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solv-int9904019.txt |@word represent:1 lakshmanan:1 consider:4 four:2 eds:1 guwahati:2 follow:1 research:1 whose:1 inverse:4 depend:1 fellowship:1 γs:1 undistorted:1 equivalence:1 finally:1 compensate:1 present:1 th:1 under:1 tg:1 case:10 straightforward:2 very:1 connects:1 wave:3 electron:1 novel:2 matrices:1 condition:1 generalised:1 leads:1 turns:3 solution:3 vector:1 relation:6 optics:1 akns:1 upper:1 compensated:1 pulse:1 consists:1 integrability:13 go:1 further:1 dynamics:1 situated:1 aim:1 nonlinear:10 appear:1 expressed:1 indian:1 above:1 3c:1 3b:1 3a:2 method:6 full:1 simultaneously:1 respectively:1 here:1 dimensionality:2 address:1 along:1 marchenko:1 equations:4 obtained:3 balance:1 singapore:1 institute:1 study:3 studied:1 published:2 iλσ:1 emerge:1 via:1 although:1 family:6 apr:1 vis:2 viz:1 ipx:1 takes:2 would:2 remains:1 jpn:1 calculation:1 therefore:3 type:2 more:3 solitons:6 operators:6 stolen:1 odinger:3 award:1 known:4 cases:3 evolves:1 springer:1 valued:2 equation:49 modified:1 values:4 following:1 numbers:1 process:1 neglected:1 spm:1 ist:9 ernet:2 eni:1 travel:1 steepening:1 far:1 parameter:1 upto:1 may:7 applications:1 plane:1 lax:29 choice:1 data:1 compatibility:1 o:1 e24:1 sz:1 short:1 e21:1 e22:3 e23:1 ss:1 light:2 explicit:2 element:1 ones:2 so:2 sc:1 subsequently:1 order:9 over:2 produced:3 course:1 paper:2 pulses:4 enn:1 existence:2 ieee:1 its:1 solitary:1 group:1 thank:1 chosen:3 interesting:5 solving:3 stimulated:2 choose:3 eventually:1 scaling:3 band:1 effects:2 they:2 half:1 now:4 eigenvalue:5 term:1 establishing:1 γ2s:3 each:2 found:3 subset:1 financial:1 related:2 frequency:1 quantum:1 our:2 out:3 shown:6 matrix:9 since:1 rev:3 smp:1 modulation:1 daniel:1 iλx:1 issue:1 math:2 telecommunication:1 envelop:2 diagonal:1 possibility:2 admits:1 clarify:1 care:1 definition:1 pairs:9 times:1 motion:6 gordon:2 first:2 already:2 third:1 number:2 exact:1 another:2 electronic:1 given:4 kodama:1 their:1 manakov:1 relations:1 needed:1 tod:1 gives:1 relationship:1 optical:13 authors:1 than:1 coefficients:19 dynamical:9 wide:2 unfortunately:1 painleve:1 preparation:1 determined:1 represents:1 india:2 aax:1 spectrum:1 hasegawa:3 elsewhere:1 zero:1 convenient:1 self:3 responsible:1 note:2 electric:1 propagate:1 significant:1 pair:5 achievement:1 soliton:19 consequences:1 considered:3 clear:1 points:1 exp:4 velocity:1 physics:1 width:2 fact:1 nls:1 intensity:2 show:4 gauge:3 solutions:11 substituting:2 fibre:9 aσ:1 ratio:6 parameters:5 e11:3 e13:1 e12:1 e14:1 being:2 only:10 integrable:3 distance:1 generalise:1 cannot:2 new:2 dp:1 evolution:11 initial:1 fields:10 arxiv:1 qe:1 through:7 fixed:1 view:1 exists:2 achieved:3 plausible:1 namely:3 result:1 terms:9 definitely:1 draws:1 pump:2 various:2 between:5 αi:5 conditions:1 notice:2 csir:1 recently:1 attention:1 however:4 jr:1 solv:1 jetp:1 both:4 last:4 many:1 σa:1 propagation:8 connection:2 utilising:1 whole:1 point:1 reasons:1 asymptotically:1 