简介:AsubalgebraofloopalgebraA2isestablished.Therefore,anewisospectralproblemisdesigned.BymakinguseofTu''sscheme,anewintegrablesystemisobtained,whichpossessesbi-Hamiltonianstructure.Asitsreductions,aformalismsimilartothewell-knownAblowitz-Kaup-Newell-Segur(AKNS)hierarchyandageneralizedstandardformoftheSchrodingerequationarepresented.Inaddition,inorderforakindofexpandingintegrablesystemtobeobtained,aproperalgebraictransformationissuppliedtochangeloopalgebraA2intoloopalgebraA1.Furthermore,ahigh-dimensionalloopalgebraisconstructed,whichisdifferentfromanypreviousone.Anintegrablecouplingofthesystemobtainedisgiven.Finally,theHamiltonianformofabinarysymmetricconstrainedflowofthesystemobtainedispresented.
简介:<正>Inthispaper,adistortiontheoremandsomeequicontinuityandcompactnesstheoremsareobtainedforthehomeomorphismfwiththespheredilatationH(x,f)∈Lloc(D).
简介:WeinvestigatesomeintegrablemodifiedHeisenbergferromagnetmodelsbyusingtheprolongationstructuretheory.ThroughassociatingthemwiththemotionofcurveinMinkowskispace,thecorrespondingcoupledintegrableequationsarepresented.
简介:<正>Inthispaper,wemakeacompletestudyoftheunfoldingofaquadraticintegrablesystemwithahomoclinicloop.MakingaPoincaretransformationandusingsomenewtechniquestoestimatethenumberofzerosofAbelianintegrals,weobtainthecompletebifurcationdiagramandallphaseportraitsofsystemscorrespondingtodifferentregionsintheparameterspace.Inparticular,weprovethattwoisthemaximalnumberoflimitcyclesbifurcatingfromthesystemunderquadraticnon-conservativeperturbations.
简介:在这份报纸,积极明确的矩阵functionals在一套方形的integrable矩阵上定义珍视的功能被介绍并且学习。最好的近似问题以矩阵Fourier系列被解决。Riemann-Lebesgue矩阵性质和Bessel-Parseval矩阵不平等被给。
简介:Inthispaper,thenewcoupledMKdVhierarchyandtheirLsxpairsareoinained,Throughintroducingasuitablecomplexformofsymplecticstructure[5,8],anewintegraHesys-temofthecomplexformintheLiouvillesenseisgenerated.Moreover,therepresentationsofthesolutionforthecoupledMKdVhierarchyaregivenbytheinvohifivesolutionsofthecommutable.
简介:TheMelnikovmethodwasextendedtoperturbedplanarnon-Hamiltonianintegrablesystemswithslowly-varyingangleparameters.Basedontheanalysisofthegeometricstructureofunperturbedsystems,theconditionoftransverselyhomoclinicintersectionwasestablished.ThegeneralizedMelnikovfunctionoftheperturbedsystemwaspresentedbyapplyingthetheoremonthedifferentiabilityofordinarydifferentialequationsolutionswithrespecttoparameters.ChaosmayoccurinthesystemifthegeneralizedMelnikovfunctionhassimplezeros.