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：Inthisletter,anewloopalgebraGisconstructed,fromwhichanewisospectralproblemisestablished.Itfollowsthatintegrablecouplingsofthewell-knowncoupledBurgershierarchyareobtained.

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：ThegeneralLiepointsymmetrygroupsoftheNizhnik-Novikov-Vesselov(NNV)equationandtheasymmetricNNVequationaregivenbyasimpledirectmethodwithhelpoftheirweakLaxpairs.

简介：TheMelnikovmethodwasextendedtoperturbedplanarnon-Hamiltonianintegrablesystemswithslowly-varyingangleparameters.Basedontheanalysisofthegeometricstructureofunperturbedsystems,theconditionoftransverselyhomoclinicintersectionwasestablished.ThegeneralizedMelnikovfunctionoftheperturbedsystemwaspresentedbyapplyingthetheoremonthedifferentiabilityofordinarydifferentialequationsolutionswithrespecttoparameters.ChaosmayoccurinthesystemifthegeneralizedMelnikovfunctionhassimplezeros.