简介：作者主要学习追踪算法到稳定的Euler系统和等温的Euler系统的波浪前面产生的弱答案的差别。在起始的数据足够地具有的假设下面小全部的变化，稳定的Euler系统和等温的超声的流动的系统的解决方案之间的差别能被起始的不安的全部的变化的立方体围住，这被证明。

简介：Inthispaper,theClarkson–Kruskaldirectapproachisemployedtoinvestigatetheexactsolutionsofthe2-dimensionalrotationalEulerequationsfortheincompressiblefluid.Theapplicationofthemethodleadstoasystemofcompletelysolvableordinarydifferentialequations.Severalspecialcasesarediscussedandnovelnonlinearexactsolutionswithrespecttovariablesxandyareobtained.Itisofinteresttonoticethatthepressurepisobtainedbythesecondkindofcurvilinearintegralandthecoefficientsofthenonlinearsolutionsaresolitarywavetypefunctionsliketanh(kt/2)andsech(kt/2)duetotherotationalparameterk=0.SuchphenomenonneverappearintheclassicalEulerequationswhereintheCoriolisforcearisingfromthegravityandEarth’srotationisignored.Finally,illustrativenumericalfiguresareattachedtoshowthebehaviorsthattheexactsolutionsmayexhibit.

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简介：与阻抗类型边界在2由一个裂缝散布问题的波浪被考虑。这个问题由薄两方面的圆柱的屏幕为波浪的衍射建模。为解决这个问题的一个数字方法被开发。这个问题的答案在联合尖潜力和单个层的潜力形式被代表。密度功能满足的线性不可分的方程为一般parameterized弧被导出。弱单个的积分和Cauchy在这些方程的单个不可分的产生与截断错误分析用一个高度精确的计划被计算。计划的优点在这份报纸建议在一只手里，我们不需要裂缝的analyticity性质，我们允许不同建筑群的事实被珍视在裂缝的双方的表面阻抗。在另外的手里，我们避免超积分。显示出计划的有效性的数字实现被介绍。[从作者抽象]

简介：当起始的数据是小的时，这篇论文在2-dimensionalRiemannianmanifolds上与边界反馈认为半的全球光滑的解决方案的存在是线性schrödinger方程。作者证明全球答案的存在边界反馈取决于不仅，而且在一个Riemannian度量标准上，由原则部分和原来的度量标准的系数给歧管。特别地，authers证明系统的精力指数地腐烂。

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简介：Usingtheextensionhomogeneousbalancemethod,wehaveobtainedsomenewspecialtypesofsolitonsolutionsofthe(2+1)-dimensionalKdVequation.Startingfromthehomogeneousbalancemethod,onecanobtainanonlineartransformationtosimple(2+1)-dimensionalKdVequationintoalinearpartialdifferentialequationandtwobilinearpartialdifferentialequations.Usually,onecanobtainonlyakindofsoliton-likesolutions.Inthisletter,wefindfurthersomespecialtypesofthemultisolitonsolutionsfromthelinearandbilinearpartialdifferentialequations.``

简介：The(2+1)-dimensionalBKPequationintheHirotabilinearformisstudiedduringthiswork.WronskianandGrammiantechniquesareappliedtotheconstructionofWronskianandGrammiansolutionsofthisequation,respectively.ItisshownthatthesesolutionscanbeexpressedasnotonlyPfaffiansbutalsoWronskiansandGrammians.

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简介：Weinvestigateanewclassofperiodicsolutionsto(2+1)-dimensionalKdVequations,byboththelinearsuperpositionapproachandthemappingdeformationmethod.Thesenewperiodicsolutionsaresuitablecombinationsoftheperiodicsolutionstothe(2+1)-dimensionalKdVequationsobtainedbymeansoftheJacobianellipticfunctionmethod,buttheypossessdifferentperiodsandvelocities.

