 bi:2 bj:1 br:4 properties:2 tm0:1 would:1 getting:1 theorems:2 o:1 extensions:1 introduced:2 perelomov:1 soc:10 into:5 within:1 functional:44 references:1 sov:1 rows:1 hep:2 log:1 transfer:8 there:3 question:2 appl:2 lot:1 ed:1 was:6 suzuki:6 function:7 form:2 but:2 hm:9 removed:1 truncation:1 commun:3 compactly:2 whether:1 cij:4 uq:4 krichever:1 discretized:7 limit:1 minor:1 problem:1 similar:3 called:1 detailed:1 taylor:1 constant:1 ai:2 abstract:1 aj:1 denote:1 imai:1 commuting:1 physical:1 pfaffian:6 field:10 tary:1 other:3 tij:5 papers:1 node:4 elements:3 models:3 resembles:1 vertex:2 polynomials:3 deriving:1 a9:2 structure:1 auxiliary:4 assume:1 hirota:8
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solv-int9610012.txt |@word chain:13 magnetic:4 vasiliev:1 trigonometric:1 commute:1 follow:1 issues:1 inverse:1 terms:2 remarkable:1 quasi:1 present:2 th:2 under:3 include:3 indicating:1 subtleties:1 flicker:1 straightforward:1 zhang:1 far:1 erale:1 rise:1 translations:1 results:6 electron:2 wishes:1 difference:1 matrices:1 condition:1 hamiltonian:9 positions:1 t4:1 large:1 solved:4 math:3 relation:1 periodicity:1 consistent:1 sin2:1 jump:1 integrability:13 further:1 odd:1 linear:1 spectral:1 established:1 hansson:1 sum:4 uniform:3 version:3 3n:1 above:1 new:1 ever:1 filled:1 satisfy:1 condensed:2 full:2 exchange:4 here:1 agreement:1 asymmetry:1 involved:1 studied:2 allows:1 periodic:10 resulting:2 permutation:4 makes:1 cancellation:1 composed:1 regardless:2 projection:1 hermite:1 translational:1 summation:1 use:1 takes:2 usa:1 remains:1 therefore:1 type:1 until:1 untwisted:1 introducing:2 ecole:1 becomes:2 operators:7 surprisingly:1 basically:1 particular:3 known:1 hole:1 fermionic:2 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solv-int9610013.txt |@word partial:4 consider:1 generalize:2 consists:1 dist:1 disk:1 inverse:3 tu:2 manifolds:1 norm:2 far:1 wave:1 nonlinearity:1 linearizability:1 exact:1 condition:1 school:1 solves:1 ref:1 notes:1 t2:1 solution:5 solved:1 small:4 10n:1 estimates:1 direct:1 painlev:11 evaluated:1 aim:2 nonlinear:9 section:3 poles:1 above:3 sup:5 new:1 method:9 coefficient:1 respectively:1 here:4 desired:2 11k:2 alone:1 equations:13 implicit:1 change:1 obtained:2 kistler:1 convert:1 study:1 wherever:2 step:1 usually:1 suitable:4 makes:1 app:1 apply:5 use:1 would:1 prove:2 recalling:1 positive:3 contains:1 next:1 therefore:1 taken:1 australian:1 type:2 more:2 formally:2 definition:3 solitons:2 parabolic:1 surface:3 ramani:2 keeping:1 valued:1 equation:28 work:2 london:1 oct:1 deficiencies:1 obvious:1 following:4 petersen:2 example:1 proof:15 stated:1 process:1 numbers:4 council:1 sense:1 rescaling:1 conversely:1 influenced:1 end:1 notation:1 six:2 pure:1 ordinary:2 fr:1 fu:1 replacing:1 fran:1 after:2 singularities:2 movable:6 plane:5 da:34 clarkson:1 lemmas:1 element:1 hypotheses:1 so:7 order:3 sd:1 subsections:1 developed:1 produced:1 paper:2 through:5 satisfies:2 cole:2 its:2 difference:1 thank:1 ln:4 writing:1 osgood:1 wales:1 overcome:1 integrands:1 thereby:1 conversations:1 dan:4 practice:1 differentiated:1 daj:1 they:1 singularity:6 now:7 transparent:1 possess:1 represents:1 february:1 always:1 university:2 drop:1 sufficiently:2 each:2 found:2 2k:1 subset:1 domain:1 arxiv:1 series:7 deficiency:1 used:3 our:10 neighbourhood:4 rt:1 accomplish:1 furthermore:1 since:2 research:2 may:2 contained:1 geom:1 stud:1 lecture:1 get:15 induction:1 math:5 shows:1 tildes:1 linear:2 quart:1 aerodynamics:1 put:1 estimate:3 remainder:1 advance:1 recast:2 could:1 iterative:4 linearized:1 int:1 gordon:1 u22:1 hence:5 south:1 first:4 origin:3 there:4 variables:2 number:5 transform:1 restrict:1 simplified:1 blows:1 open:2 a3n:1 given:18 checked:1 similarly:1 introduction:1 leading:1 carnevale:1 their:2 echet:1 appl:2 a2n:1 statement:1 eqn:9 siam:1 1l:1 gives:4 holomorphic:14 calculations:1 recursively:2 proving:1 part:1 occurring:1 than:1 coefficients:1 roles:1 iteration:10 second:2 were:1 powers:1 generality:1 nuovo:1 ann:1 generalization:2 