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solv-int9903016.txt \|@word consider:2 chain:4 similarity:1 magnetic:3 results:1 grateful:1 follow:1 expressions:1 compact:1 preserves:2 inverse:2 depend:1 calculate:3 eigenbasis:2 tr:14 finally:1 program:1 petersburg:2 th:2 equalities:1 case:1 r12:10 straightforward:2 springer:2 choice:1 corollary:1 entries:1 difference:2 matrices:2 hamiltonian:4 xyz:1 sklyanin:5 list:1 solution:1 leave:2 admissible:1 stay:1 der:1 takhtajan:1 consistent:1 direct:1 second:2 canonical:4 spectral:4 trick:1 nonlinear:3 brackets:8 expressed:1 poles:1 above:1 new:1 consisting:1 groupe:1 respectively:1 papageorgiou:1 leeds:1 ansatz:4 separation:1 quite:3 equations:10 obtained:1 institute:1 studied:1 products:1 procedure:1 poisson:11 permutation:1 formulated:1 useful:1 requiring:1 apply:1 use:1 would:1 nijhoff:3 recalling:1 suppl:1 next:1 linear:3 doubt:1 associated:2 type:2 more:4 linden:1 introducing:1 fontanka:1 started:1 solitons:2 apparent:1 odinger:2 berlin:2 appendix:1 particular:1 known:1 cases:2 must:1 account:1 mm:1 ml:1 equation:5 work:2 det:2 cancellations:1 following:2 my:1 proof:5 calculation:2 preserving:1 needs:1 rather:1 verify:1 discussion:1 write:2 how:1 ens:2 answer:1 parameter:2 massive:1 mar:1 includes:1 after:1 epsrc:1 lax:5 dynamical:4 st:2 darboux:1 so:1 sl:3 subsequently:1 order:1 paper:4 satisfies:1 steklov:1 its:1 derive:1 fix:1 solving:1 lect:1 systems:3 mail:1 defining:2 possessing:1 them:1 quispel:1 acklund:10 introduce:2 p11:5 p12:14 now:2 equality:1 invariants:2 university:1 side:2 constraints:1 baxter:1 financial:1 ee:1 ed:1 related:1 operator:2 toda:2 obtains:2 our:6 ru:1 shown:2 matrix:22 space:1 res:1 since:1 formula:1 math:2 benefited:1 theory:3 little:1 free:3 standard:2 generate:2 determining:2 could:1 int:3 isotropic:1 consequence:1 first:2 already:1 miura:1 variables:5 given:4 publication:1 system:6 relations:1 their:1 1m:1 1l:3 gives:1 progr:1 continuous:1 proving:1 part:1 mclaughlin:2 magnet:1 determined:3 supposed:1 russia:1 20a:1 20b:1 ras:1 cumbersome:1 any:2 depending:1 convenient:1 self:1 mian:1 physique:2 note:3 generalized:1 reparametrization:1 heisenberg:4 cnrs:1 though:1 polynomiality:1 mimics:1 phase:1 acknowledgements:1 class:2 adopt:1 physica:1 yang:1 show:3 gauge:1 substituting:2 find:1 pkl:1 parameters:7 explain:1 should:2 only:3 notes:1 employed:1 hamiltonians:2 capel:1 do:1 notation:3 de:3 integrable:6 during:1 du:1 gen:1 differentiating:1 arxiv:1 method:1 view:1 body:1 constructing:1 bts:2 δjk:1 respect:1 observed:1 see:3 p21:11 w2:13 w1:13 p22:5 discussions:1 euclid:1 lyon:3 satisfying:1 written:2 between:2 invariant:3 approach:3 preserve:2 terms:1 matveev:1 however:1 wi:1 solv:3 undetermined:1 both:1 last:1 limits:1 many:1 taking:1 equal:1 symplectic:1 expression:3 lm:1 conclude:2 simple:1 16a:1 16b:1 16c:1 polynomial:1 pil:1 pq:5 transformations:6 due:1 been:2 canonicity:7 interest:1 choose:1 corresponding:4 