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

简介：Weprovideanewclassofinteriorsolutionofa(2+1)-dimensionalanisotropicstarinFinchandSkeaspacetimecorrespondingtotheBTZblackhole.WedevelopthemodelbyconsideringtheMITbagmodelEOSandaparticularansatzforthemetricfunctiongrrproposedbyFinchandSkea[M.R.FinchandJ.E.F.Skea,Class.Quantum.Grav.6(1989)467].Ourmodelisfreefromcentralsingularityandsatisfiesallthephysicalrequirementsfortheacceptabilityofthemodel.

简介：Startingfromthevariableseparationsolutionobtainedbyusingtheextendedhomogenousbalancemethod,anewclassofcombinedstructures,suchasmulti-peakonandmulti-dromionsolution,multi-compactonandmultidromionsolution,multi-peakonandmulti-compactonsolution,forthe(2+1)-dimensionalNizhnik-Novikov-Veselovequationarefoundbyselectingappropriatefunctions.Thesenewstructuresexhibitnovelinteractionfeatures.Theirinteractionbehaviorisverysimilartothecompletelynonelasticcollisionsbetweentwoclassicalparticles.

简介：Liquid-phase-exfoliationtechnologywasutilizedtopreparelayeredMoS2,WS2,andMoSe2nanosheetsincyclohexylpyrrolidone.Thenonlinearopticalresponseofthesenanosheetsindispersionswasinvestigatedbyobservingspatialself-phasemodulation（SSPM）usinga488nmcontinuouswavelaserbeam.ThediffractionringpatternsofSSPMwerefoundtobedistortedalongtheverticaldirectionrightafterthelasertraversingthenanosheetdispersions.Thenonlinearrefractiveindexofthethreetransitionmetaldichalcogenidesdispersionsn2wasmeasuredtobe10-7cm2W-1,andthethird-ordernonlinearsusceptibilityχ（3）10-9esu.TherelativechangeofeffectivenonlinearrefractiveindexΔn2e∕n（2e）oftheMoS2,WS2,andMoSe2dispersionscanbemodulated0.012–0.240,0.029–0.154,and0.091–0.304,respectively,bychangingtheincidentintensities.Ourexperimentalresultsimplynovelpotentialapplicationoftwo-dimensionaltransitionmetaldichalcogenidesinnonlinearphasemodulationdevices.

简介：作者调查eigen的系统或2的根向量的完全性

简介：与联系的谎言点对称新(2+1)维的KdVequationu_t+3u_xu_y+u_(xxy)=0被调查。一些类似减小被解决相应特战程导出。为这个方程的Painleve分析也被介绍，孤立子答案从Baecklund转变直接被获得。

简介：Withthehelpofanextendedmappingapproach,anewtypeofvariableseparationexcitationwiththreearbitraryfunctionsofthe(2+1)-dimensionaldispersivelong-waterwavesystem(DLW)isderived.Basedonthederivedvariableseparationexcitation,abundantnon-propagatingsolitonssuchasdromion,ring,peakon,andcompactonetc.arerevealedbyselectingappropriatefunctionsinthispaper.

简介：InthispaperwedevelopakindofdissipativediscreteschemeforthecomputationofhomoclinicorbitsnearTB-pointinHamiltoniansystems.Itisprovedbyusingcontinuationmethodthatwhenthedissipativetermanditscoefficientaresuitablychosen,thisschemepossessesdiscretehomoclinicorbits,whichapproximatethecontinuoushomoclinicorbitswithsecondorderaccuracyw.r.totime-stepsize.

简介：TheextendedRiccatimappingapproachisfurtherimprovedbygeneralizedRiccatiequation,andcombineitwithvariableseparationmethod,abundantnewexactcomplexsolutionsforthe(2+1)-dimensionalmodifieddispersivewater-wave(MDWW)systemareobtained.Basedonaderivedperiodicsolitarywavesolutionandarationalsolution,westudyatypeofphenomenonofcomplexwave.

简介：对称一(2+1)维的浅水波浪系统，最新通过使用分析力学的变化原则被构造，在这篇论文被研究。谎言对称和相应减小借助于古典谎言组途径被获得。(1+1)维的排水量当特殊对称参数被选择时，浅水波浪方程能从减小被导出。