already:2 ka0:2 any:5 zero:1 min:4 lim:4 converges:1 note:9 take:1 vn:6 begin:1 philadelphia:1 cois:1 though:1 satisfy:1 pair:1 acknowledgements:1 tξ:3 laurent:1 consequences:1 segur:3 show:3 supported:1 12l:2 converge:1 implying:1 spaces:2 joshi:4 solutions:3 find:3 completion:1 devries:2 indicator:1 inductive:1 ba1:4 written:2 should:2 analytic:1 only:2 equipped:1 integrate:2 integrable:2 hopf:2 continuity:1 dominant:1 klein:1 means:1 obtain:1 dt:1 dr:1 evolution:3 showed:1 conditions:1 differential:6 expansions:2 da0:4 fixed:5 bak:3 ignored:1 set:1 exists:3 bounds:1 namely:1 result:1 surfaces:1 said:1 learnt:1 give:1 enough:2 between:1 approach:2 meromorphic:3 notice:1 terms:3 uux:2 nature:1 uut:1 however:1 reproduces:1 hypothesis:3 key:1 solv:1 last:2 reported:1 according:1 connection:1 comm:2 pde:3 arbitrarily:1 point:6 adaptation:1 moreover:3 throughout:2 diff:1 described:1 union:1 locally:3 odes:1 been:2 johannes:1 35q53:1 dropping:1 u12:1 ak:1 define:5 corresponding:1 5k:1 sufficient:3 6k:4 derivative:2 c2:5 general:2 present:3 noncharacteristic:4 case:1 reciprocal:1 straighten:1 value:1 will:12 near:6 suppose:3 property:6 procedure:2 vj:3 uxx:1 ii:1 itself:1 vanish:2 different:1 develop:1 φx:1 lett:1 same:1 complex:1 widely:2 showing:1 φn:1 literature:1 see:3 nj:1 v0:4 ablowitz:5 expand:1 relies:1 off:3 changes:1 well:1 burgers:13 without:1 solve:1 convenient:1 manifold:4 proposed:1 newton:1 solvability:1 using:7 scattering:3 blow:2 announcement:1 regarded:1 conclude:1 except:1 weiss:2 location:1 sydney:1 theorem:12 okn:2 transformation:2 real:2 australia:1 around:2 depends:1 2u:1 replaced:1 biholomorphism:1 term:1 early:1 press:1 integer:3 ams:1 unique:1 formal:3 loss:1 necessary:3 like:1 follows:2 yields:1 arbitrary:4 become:1 mathematical:1 because:4 classical:1 sequence:6 some:1 oln:5 respect:1 proofs:1 kowalevski:2 integration:1 does:4 korteweg:2 o4:1 o1:1 o0:3 ba:1 power:2 tabor:1 11l:2 kruskal:3 martin:1 expansion:4 ol2:1 although:2 substitution:2 refers:1 properties:1 about:2 ol:1 ok:7 quasilinear:1 o:2 informing:1 os:5 cambridge:2 convergent:1 into:3 integral:4 lies:2 references:2 lemma:11 operator:2 nsw:1 nirenberg:3 assumed:4 initial:1 u1:15 u0:7 u2:10 start:1 cauchy:4 treves:1 was:4 function:11 form:5 extended:1 volume:1 heat:2 convergence:3 line:2 pdes:1 iterates:3 made:1 ux:2 society:1 whether:1 ut:7 up:5 us:1 un:26 limit:2 utt:1 stages:1 similar:1 agree:2 taylor:1 defined:2 abstract:4 denote:2 single:1 proves:1 interchanged:1 check:1 functions:3 cim:1 integrability:1 no:2 fixing:1 other:1 details:1 test:1 mathematics:2 elements:1 symbol:1 a0:4 meaning:1 bounded:3 variable:1 implies:4 assume:7 dτ:9 together:1 littman:2 having:1 once:1
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solv-int9611001.txt |@word sci:1 consider:7 global:1 rod:1 results:1 four:2 disc:1 edu:2 go:1 primes:1 research:2 compact:5 whose:6 preserves:1 maximally:1 depend:1 paris:2 concerned:1 γj:1 those:2 elliptic:7 under:3 hermann:1 analogous:1 norm:2 applied:1 stud:2 erale:2 continues:1 connects:1 choice:2 corollary:5 every:1 summarized:1 fac:1 fǫ:10 condition:2 entire:3 school:1 riemann:6 level:2 positions:1 tokyo:1 solution:16 large:4 solved:1 small:15 rk:6 noted:1 degeneracy:4 upper:2 encloses:1 mi:3 estimates:3 direct:2 sign:1 surrounding:1 painleve:1 zy:4 pass:2 odd:1 theory:4 residue:1 aim:1 nonlinear:2 appear:1 rate:2 giving:3 section:7 expressed:1 poles:26 odes:2 above:4 sup:11 new:8 contributes:1 method:1 satisfy:2 respectively:2 component:2 here:2 drei:1 reported:1 les:3 pub:1 path:17 along:5 equations:33 z1:36 z2:3 z3:1 obtained:2 search:3 rigorously:1 study:1 garnier:1 zn:1 commonly:1 spheres:3 resulting:2 published:1 makes:2 york:2 via:1 regardless:1 projection:3 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solv-int9611004.txt |@word consider:5 chain:3 magnetic:2 results:2 kato:1 compact:2 finally:1 th:1 under:5 include:1 supported:1 g1:5 zhang:1 very:1 erale:1 electron:4 exact:2 condition:24 hamiltonian:3 large:1 kondo:1 pbc:1 dealing:1 sin2:2 zero:1 