ultrashort:3 dimensional:12 pole:1 moreover:3 levitan:1 described:1 pz:1 three:4 been:3 universal:1 systems:1 6a:1 6b:2 xxx:7 6l:2 agrawal:1 observe:2 evidence:1 those:1 e42:1 e43:1 e41:1 laser:1 e44:1 pacs:1 choices:4 will:6 invoking:1 eii:1 eij:1 ein:1 coupled:1 thus:4 ii:1 ij:1 auxilliary:1 heidelberg:1 conf:1 ib:2 technology:1 different:8 admit:2 same:3 unity:1 complex:1 higher:7 independent:1 see:2 again:1 effect:1 hand:1 recent:1 schr:3 expression:2 well:2 analysis:1 academic:1 easily:1 dimension:1 gelfand:1 appropriately:1 transmitting:1 obtain:7 rest:2 press:1 shape:1 identify:1 integer:4 scattering:7 previous:1 ny:1 conclude:1 jost:2 simple:5 lett:5 5a:1 transformation:1 5b:1 opt:3 depends:2 nandy:3 possible:3 iη:1 govt:1 using:1 unique:1 loss:4 like:1 follows:1 reduces:4 manifest:1 shapes:1 yields:1 either:1 arbitrary:1 become:1 works:1 interestingly:1 because:1 methods:1 some:3 understood:1 examples:1 choosing:1 fibres:1 duration:1 kdv:1 specific:3 dimensions:6 lead:3 gvd:2 proc:1 equivalent:1 agreement:1 shifting:1 ratios:10 explicitely:1 kundu:1 world:1 scott:1 srs:1 range:2 important:1 nothing:1 obeys:1 consequently:4 soc:1 within:1 due:2 phase:1 appropriate:2 exploiting:1 references:1 sov:1 operator:5 ηx:1 schrodinger:2 additional:1 support:1 there:1 long:1 dispersion:2 start:1 restricts:1 appl:1 lot:1 raman:4 complete:3 form:8 but:9 junior:1 gedalin:1 evident:2 us:2 liouville:1 problem:5 detailed:1 ln:2 int:2 abstract:1 describe:1 direction:1 general:2 exist:1 ax:2 constructed:1 satsuma:2 functions:2 e34:1 e33:2 e32:1 e31:1 no:3 when:3 field:3 other:2 becomes:4 department:1 ξx:1 elements:1 time:2 a2:3 sech:1 auxiliary:1 assume:1 ghosh:3 sasa:3 hirota:4 once:1 4b:1 original:1 4a:1
solv-int9904020.txt |@word partial:1 rev:8 four:1 remarkably:1 localized:2 compact:9 those:2 stable:1 worth:1 dey:2 rise:1 wave:1 lyapunov:1 school:1 hamiltonian:1 ref:1 shock:1 solution:23 solved:1 optics:3 hasegawa:1 second:1 further:2 10q:1 odd:1 even:1 nonlinear:15 plays:1 3p:2 cai:1 reminiscent:1 above:1 judicious:1 new:1 respectively:2 here:1 understanding:1 behaviour:2 cos2:9 strong:3 equations:18 derivable:1 search:1 drops:1 study:1 periodic:2 khare:2 u3x:4 useful:1 family:2 apr:1 highly:1 derivatives:2 would:3 negative:1 next:1 taken:1 type:5 solitons:7 under:1 odinger:3 particular:1 baby:1 kumar:1 none:1 equation:17 work:1 modified:3 mw:1 values:4 following:3 confining:1 arrive:1 root:1 compare:2 give:2 process:1 india:2 collision:1 sense:1 needs:2 feature:2 srinivasan:1 criterion:1 parameter:3 may:1 earlier:1 derived:1 straightforwardly:1 waves:3 realized:1 liquid:1 light:1 fundamental:1 order:7 dx:3 stability:4 through:1 existence:2 satisfies:1 still:1 its:1 solitary:2 acknowledge:1 lu:1 choose:1 derivative:1 non:1 amenable:1 they:1 identically:1 now:1 possess:2 represents:1 term:4 fully:2 university:1 possibilities:1 2k:1 arxiv:1 ei:1 energy:2 related:1 manifests:1 our:1 eq:2 es:1 out:1 shown:5 furthermore:1 since:2 lagrangian:2 u2x:2 linear:1 panigrahi:1 