finishes:1 xxz:1 xxx:1 c2:2 present:2 p2:2 p1:1 aim:2 suppose:2 situation:1 pdmi:1 thus:1 ii:1 flaschka:2 dual:1 landaulifshitz:2 vanish:1 righthand:1 perform:1 lett:1 same:3 complex:1 resulting:3 proved:1 arrives:1 rmatrix:1 laboratoire:1 published:1 hand:1 implicitely:1 identity:1 schr:2 well:3 solve:1 model:2 arising:1 left:1 proposed:1 being:5 obtain:2 λi:3 scattering:1 point:1 parametrization:2 lattice:5 transformed:1 treatment:1 easy:1 trudy:1 transformation:11 march:1 eorique:1 using:5 necessary:1 mathematical:1 salle:1 methods:1 classical:1 some:2 trends:1 gaudin:1 choosing:2 specified:1 kdv:1 moskow:1 reasons:1 happens:1 umr:1 shall:3 comments:1 does:2 demonstrated:1 faddeev:1 bt:10 step:1 2µp:1 2µq:1 properties:1 recollect:1 practical:1 remains:1 projectors:2 kuznetsov:2 into:2 integral:1 down:4 appropriate:1 references:1 elementary:2 france:1 van:1 support:1 there:1 question:2 long:1 why:1 italie:1 was:2 function:3 form:5 denoting:1 atom:1 us:4 below:2 limit:1 problem:1 similar:1 detailed:2 pii:2 pij:3 constant:1 nauka:1 defined:2 abstract:1 am:1 covers:1 general:2 governed:3 formalism:1 commuting:1 check:1 bracket:4 functions:1 ingredients:1 when:1 valid:1 department:1 mathematics:1 theor:1 models:5 problems:1 prepared:2 important:1 structure:1 together:1 requires:1 original:1

solv-int9903017.txt \|@word consider:2 chain:5 similarity:3 illustrated:1 proposition:1 grateful:1 consists:1 devoted:1 whose:3 preserves:1 inverse:1 depend:1 technique:3 unanswered:1 petersburg:2 th:2 ti:12 degeneration:2 r12:5 straightforward:3 very:1 choice:2 entries:1 difference:1 matrices:4 hamiltonian:4 turns:2 sklyanin:5 solution:2 leave:1 solved:1 commute:1 math:2 indices:1 relation:1 dimer:1 degeneracy:1 work:3 periodicity:1 det:1 direct:3 second:1 canonical:16 spectral:3 what:1 nonlinear:1 bλ1:2 brackets:8 section:7 expressed:2 henceforth:1 above:1 new:3 method:1 groupe:1 respectively:1 modify:1 here:2 leeds:1 ansatz:3 standard:2 equations:5 obtained:3 remark:2 institute:1 study:2 bessel:1 allows:2 periodic:1 resulting:2 procedure:1 poisson:7 permutation:2 useful:1 family:1 addressed:1 1st:2 use:1 prove:1 remains:1 next:1 associated:2 more:1 nauka:1 fontanka:1 started:1 solitons:1 odinger:1 berlin:1 pasquier:1 particular:1 must:1 springer:1 equation:4 mn:2 mi:14 rλ:6 following:1 my:1 example:5 proof:10 impose:3 give:1 calculation:1 preserving:1 sense:1 rather:1 verify:1 discussion:1 far:1 ens:2 instead:1 parameter:1 simplicity:1 product:4 mar:1 suppose:3 after:2 epsrc:1 applications:1 lax:8 sy:3 natural:1 lines:1 st:9 si:16 so:4 sl:5 order:1 restriction:1 fλ:19 paper:5 london:2 statistical:1 omitting:1 existence:1 steklov:1 planning:1 ln:2 exact:1 choose:1 mail:1 yi:22 was:2 acklund:14 introduce:1 p12:4 now:5 yt:2 easily:1 term:1 finite:1 equality:3 invariants:3 university:1 characterized:1 mean:1 baxter:4 financial:1 ee:1 idea:1 operator:5 toda:2 used:1 obtains:1 quantum:6 our:9 beyond:1 out:1 