odd:5 linear:1 even:3 sub:3 section:2 current:6 ever:1 satisfy:1 condensed:2 full:13 exchange:4 here:1 understanding:1 threads:1 strong:1 obtained:3 great:1 antisymmetric:1 study:1 studied:1 conduction:1 periodic:1 formulated:3 translational:1 total:1 takes:4 distinct:1 negative:4 next:1 few:1 therefore:1 taken:1 ecole:1 yokoyama:1 cases:1 hold:1 iii:1 fermionic:4 keeping:1 science:1 work:2 following:8 wang:8 states:1 subregion:1 numbers:6 provide:1 divided:1 length:1 write:1 how:1 symposium:1 coleman:1 sin:12 product:2 mat:3 may:3 plane:2 waves:2 correlation:1 discussion:1 wiegmann:1 prefactor:1 eigen:2 ruckenstein:1 satisfied:2 through:1 japan:1 satisfies:4 still:1 before:4 regions:2 thank:1 energies:3 interesting:2 boson:4 systems:3 non:5 propose:1 half:1 nov:1 now:1 discuss:1 eigenvalue:4 finite:1 filling:2 l2:9 each:1 found:5 ed:1 energy:15 idea:1 quantum:5 our:2 operation:1 eq:6 hcs:6 impurity:1 space:2 since:5 rev:19 particles:4 denoted:2 math:3 foundation:1 theory:1 interactions:1 care:1 interaction:2 chiral:1 kunz:1 impose:1 stafford:1 first:2 xj:27 xi:33 xn:32 symmetry:2 number:2 system:10 reached:1 ring:4 sutherland:12 taniguchi:1 given:10 twisted:15 indicate:1 zeros:1 fermions:5 exactly:3 part:2 x2:20 x3:6 x1:13 roles:1 sections:1 matter:2 perturbative:1 mind:1 spectrum:9 exchanging:2 take:2 any:3 studying:1 calogero:6 physique:1 liu:4 insights:1 shastry:5 luttinger:1 typeset:1 proceedings:1 yang:3 physics:2 doped:1 solutions:2 find:3 ground:25 spite:1 inozemtsev:1 gebhard:1 state:25 should:3 only:1 do:1 de:2 yielded:1 ones:1 mattis:1 arxiv:1 summary:2 activity:1 switzerland:1 16th:1 national:1 correlations:1 lausanne:2 satisfying:1 symmetric:3 written:2 closed:1 invariant:1 boundary:19 approach:1 available:1 however:1 ln2:4 jm:1 wu:1 solv:1 both:1 σi:4 σn:4 many:1 region:10 eth:1 disappears:1 ch:1 simple:1 corresponds:1 anti:2 cs:4 described:1 due:1 been:1 int:1 define:2 corresponding:2 furuya:1 andrei:1 spin:4 those:1 case:5 pacs:1 will:2 while:2 suppose:1 situation:2 property:1 taking:1 played:1 site:2 ii:1 need:1 cond:3 fermion:5 currents:1 different:2 hubbard:2 check:1 conversations:1 several:1 phb:1 effect:1 moving:1 hopping:1 well:1 obviously:1 kawakami:1 without:3 swiss:1 model:12 usual:1 eigenenergy:2 haldane:6 lett:10 kuramoto:2 iπ:1 solvable:3 eigenstate:1 iφ:4 spinless:15 eorique:1 using:3 variants:1 mod:2 follows:3 reduces:3 flux:11 polytechnique:1 translated:3 therein:1 parity:1 deal:1 b4:1 examples:1 provided:4 affects:1 tube:2 wavefunctions:4 notable:1 revtex:1 eiφ:4 integers:4 discussed:1 range:2 r1:10 obeys:1 introduced:1 lieb:2 presence:4 into:1 references:2 bosonic:2 statistics:1 institut:1 there:6 long:2 anderson:1 bosons:5 way:2 was:1 eg:5 function:5 form:7 but:1 delta:1 ha:1 considerable:1 made:1 compute:2 wish:1 inside:6 us:4 below:3 limit:1 problem:4 similar:1 constant:1 defined:4 exist:1 gruber:3 ni:7 nj:21 no:1 wavefunction:24 when:8 other:3 lowenstein:1 details:2 stat:1 excitation:3 models:2 gas:11 important:2 jastrow:3 independently:1 coupling:1 assume:1 holes:1 persistent:7
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solv-int9611005.txt |@word represent:2 since:1 consider:2 trigonometric:1 eds:1 commute:2 entropy:1 2n2:8 expressions:2 nwo:1 compact:1 whose:3 eα:8 supported:1 quasi:2 onderzoek:1 excluded:1 materie:1 analogous:1 must:1 tb:4 ta:11 octagonal:2 choice:1 every:1 entries:1 li:1 matrices:1 wipe:1 trh:1 tilings:1 tra:2 solution:2 labels:2 solved:5 convenience:1 vector:2 indices:1 relation:1 noted:1 configurations:7 upper:3 zn:2 periodicity:1 cosh:1 past:1 fold:1 integrability:4 canonical:2 spectral:1 abc:1 invertible:2 incompatible:1 diag:1 sum:7 associate:1 analogously:1 aperiodic:1 subspaces:1 method:1 contrast:1 satisfy:4 full:1 respectively:1 here:3 following:6 ansatz:10 sinh:105 xν:2 xβ:4 xα:4 equations:8 change:1 obtained:1 vectors:4 allows:1 rhombus:1 accomplished:1 products:1 permutation:2 action:7 makes:1 der:1 y12:4 via:2 family:2 a21:3 a22:1 a23:4 sgn:1 summation:1 apply:1 clockwise:1 use:2 projector:1 