tappert:1 possibility:1 admits:1 formation:2 r1:1 could:1 motion:1 hence:4 generalizations:1 first:3 hyderabad:2 possessing:1 number:3 enlarged:1 dispersive:2 given:3 similarly:1 their:1 appl:1 variational:1 structures:1 gives:1 relative:1 scheme:1 zero:1 amplitude:3 san:1 emphasizing:1 seem:1 note:4 generalized:2 unconstrained:1 electric:1 opposite:1 involving:2 significant:1 nagaraja:1 phase:1 compactons:8 acknowledgements:1 class:2 soliton:2 kf:1 considered:1 compacton:12 principle:2 velocity:3 ky:1 physics:1 fact:1 laws:2 show:4 supported:1 solutions:22 fifth:1 fibre:1 knowledge:1 parameters:1 only:3 explicitly:1 integrable:6 local:2 fluid:1 closely:1 evolution:2 differential:1 ut:6 exists:1 ωt:2 detection:1 depends:2 discussions:1 best:1 pattern:1 currently:1 dipole:1 boundaries:3 outside:1 simplest:1 csir:1 terms:2 kei:1 however:1 solv:1 5u2:1 discontinuous:2 both:1 cos:1 region:2 paranjape:1 admit:1 context:3 expression:1 experimental:2 otherwise:2 relevant:1 16k:3 appeared:2 mkdv:7 ps:1 been:4 int:1 interest:1 families:1 mu4:1 quantities:4 great:1 representative:1 careful:1 present:1 unlike:2 pacs:1 e48:1 will:2 situation:2 characterizing:1 va:1 shepard:1 them:1 reads:1 vt:3 vanish:1 agarwal:1 different:1 media:1 make:1 same:1 parts:1 finite:3 higher:4 independent:2 literature:1 singapore:1 numerical:1 arose:1 hand:1 edges:1 moving:1 purpose:1 infinite:1 lower:1 schr:3 3x:1 rosenau:2 well:3 analysis:1 enquire:1 academic:1 arising:3 λt:4 das:1 sources:1 world:1 yet:1 nlse:4 vψ:1 point:1 except:1 source:5 add:1 lett:3 momentum:2 real:1 admitting:1 press:1 using:1 vξ:1 occurring:1 like:16 interestingly:1 admitted:1 arbitrary:1 qxx:1 therein:1 sequence:1 plausible:1 phenomena:1 understood:1 choosing:2 kdv:11 cooper:2 though:2 integration:1 dipoles:1 prof:1 cnk:1 scientific:1 sodano:1 although:1 imaginary:1 exciting:1 properties:2 christened:1 about:1 obeys:1 skyrmions:1 square:1 references:1 strip:1 proportional:1 span:1 elastic:1 pc:1 u4:1 support:5 there:2 question:1 u2:3 dispersion:1 width:3 conservation:2 was:2 medium:1 form:5 some:3 ec:1 truncation:1 ux:7 iqt:1 up:2 us:1 postive:1 um:1 ul:1 un:1 ωa:1 similar:3 uc:8 constant:1 defined:2 evidence:1 conserved:3 diverse:1 formulation:1 corresponding:2 check:1 physical:2 diego:1 functions:1 compared:1 infact:1 when:2 field:1 other:6 role:2 conclusion:1 separate:1 models:2 problems:1 a3:1 a2:1 4p:1 4q:1 mimic:1 weights:1 4k:7 hyman:1 oran:1
solv-int9904021.txt |@word ψ1x:1 sector:1 gt:1 lakshmanan:2 consider:4 pth:1 magnetic:1 satify:1 gx:2 leads:4 roy:3 generalize:1 francesco:1 guwahati:2 follow:3 expressions:1 research:1 rigidity:1 compact:1 whose:4 inverse:6 depend:1 integral:6 fellowship:1 xiong:1 equivalence:5 γj:1 charge:1 does:1 those:1 th:4 under:5 characterised:1 case:5 conjecture:1 kundu:2 izv:1 broadly:1 eiλx:6 very:1 rise:2 conditions:3 dokl:1 wave:1 prog:2 electron:1 laser:1 sssr:2 matrices:3 condition:3 generalised:2 obvious:1 implying:1 transmission:1 notes:1 solution:4 intriguing:1 