ru:1 shown:2 matrix:20 space:4 dst:6 since:2 induces:1 publish:1 mλ:6 benefited:1 theory:2 given:6 quite:2 completely:1 complicated:1 generate:1 definition:1 omit:1 int:2 isotropic:1 δij:2 first:4 xj:3 xi:24 variables:9 preservation:1 ℓj:2 ℓi:13 ℓn:1 another:2 xs:2 illustrate:2 moskow:1 similarly:1 introduction:1 system:4 construct:2 their:1 realization:2 scheme:3 1l:2 abovementioned:1 exactly:1 proving:1 part:2 than:1 kind:2 determines:1 magnet:3 namely:2 preparation:1 determined:1 contrary:1 russia:1 7b:1 7a:1 spectrum:1 generalization:1 say:1 ras:1 recover:1 any:2 multiparametric:1 mian:1 physique:2 note:3 instance:1 concerns:1 take:1 analogy:1 heisenberg:4 cnrs:1 trace:1 though:1 systems:3 simplify:1 connected:1 phase:4 acknowledgements:1 why:2 coincides:1 dimension:2 yang:2 typically:1 fact:1 show:1 chapters:1 spaces:1 gauge:2 find:1 explain:1 only:3 integrable:7 hamiltonians:3 local:7 goes:1 notation:2 means:1 express:1 famous:1 progress:1 during:1 du:1 gen:2 resolve:2 conditions:1 arxiv:1 body:1 set:1 exists:1 imposing:3 depends:1 discussions:1 euclid:1 analog:2 lyon:3 between:2 invariant:5 subscript:1 approach:3 notice:2 terms:2 parallels:1 extend:1 solv:2 many:2 taking:1 etc:2 sketchy:1 finds:1 mechanics:1 ci:6 conclude:1 simple:2 dimensional:1 pole:1 applicability:1 respect:2 bλ:9 ensures:1 pq:4 described:2 transformations:7 due:2 mark:1 canonicity:8 reduction:2 interest:1 expected:1 define:1 generating:7 relations:1 families:1 xxx:1 ensuring:1 systematic:1 c2:4 spin:1 present:2 case:3 will:2 replaced:1 monodromy:2 pdmi:1 thus:1 ii:1 different:1 recursion:1 make:1 connection:1 same:4 complex:1 modification:2 proved:1 several:1 composition:1 independent:1 extended:2 see:1 laboratoire:1 published:1 supposing:1 identity:1 schr:1 obviously:1 academic:1 de:3 sets:1 model:5 parametric:3 possesses:1 left:1 manifold:1 being:3 able:1 obtain:2 bµ:2 previous:4 lattice:1 easy:1 trudy:1 transformation:23 march:1 matrice:1 possible:1 eorique:1 press:1 using:2 like:2 follows:2 works:1 mathematical:1 often:1 classical:4 some:1 gaudin:1 indirect:1 provided:2 umr:1 shall:4 exposition:1 assuming:1 chains:1 faddeev:1 bt:3 step:1 substitution:2 2µq:1 simpler:1 constraint:8 nijhoff:1 consequently:2 mλ1:4 kuznetsov:3 into:2 references:1 elementary:3 france:1 methods:1 assumed:1 support:1 there:2 question:1 noticed:1 italie:1 way:3 salerno:1 sections:1 naturally:1 function:7 elsewhere:1 form:2 but:3 construction:6 hn:2 takhtajan:1 auxiliary:1 up:1 us:3 problem:2 called:2 detailed:1 constant:2 introducing:1 defined:1 abstract:1 describe:1 am:1 general:7 proves:1 exist:1 corresponding:7 commuting:2 simplest:1 functions:2 no:2 when:1 application:1 supplementing:1 other:1 department:1 mathematics:1 accidental:1 models:2 stay:1 important:2 structure:1 implies:1 factorized:1 assume:2 resolving:1 governed:2 original:3 equivalently:1 observe:1 4b:3 having:3 4a:3

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