would:1 sake:1 abbreviations:1 contains:1 substitutions:1 depicted:1 going:1 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solv-int9611006.txt |@word ibid:1 homomorphism:2 consider:6 chain:3 rev:3 unique:2 results:7 integration:1 vpm:3 scalar:28 proposition:40 mp2:3 computation:8 mp1:3 follow:4 expressions:2 centers:1 kurims:2 whose:3 inverse:1 calculate:2 eigenbasis:14 eigenvalues:3 technique:1 contained:1 tn:3 those:1 th:4 under:2 analogous:1 must:1 tb:12 tc:5 norm:9 ta:36 kσ:10 case:33 ωm0:9 vǫ:2 r12:1 straightforward:3 orthogonal:15 far:1 mpm:3 exception:1 dokl:2 corollary:1 isomorphism:3 putting:1 jack:17 entries:2 emphasized:1 difference:1 exact:2 condition:4 partitions:1 entire:2 obvious:1 hamiltonian:13 irreducible:28 notes:1 t2:3 t0:11 t1:3 large:1 involution:1 vector:20 math:10 indices:1 relation:15 cms:1 degeneracy:1 application:1 zn:33 mn:56 zi:27 zj:15 submodules:6 ρm:5 sin2:1 direct:1 sign:2 past:1 second:3 proved:1 dynamics:1 canonical:3 spectral:1 established:1 what:2 appear:2 invertible:1 giving:2 d2:1 specification:2 ρs:2 expressed:1 version:2 poles:1 tkm:1 subspaces:4 bm:49 gl1:3 gl2:2 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solv-int9611007.txt |@word partial:2 rev:4 results:2 commute:1 grateful:1 expressions:1 contributions:3 row:1 particles:3 inverse:2 calculate:1 fellowship:1 those:1 fermionic:3 straightforward:1 wishes:1 every:1 difference:1 matrices:6 condition:1 hamiltonian:7 sklyanin:2 solution:2 indices:1 originally:2 foundation:1 arnimallee:1 sign:1 integrability:3 picked:1 iσ3:1 canonical:1 spectral:6 nonlinear:1 iterating:1 sum:1 above:2 new:1 method:2 satisfy:1 exchange:1 respectively:1 here:5 growing:1 china:1 ansatz:2 sinh:15 address:1 sine:2 19a:1 z1:6 z2:4 19b:1 bj:1 luther:1 institute:1 study:2 studied:1 action:4 makes:1 vic:1 integrations:1 gordon:2 decrease:1 b225:1 tools:1 b220:1 use:1 prove:2 contains:1 nucl:4 relativistic:2 type:3 bethe:2 more:2 introducing:1 xian:1 operators:2 award:1 eν:2 berlin:2 known:1 hold:1 must:3 deformed:1 equation:11 zhao:1 vega:2 following:1 example:2 indicated:1 give:3 calculation:2 expanding:1 numbers:1 sense:2 information:1 fortunately:1 s1:1 means:1 nontrivial:1 pure:1 coleman:1 parameter:4 sin:10 yangbaxter:1 product:4 fu:1 algebra:2 after:3 different:2 fb:1 lax:1 physik:1 kulish:1 explicit:1 korepin:1 su:1 st:3 ones:1 so:5 sl:1 sb:1 order:4 six:5 fν:3 course:1 its:3 before:3 derive:1 rapidly:1 thank:1 τi:1 ln:2 interesting:2 destri:1 actually:1 systems:1 main:1 defining:3 b275:1 they:1 nov:1 now:2 yu:1 easily:1 term:1 university:1 2c:3 found:2 mean:1 baxter:5 int:2 differential:4 ei:2 series:1 related:1 inhomogeneous:1 obtains:1 quantum:7 out:1 shown:3 matrix:37 space:3 since:3 crucial:1 research:1 increase:1 attracted:1 stud:1 math:3 shows:1 commutation:1 mφ:1 theory:1 diagonal:2 wanted:1 definition:1 interaction:1 derivation:1 counterpart:1 ordering:1 length:1 massive:6 hence:3 teor:2 think:1 first:2 staggered:1 humboldt:1 variables:5 relations:2 directly:2 given:6 introduction:1 equ:6 system:7 construct:2 fermions:2 equs:3 gives:4 discussion:1 takhtadzhyan:2 nahm:1 part:3 authors:1 b230:1 cosh:3 coefficients:2 determines:2 zero:1 limiting:1 were:1 rewrite:1 ann:1 modern:1 manner:1 seen:1 rittenberg:1 strength:1 angle:4 depending:1 lim:1 latter:1 note:4 finding:1 even:1 trace:1 normal:1 decreasing:1 most:1 connected:1 pair:1 tensor:4 fiz:2 especially:1 calculated:1 zhou1:1 yang:5 exp:3 left:3 physics:1 show:3 relation:3 find:3 postulates:1 parameters:2 should:2 entities:1 only:1 generators:3 factor:1 integrable:4 exchanged:1 get:2 de:2 cannot:1 dz:2 schotte:2 dx:2 dt:1 alexander:1 continuum:2 fields:2 arxiv:1 expansions:2 common:1 constructing:1 see:4 result:1 interacting:1 between:2 fermi:1 boundary:1 approach:1 multiplied:1 however:2 solv:1 jetp:1 both:1 σi:2 last:1 limits:1 taking:3 equal:1 april:1 q11:2 contribution:1 b290:1 colons:1 simple:3 dimensional:1 distinguish:1 simply:1 respect:1 frg:1 transformations:1 pu:1 equations:2 been:1 defined:2 much:1 interest:1 choose:1 