deals:1 vector:15 indices:1 relation:1 optics:4 hasegawa:2 version:2 miura:2 σa2:1 fibres:1 direct:2 pulse:2 approximation:1 elegant:1 integrability:7 compensates:1 further:3 dynamics:3 odd:1 quite:2 ψ2x:1 even:2 will:13 nonlinear:30 section:9 expressed:4 shadwick:1 indian:1 poles:2 lifshitz:11 dλ:4 3b:2 3a:4 row:1 method:17 funtion:1 satisfy:5 condensed:1 αik:1 c0i:1 respectively:3 component:9 here:1 behaviour:1 desired:1 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solv-int9905007.txt |@word aln:2 bazhanov:2 gt:28 partial:1 consider:8 chain:15 gp:1 osp:2 magnetic:5 results:14 four:4 alm:8 generalize:2 per:1 grateful:1 intricate:1 gn:3 expressions:2 contributions:1 centers:4 alp:2 poorly:1 devoted:1 whose:4 inverse:4 depend:1 appears:2 handle:1 irrelevant:3 send:1 b265:2 finally:3 compensate:1 bqr:1 those:4 th:3 under:1 must:1 alternating:1 p2:1 belonging:1 supported:1 string:4 made:2 zhang:1 very:13 fermionization:1 rise:9 keeping:1 choice:2 denoted:1 b215:1 every:8 zsr:1 stays:1 affect:1 difference:4 matrices:5 deformations:3 condition:1 leads:2 b198:1 level:13 turns:2 anisotropy:2 t2:2 solution:6 correct:1 large:17 solved:1 kondo:5 phase:1 filling:3 fadeev:1 small:10 entropy:2 superalgebras:3 added:1 rozansky:1 upper:1 smaller:2 disordered:2 takhtajan:1 blatter:1 literature:1 sign:2 approximation:1 go:1 zero:3 cost:1 evaluated:1 morel:1 follow:1 further:6 ρn:16 odd:2 bosonize:1 even:4 index:2 what:12 ˆt:1 sub:1 giving:3 section:8 rescale:1 ǫq:2 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solv-int9905008.txt |@word funct:1 rev:1 scalar:1 consists:2 naukova:1 inverse:1 γg:1 fay:1 dokl:1 wave:2 lecture:1 difference:1 matrices:2 condition:4 dubrovin:1 riemann:5 notes:1 sklyanin:1 solution:3 t0:3 large:2 involution:2 vector:6 div:1 infinities:1 upper:1 tex:1 second:2 dynamics:1 situated:1 canonical:1 diag:1 poles:1 lifshitz:7 method:2 coefficient:1 led:1 here:5 represented:1 path:2 equations:3 change:1 obtained:1 remark:1 divisor:3 institute:1 lomi:1 study:3 studied:1 periodic:2 composed:1 kosevich:1 use:1 asymptotic:1 positive:1 contains:1 vol:1 linear:2 usp:1 type:1 initiated:1 berlin:1 cycles:2 normalized:1 known:1 springer:1 equation:5 det:1 following:5 f1:3 f2:3 figure:1 sense:1 algebrogeometric:1 axis:1 s3:1 s1:1 exceptional:1 antiholomorphic:1 map:1 mat:2 singular:2 may:1 algebro:1 after:1 collection:1 plane:1 waves:6 choice:1 data:2 compatibility:1 constants:1 sx:1 third:1 light:1 explicit:1 λ2g:8 st:1 green:1 decreasing:1 order:1 developed:1 pointed:1 paper:2 through:1 existence:1 its:2 fis:1 ln:5 solving:2 tori:1 choose:2 main:2 them:1 landau:7 sssr:1 they:1 rotation:1 kovalev:1 term:2 finite:7 2g:3 each:1 2i:1 consolidate:1 journ:1 our:3 out:1 ru:1 shown:3 matrix:1 vectorial:1 denotes:1 re:1 investigation:1 fti:1 formula:1 theory:3 admits:1 completely:1 base:1 lab:1 org:1 sowjetunion:1 anal:1 e2:2 interaction:1 asymptotical:3 transition:1 int:2 gardner:1 teor:1 first:2 miura:1 relations:1 interchange:1 given:6 sheet:2 manakov:1 leading:1 