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：3×3矩阵光谱问题和一个Liouvilleintegrable层次被设计环代数学Ã2的新潜水艇代数学构造。而且，相应层次的高顺序的二进制对称限制被使用二进制nonlinearization方法获得。最后，根据环代数学Ã2,的另一新潜水艇代数学，它的integrable政变石楠被建立。

简介：Inthisletter,anewloopalgebraGisconstructed,fromwhichanewisospectralproblemisestablished.Itfollowsthatintegrablecouplingsofthewell-knowncoupledBurgershierarchyareobtained.

简介：WeinvestigatesomeintegrablemodifiedHeisenbergferromagnetmodelsbyusingtheprolongationstructuretheory.ThroughassociatingthemwiththemotionofcurveinMinkowskispace,thecorrespondingcoupledintegrableequationsarepresented.

简介：在这份报纸，我们把Hirota的discretisation用于一个三维的integrableLotka-Volterra系统。由分析结果的三维的修改方程数字方法，我们证明它是保存卷的，并且首先有二个独立人士积分。而且，它能正式经由volumepreserving转变在一种尺寸被归结为一个系统。如果给定的起始的值位于积极卦限，我们证明数字解决方案被限制到一一个维连接并且是到一个圆的diffeomorphic的紧缩的空格。[从作者抽象]

简介：<正>Inthispaper,wemakeacompletestudyoftheunfoldingofaquadraticintegrablesystemwithahomoclinicloop.MakingaPoincaretransformationandusingsomenewtechniquestoestimatethenumberofzerosofAbelianintegrals,weobtainthecompletebifurcationdiagramandallphaseportraitsofsystemscorrespondingtodifferentregionsintheparameterspace.Inparticular,weprovethattwoisthemaximalnumberoflimitcyclesbifurcatingfromthesystemunderquadraticnon-conservativeperturbations.

简介：在这份报纸，我们考虑强壮的近似为局部地square-integrable鞅。在我们的结果，限制过程可以是一个过程与跳。这是以前的结果的延期。

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：二种高度维的谎言代数学和他们的环代数学被介绍，为哪个象TB层次一样包括BroerKaup(放射性元素)层次和散长波浪(DLW)层次的联合integrablecouplings扩展integrable模型的一些被获得。从联合integrablecouplings的减小，BK方程，DLW方程，和TB方程的相应联合integrablecouplings分别地被获得。特别，TB方程联合的联合integrable归结为著名mKdV方程的一些integrablecouplings。分别地，三种soliton层次的联合integrablecouplings的Hamiltonian结构被采用变化身份得出。最后，我们把进化方程的BK层次分解成代表和宽松的对被给其伴随的抑制x的流动和抑制tn的流动。

简介：Inthispaper,thenewcoupledMKdVhierarchyandtheirLsxpairsareoinained,Throughintroducingasuitablecomplexformofsymplecticstructure[5,8],anewintegraHesys-temofthecomplexformintheLiouvillesenseisgenerated.Moreover,therepresentationsofthesolutionforthecoupledMKdVhierarchyaregivenbytheinvohifivesolutionsofthecommutable.

简介：Inthispaper,anewcompletelyintegrablesystemrelatedtothecomplexspectralproblem—φ_(xx)+(i/4)uφ_x+(i/4)(uφ)_x+(1/4)vφ=iλφ_xandtheconstrainedBowsoftheBoussinesqequationsaregenerated.AccordingtotheviewpointofHamiltonianmechanics,theEuler-LagrangeequationsandtheLegendretransformations,areasonableJacobi-Ostrogradskycoordinatesystemisobtained.Moreover,bymeansoftheconstrainedconditionsbetweenthepotentialu,vandtheeigenfunctionφ,theinvolutiverepresentationsofthesolutionsfortheBoussinesqequationhierarchyaregiven.

简介：ThegeneralLiepointsymmetrygroupsoftheNizhnik-Novikov-Vesselov(NNV)equationandtheasymmetricNNVequationaregivenbyasimpledirectmethodwithhelpoftheirweakLaxpairs.

简介：Undertheframeofthe(2+1)-dimensionalzerocurvatureequationandTumodel,the(2+1)-dimensionaldispersivelongwavehierarchyisobtained.Furthermore,theloopalgebraisexpandedintoalargerone.Moreover,aclassofintegrablecouplingsystemfordispersivelongwavehierarchyand(2+1)-dimensionalmulti-componentintegrablesystemwillbeinvestigated.

简介：WepresentanewdiscreteintegrablecouplingsystembyusingthematrixLaxpairU,V∈sl(4).AnovelspectralproblemofmodifiedTodalatticesolitonhierarchyisconsidered.Then,anewdiscreteintegrablecouplingequationhierarchyisobtainedthroughthemethodoftheenlargedLaxpair.Finally,weobtaintheHamiltonianstructureoftheintegrablecouplingsystemofthesolitonequationhierarchyusingthematrix-formtraceidentity.ThisdiscreteintegrablecouplingsystemincludesakindofamodifiedTodalatticehierarchy.

简介：由考虑(2+1)维的non-isospectral分离零个弯曲方程，(2+1)维的non-isospectralToda格子层次在这篇文章被构造。因而一些减小(2+1)维的Toda格子层次被给。最后，(2+1)联合Toda格子层次的系统的维的integrable通过扩大被获得光谱问题。

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

简介：Basedonthecovariantprolongationstructuretechnique,weconstructtheintegrablehigher-orderdeformationsofthe(2+1)-dimensionalHeisenbergferromagnetmodelandobtaintheirsu(2)×R(λ)prolongationstructures.ByassociatingthesedeformedmultidimensionalHeisenbergferromagnetmodelswiththemovingspacecurveinEuclideanspaceandusingtheHasimotofunction,wederivetheirgeometricalequivalentcounterparts,i.e.,higher-order(2+1)-dimensionalnonlinearSchrdingerequations.