zamolodchikov:1 corresponding:1 quantities:2 berezin:1 present:2 case:2 exponential:1 pacs:1 will:2 dept:1 monodromy:6 refs:2 thus:1 im:1 ic:6 fermion:2 lengthy:1 d11:1 d19:1 same:1 northwest:1 pauli:2 used:4 moving:2 identity:1 pht:1 off:1 acknowledgement:1 studying:1 model:26 self:1 usual:2 graded:2 just:1 summed:1 scattering:1 adv:1 weiss:1 add:1 other:2 combine:1 lett:3 easy:1 solvable:1 transformation:1 momentum:2 iφ:2 australia:1 press:2 using:3 postal:1 saleur:1 mod:3 reshetikhin:1 like:1 specific:1 anti:1 works:1 therein:1 right:3 classical:1 q22:2 choosing:1 neglecting:1 univ:1 dz1:2 dz2:2 refer:1 faddeev:2 equivalent:1 expansion:1 described:1 imaginary:3 super:5 von:1 about:1 dze:1 algebraic:3 column:1 melbourne:1 consequently:1 integral:2 references:2 sov:1 operator:1 bosonic:3 transfer:4 u2:4 describes:1 way:1 parkville:1 form:3 but:1 repeatedly:1 he:1 whether:1 mat:2 up:1 us:3 limit:2 problem:3 similar:3 called:1 constant:1 ai:1 abstract:1 conserved:3 check:1 tedious:1 whereas:2 supermatrices:1 field:1 b14:1 valid:1 really:1 conclusion:1 elements:2 generates:1 zhou:2 symbol:1 thirring:18 vertex:5 includes:1 important:1 thacker:2 parities:1 structure:1 implies:1 auxiliary:1 saclay:1 weights:1 time:1 starting:1
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solv-int9611008.txt |@word represent:1 partial:2 consider:13 gq:2 nonsingularity:4 results:1 leads:1 roy:1 commute:1 grateful:1 consists:1 customary:1 expressions:3 research:2 gj:8 gi:30 3m:1 devoted:2 inverse:1 depend:7 calculate:2 aνµ:14 ego:1 presents:4 funk:1 th:1 under:19 analogous:6 applied:3 expressing:1 orthogonal:4 very:2 frequencies:2 dokl:2 choice:2 corollary:3 every:3 scholarship:1 difference:1 condition:9 founded:1 dubrovin:16 riemann:2 hamiltonian:28 solution:9 t0:2 leave:3 involution:1 vector:2 math:1 small:7 vµν:1 degeneracy:1 deformed:1 averaged:5 foundation:1 const:3 consistent:1 approximation:1 zero:23 tangential:3 nonhomogeneous:1 follow:3 further:2 linear:17 nonlinear:4 adds:2 appear:1 brackets:45 giving:3 sum:4 ktα:1 expressed:9 nondegeneracy:2 stα:1 above:20 replaced:3 method:19 satisfy:8 full:8 respectively:12 here:7 explore:2 situation:12 represented:4 consideration:4 along:2 maltsev:4 equations:24 appears:2 change:4 contraction:1 obtained:6 remark:1 ǫx:4 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solv-int9612001.txt |@word similarity:1 lack:1 trigonometric:5 roy:1 pearce:2 gc:9 follow:1 expressions:5 referring:1 graph:1 tl:4 present:3 presentation:1 string:1 g1:1 orthogonal:1 coloured:1 print:1 matrices:11 uwe:1 notations:1 presented:1 rmatrix:1 suffices:1 solved:1 indices:2 relation:2 unexpected:1 past:1 fold:1 wherefore:1 odd:1 spectral:1 index:3 section:1 above:2 new:5 contrast:1 satisfy:2 full:1 respectively:2 here:3 groups:2 concluding:1 fifteen:1 obtained:2 trans:1 suitably:1 colourings:1 products:1 suitable:1 quotient:2 via:1 projection:1 inverses:1 unit:1 would:1 commun:1 contains:1 nucl:2 type:7 twists:2 diagrams:3 operators:3 basically:1 known:5 cases:1 eα:18 eβ:6 equation:4 london:2 theories:1 besides:1 labeled:5 values:2 dec:1 example:1 compare:1 links:1 give:2 involve:1 sense:1 species:1 g2:1 acts:1 braids:5 rsos:3 occur:1 instead:1 ordinary:5 parameter:2 sin:15 yangbaxter:1 product:3 algebra:31 derived:2 hence:2 physik:1 representations:26 types:2 realized:1 short:1 natural:1 explicit:3 so:1 representation:7 birman:6 restriction:1 interpretation:4 indeed:1 over:1 move:1 years:1 symbols:2 course:1 including:2 statistical:1 mentioned:2 satisfies:1 braid:4 before:1 derive:1 interesting:2 affine:1 fruitful:1 defining:6 setting:1 nienhuis:2 mismatches:1 thereby:1 murakami:6 introduce:3 they:1 bazhanov:2 now:3 easily:1 inversion:1 temperley:5 invariants:2 level:1 crossing:1 universit:1 2i:1 baxter:7 ei:1 ej:3 series:2 osaka:1 idea:1 related:6 seaton:1 toda:1 expect:3 combining:1 quantum:5 eq:3 special:1 jimbo:2 matrix:7 space:5 restricted:1 furthermore:2 since:1 rev:1 denotes:2 content:1 acting:3 denoted:1 ref:7 math:4 shows:1 customarily:1 theory:4 completely:1 