construct:1 appl:1 cycle:1 hyperelliptic:2 academy:1 akad:1 part:1 center:1 ivanov:1 kind:1 see:6 final:1 determined:1 were:1 result:1 well:2 spectrum:1 generalization:1 multivalued:1 disjoint:1 any:1 depending:1 lim:1 bobenko:2 sciences:1 formulas:1 most:1 connected:1 sheets:2 formulae:1 phase:4 class:1 branching:1 tν:1 don:1 considered:1 torus:4 typeset:1 points:4 exp:3 akhiezer:1 solutions:9 d2:7 d1:5 slow:1 should:1 only:3 integrable:2 jac:3 abelian:1 means:1 nearly:1 geometric:1 processes:1 arxiv:2 expansions:1 2πi:3 nauk:2 finishing:1 fixed:1 kernel:1 constructing:1 differentials:2 depends:1 w3:2 w2:2 w1:2 contour:1 surfaces:1 phases:2 interacting:1 review:1 written:1 between:1 theta:1 boundary:1 meromorphic:1 terms:2 js:1 solv:2 ferromagnet:1 restrictions:1 kruskal:1 according:2 σq:1 σp:6 com:1 point:1 dimensional:1 ps:1 basis:1 defined:2 describes:1 slowly:1 asymptotics:5 fig:4 corresponding:1 gap:8 c3:7 c2:7 c1:7 c4:7 case:4 p0:3 p1:1 value:1 behavior:2 shift:1 periods:1 vectors:2 almost:1 borovik:1 non:3 surface:2 equal:1 vanish:1 same:1 pauli:1 constructed:2 http:3 changing:1 passing:1 e1:2 lower:1 reflection:1 infinity:3 analysis:1 coordinate:1 model:3 left:1 magnetization:6 being:1 obtain:1 rest:1 λg:1 scattering:6 multiples:2 preprint:2 zakharov:1 jost:2 instrument:1 lett:2 real:6 around:1 format:1 sharipov:4 iδ:2 ams:1 unique:1 like:2 dumka:1 stationary:1 mathematical:1 www:2 leningrad:1 describing:1 eiδ:1 integration:3 subclass:1 does:3 scientific:1 ufa:1 equivalent:1 bi:1 column:1 novikov:2 o:3 into:1 integral:1 pair:2 ussr:2 references:1 wα:2 abel:1 available:1 fast:1 gif:3 cauchy:1 was:3 pg:1 function:8 form:3 soliton:2 construction:1 laurent:1 divisors:3 whether:1 smooth:1 up:2 us:2 ωi:1 problem:1 define:2 similar:2 ai:2 abstract:1 dλ:2 file:1 sxx:1 defines:1 functions:5 no:2 fixing:1 reality:1 other:1 mathematics:1 separate:1 important:1 bounded:2 variable:1 kiev:1 baker:1 time:2 starting:1 having:1
solv-int9905009.txt |@word consider:7 chain:5 em2:1 magnetic:5 results:3 integration:1 scalar:5 gn:11 wj2:2 gj:33 gi:2 λii:3 inverse:2 const:1 calculate:1 aug:1 γs:3 tj:2 contours:1 th:8 ti:7 eβ:7 tb:11 norm:1 alternating:1 r12:2 matrices:1 condition:1 entire:1 school:1 hamiltonian:3 irreducible:1 sklyanin:3 make:2 t0:1 t1:2 try:1 solved:1 convenience:2 vector:18 symme:1 b530:1 enjoy:1 application:1 nonl:1 zk:1 renormalized:1 cosh:1 fold:1 integrability:3 evaluated:1 zw:1 odd:1 linear:2 spectral:2 section:8 expressed:1 3k:8 b441:1 3n:1 above:3 new:2 ˆj:1 increasing:1 method:2 satisfy:5 even:2 component:6 here:11 ansatz:6 sinh:2 path:1 equations:2 z1:13 z2:13 box:1 eki:1 institute:1 study:1 vectors:8 periodic:2 products:1 action:3 formulated:1 useful:1 projection:1 2δi:1 2δj:1 sgn:2 ai:1 total:1 use:2 asymptotic:2 commun:1 sports:1 ψj:5 few:1 nucl:2 call:1 therefore:8 ip:3 taken:3 type:6 bethe:4 more:1 duality:1 operators:21 under:2 appendix:2 zλi:1 ozaki:4 cases:3 eα:3 fermionic:1 ii:1 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