members:1 bwm:15 definition:1 pairs:1 hinting:1 keep:1 turn:1 technische:1 consequence:1 generalizations:1 first:1 already:1 dynkin:1 number:1 rank:1 exact:1 dilute:12 relations:11 directly:1 carry:3 2nc:3 given:7 grimm:7 introduction:2 leading:1 eqs:1 system:1 construct:2 roche:1 their:3 statement:1 underlie:1 wenzl:6 recovered:1 relationship:1 continuous:1 lists:2 branches:1 namely:1 determined:1 were:1 yba:1 ybe:5 paths:1 generalization:2 warnaar:5 any:3 lie:3 built:1 zero:1 note:3 build:1 finding:1 exactly:2 opposite:1 akutsu:1 most:1 boltzmann:1 involving:1 germany:1 pair:2 considered:1 physica:1 graphs:1 yang:5 exp:2 physics:1 precise:1 particularly:1 labels:1 discovered:1 purely:1 spaces:1 gauge:2 solutions:8 rough:1 d2:4 d1:6 q1:1 symmetric:1 q2:1 based:3 parameters:3 only:4 explicitly:1 generators:11 integrable:2 interested:1 dn:2 do:1 triangle:1 means:1 dc:8 famous:1 cannot:1 lattices:1 symmetrically:1 arxiv:1 yield:1 book:1 qc:28 diagrammatic:2 through:1 requirement:1 set:1 constructing:1 connections:1 see:2 result:1 recently:1 techniques:1 still:1 tensor:4 monoid:2 label:2 colours:6 closed:2 between:2 approach:1 irf:1 terms:1 complementary:2 solv:1 problem:3 both:2 many:2 equal:1 connection:1 expression:1 among:1 uct:1 cn:1 appeared:1 dimensional:1 non:1 polynomial:1 moreover:1 rep:1 considering:1 transformations:1 addition:1 equations:1 been:3 defined:1 reduction:2 pj:6 ph:1 algebras:7 define:1 graphical:2 bma:5 partly:1 understand:2 demand:1 general:1 spirit:1 those:2 case:2 multi:1 solid:2 theoretical:1 deguchi:1 procedure:3 planar:1 vc:1 refs:3 thus:4 site:1 ic:19 vanish:1 different:2 same:1 several:1 higher:1 used:2 trivially:1 cubic:2 i1:1 i2:1 colouring:1 task:1 scenario:1 colour:17 well:1 academic:1 without:1 sets:1 model:2 monoids:1 usual:1 obtain:1 underlying:2 scattering:1 previous:1 generator:1 exclusively:1 lattice:8 baxterization:6 lett:4 relevance:1 mod:1 solvable:13 transformation:1 generalized:1 iλ:1 around:1 results:1 possible:2 spanned:1 fusion:5 know:1 knot:3 press:1 apart:1 imposed:1 follows:2 reduces:2 yields:2 δi:1 δc:2 sketch:1 because:1 classical:1 some:2 understood:1 elements:4 examples:1 chemnitz:2 δj:1 proc:1 demonstrated:1 bc:1 problems:1 bn:1 bj:7 although:1 refers:1 simpler:1 central:2 algebraic:2 discussed:1 wadati:1 o:5 regular:1 act:3 introduced:1 projectors:2 lieb:5 soc:2 within:1 remarks:1 references:1 determine:1 institut:1 additional:1 elastic:1 quadratic:1 way:1 function:1 complete:1 form:1 denoting:1 but:1 construction:6 link:3 encoded:1 arrays:1 us:2 ur:1 ωc:8 similar:1 called:2 mechanics:1 associated:3 percolation:2 int:2 certain:4 abstract:1 am:1 denote:1 loops:2 single:1 corresponding:4 moves:1 constructed:4 nc:2 field:2 other:4 details:1 kauffman:1 mathematics:1 briefly:1 repeat:1 zhou:1 models:19 vertex:8 polynomials:1 generated:1 ising:1 jones:1 2d1:1 factorized:1 factors:3 weights:1 resembles:1 n1:1 n2:1 starting:1 strings:3 labelled:1
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solv-int9612002.txt |@word represent:1 pang:2 allows:1 possess:1 consider:2 chain:2 being:2 when:3 supported:4 results:3 chaos:1 scalar:1 commute:1 relation:1 φm:3 satisfies:1 steklov:3 nieto:2 d0:8 ground:2 rˆ:2 now:2 calculate:1 bullough:4 density:6 ln:7 explain:1 seems:1 state:2 boson:2 pomi:1 lattice:3 absence:3 potential:1 petersburg:6 th:1 factor:1 acknowledge:1 mail:3 dq:6 fin:1 momentum:2 interacting:1 non:1 comm:1 means:1 dependent:2 de:4 semin:1 comparing:1 introduce:1 eorique:1 superieure:1 they:1 vacuum:1 press:1 using:4 bogoliubov:6 du:1 represented:2 dp:6 πd0:2 easily:1 determinants:1 like:2 particle:3 hamiltonian:2 timonen:2 university:3 arxiv:1 solution:1 sin:12 leave:3 xy:1 math:2 2l:1 through:1 universit:1 hospitality:2 optics:1 vacancies:1 mean:1 mathematical:3 kernel:3 set:1 ei:5 classical:1 foundation:1 ee:2 ed:1 energy:2 journ:1 fr:2 see:3 elements:1 bare:1 quantum:1 our:1 2πij:1 odd:1 different:2 bilinear:1 will:2 lyon:4 nonlinear:1 darkness:2 eiθ:2 rep:1 rev:4 sites:2 expressed:1 research:3 particles:5 fellowship:1 defined:3 difficulties:2 simplest:1 call:1 fermi:4 before:1 method:1 filled:1 temperatures:1 satisfy:1 savoie:1 xˆ:1 recently:1 written:1 slavnov:1 here:1 standard:1 paper:1 pressure:2 cambrige:2 formation:3 ansatz:3 although:1 solv:1 equations:3 half:1 mod:1 projector:1 box:1 integers:2 limiting:1 last:1 would:1 impenetrable:1 institute:5 similar:1 finland:2 m0:2 equal:1 o:1 kitanine:3 energies:1 products:1 fredholm:4 ilp:1 published:1 identity:1 complicated:1 other:1 lakshmanan:1 first:1 therein:1 xx0:1 2nn:1 probability:4 point:1 appeared:1 more:1 formulae:1 integral:6 number:2 negative:1 r44:1 en:1 references:2 relations:2 representations:3 operator:6 total:1 zap:1 tognetti:1 kernels:2 use:1 lenard:1 temperature:4 vˆ:5 intensively:1 there:2 quasi:2 construct:1 france:1 italie:1 their:1 bosons:1 asymptotics:3 way:1 pj:2 pk:4 r33:1 was:3 bethe:5 iˆ:5 function:6 obtained:4 determinant:3 complete:1 fontanka:3 ecole:1 academy:1 operators:8 exactly:1 new:2 hu:1 nauch:1 expected:1 part:2 tan:2 integrable:2 russian:1 tft:1 general:1 peculiar:1 must:1 case:5 eip:1 p0:4 october:1 full:1 grant:1 solvable:1 equation:1 work:1 det:4 zero:4 correlators:2 project:1 while:1 determined:1 limit:3 theoretical:2 were:3 following:4 distribution:1 dec:1 matrix:3 russia:3 nikolai:1 studied:1 iθ:2 int:1 ip:1 abstract:1 site:1 hµ:1 states:2 sphere:1 ij:1 dθ:2 enslapp:4 handled:1 r23:1 r22:1 constructed:1 functions:9 emptiness:1 thermodynamical:1 form:6 depending:1 rather:1 occupied:1 fractals:1 r11:1 physique:1 eigenenergies:1 same:1 fermion:2 chemical:1 very:2 ens:1 thermodynamics:2 solitons:1 department:3 so:1 φj:1 finite:1 izergin:3 φn:3 heisenberg:1 even:1 cnrs:2 used:2 fundamental:1 excitation:1 shall:1 models:3 laboratoire:1 time:2 nj:1 dependence:1 express:1 algebraic:3 property:1 mae:2 representation:4 phase:12 fi:1 associ:1 shown:2 commutation:2 eigenvectors:1 normale:1 calculation:2 ura:1 hopping:2 helsinki:3 considered:1 values:1 calculated:1 no:1 korepin:3 st:6 proposed:1 points:1 solve:1 free:2 exp:12 correlation:10 thank:1 velocity:1 model:20 physics:2 lett:3 lynch:1
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solv-int9612006.txt |@word consider:1 pointing:2 results:2 existing:1 four:2 go:1 expressions:1 research:1 reasoning:1 devoted:1 const:1 paris:1 subjected:1 finally:3 elliptic:1 dressing:1 case:1 ginn:1 erale:1 rise:6 difference:4 condition:1 presented:1 turns:1 leave:1 discrete:31 vector:2 small:3 gauge:1 der:1 sapienza:1 za:1 second:3 further:1 dynamics:1 linear:1 bilinear:1 what:1 nonlinear:1 appear:4 section:3 version:4 sur:1 above:6 new:4 net:9 method:4 satisfy:1 full:2 objects:1 tangent:5 address:1 directions:5 consideration:1 sine:1 equations:15 z2:2 remark:5 dec:1 institute:1 vectors:1 periodic:3 suitable:1 via:1 useful:2 family:3 pinkall:2 santini:4 des:1 use:2 proceed:1 working:1 nijhoff:3 jpn:2 negative:1 next:1 m1:8 moro:1 m2:2 type:1 theoretical:1 linden:1 th:2 company:1 under:1 curvature:1 berlin:1 particular:2 known:2 projective:7 ward:1 must:3 springer:1 recall:2 equation:19 work:1 remain:1 following:4 trans:1 example:2 stimulating:1 korepanov:1 give:3 ratio:2 darboux:2 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solv-int9612007.txt |@word partial:1 consider:2 pointing:2 varying:1 results:1 four:7 eds:3 scalar:2 edu:1 follow:1 research:1 inverse:6 bogoliubov:1 paris:1 assigning:1 γk:1 γj:2 γi:14 ajk:5 tj:16 those:2 th:2 dressing:2 geom:2 applied:1 ginn:1 t12:1 preserved:1 orthogonal:1 very:1 construction:13 rise:2 conditions:2 every:1 formula:2 ma:1 difference:2 matrices:1 condition:4 level:1 turns:1 t4:7 list:1 solution:3 t1:35 large:1 discrete:36 vector:2 inscribed:1 warszawa:1 stating:1 der:1 zn:7 sapienza:4 ten:1 10b:1 takhtajan:1 10a:1 za:1 integrability:6 equal:1 reine:1 linear:12 bilinear:1 established:1 nonlinear:4 appear:1 d2:3 section:9 pijk:1 analogously:1 agrees:1 version:2 sur:1 intersect:2 new:7 net:6 method:5 satisfy:3 here:1 papageorgiou:1 5dimensional:1 objects:4 tangent:4 directions:2 based:1 november:1 lomi:1 equations:41 z2:4 obtained:5 remark:3 suitably:1 shift:1 studied:1 allows:6 reason:2 contradiction:1 akj:3 studies:2 involves:1 uniquely:8 via:1 useful:1 pinkall:2 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solv-int9612008.txt |@word consider:2 chain:5 results:1 reˇ:1 aligned:1 nonlocal:2 ℜe:1 under:1 case:6 far:1 wave:7 difference:3 matrices:1 condition:4 hamiltonian:1 solution:7 convenience:1 quasiperiodicity:1 oscillation:1 sin2:1 direct:1 cosh:2 second:2 odd:1 canonical:1 spectral:1 appear:1 sum:1 expressed:2 above:2 new:1 exchange:5 sinh:3 consideration:1 extrema:1 respect:2 appears:4 change:1 institute:2 involved:1 larger:1 scatter:1 periodic:1 action:1 via:3 total:6 linearly:1 prove:1 distinct:1 positive:1 whittaker:1 next:1 taken:1 type:8 bethe:2 more:3 zeroes:3 becomes:1 operators:1 known:3 hold:1 must:3 account:2 equation:6 work:1 values:8 following:1 dec:1 example:1 nearest:5 give:1 states:9 minimum:1 unphysical:1 np1:1 np2:1 end:2 holds:1 till:1 nontrivial:3 parameter:2 fp:15 mat:1 faculty:1 representations:2 choice:1 types:2 imply:1 used:1 sn:3 allow:1 representation:1 restriction:1 quasiperiodic:1 over:1 satisfied:1 course:1 mentioned:1 existence:3 excitations:1 its:1 roots:2 ln:1 interesting:1 destroyed:1 absence:1 choose:2 derivative:3 might:1 identically:1 now:2 easily:1 always:3 university:2 sufficiently:1 inequality:4 2a:26 each:2 found:4 2n:1 2h:1 side:3 domain:2 ei:2 series:1 energy:3 related:1 decays:1 quantum:2 our:3 shown:2 since:4 crucial:1 acting:1 investigation:1 formula:1 math:2 sinh2:8 doppler:1 theory:1 possibility:2 admits:1 small:2 besides:1 usual:1 estimate:1 dubna:1 interaction:6 exponentially:1 teor:1 first:5 ono:1 relations:1 another:1 open:1 given:4 πa:1 rewritten:1 least:1 their:2 returns:1 gives:1 academy:1 continuous:1 serve:1 ascr:1 sign:1 than:1 third:1 double:2 zero:2 matter:1 determined:1 russia:1 modern:1 spectrum:1 say:1 seen:1 any:1 lie:1 strength:1 majumdar:1 note:5 sciences:2 concerns:1 heisenberg:5 fundamental:2 shall:2 complexes:1 letter:1 phase:1 fiz:1 considered:1 magnon:8 later:1 coincides:1 definitely:1 oscillates:1 physics:2 technical:1 fact:1 phenomenon:1 supported:1 solutions:2 superimposed:1 magnons:4 trivial:1 find:2 ground:2 criterium:1 inozemtsev:2 should:5 only:3 transcendental:2 factor:1 integrable:1 do:1 means:4 famous:1 watson:1 ones:1 coth:8 continuum:1 arxiv:1 investigate:2 analytical:1 fixed:1 set:1 exists:1 prague:1 up:1 relative:1 see:3 result:1 japan:1 nuclear:2 definite:1 state:17 simplest:1 boundary:1 terms:1 however:1 vanishing:1 solv:1 σk:1 both:1 cos:5 cot:3 taking:1 pcr:14 exceeds:1 expression:1 finds:1 point:1 asymptotically:1 corresponds:2 dimensional:1 cz:1 moreover:1 zeta:1 described:2 equations:1 create:1 due:4 been:2 int:1 describes:1 interest:1 universal:1 corresponding:2 σj:2 2iq:1 weierstrass:4 spin:3 present:2 2ia:3 p2:20 p1:20 value:3 will:2 cast:1 suppose:1 situation:2 property:1 iq:4 ip:16 thus:1 site:1 ii:3 reads:3 ia:11 vanish:1 disappear:1 different:1 grant:2 gacr:1 member:1 complex:2 pauli:1 proved:1 finite:4 investigated:2 hand:4 lower:2 oguchi:1 analysis:1 model:2 parametric:1 left:3 just:3 being:1 σnx:1 scattering:1 previous:1 decayed:1 eigenequation:1 treatment:2 iπ:13 iχ:2 real:10 cf:1 press:1 follows:2 rearrangement:1 works:1 spins:1 mathematical:1 methods:1 czech:3 some:3 sight:1 specified:1 oscillations:1 does:2 chains:1 equivalent:1 oscillating:2 substitution:2 properties:1 about:1 ferromagnetic:3 anything:1 getting:1 commun:1 range:4 neighbor:7 soc:1 cambridge:1 presence:3 into:5 within:1 bound:17 references:1 operator:2 there:7 much:1 way:1 jinr:1 was:3 function:14 complete:1 form:4 but:3 pseudomomentum:7 attached:1 maximum:2 us:5 limit:3 critical:1 problem:3 similar:2 detailed:1 associated:1 defined:1 abstract:1 general:1 engineering:1 exist:1 periods:1 ℑm:1 physical:2 functions:2 no:4 vanishes:1 other:3 republic:2 conclusion:1 dittrich:1 variation:1 variable:3 structure:1 interval:12 n1:21 n2:21 4a:6
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