简介：<正>ThetruncationequationforthederivativenonlinearSchrodingerequationhasbeendis-cussedinthispaper.TheexistenceofaspecialheteroclinicorbithasbeenfoundbyusinggeometricalsingularperturbationtheorytogetherwithMelnikov’stechnique.

简介：Abstract.Inthepresentpaper,wedealwiththelong-timebehaviorofdissipativepartialdifferenttialequations,andweconstructtheapproximateinertialmardfoldsforthenonlbaearStringerequationwithazeroorderdlssipation.Theorderofapproximationofthesemanlfoldetotheglobalattractorisderived.

简介：ThedynamicalcharacterforaperturbedcouplednonlinearSchrodingersystemwithperiodicboundaryconditionwasstudied.First,thedynamicalcharacterofperturbedandunperturbedsystemsontheinvariantplanewasanalyzedbythespectrumofthelinearoperator.Thentheexistenceofthelocallyinvariantmanifoldswasprovedbythesingularperturbationtheoryandthefixed-pointargument.

简介：Usingthewavepackettheory,weobtainallthesolutionsoftheweaklydampednonlinearSchrodingerequation.Thesesolutionsarethestaticsolution,andsolutionsofplanarwave,solitarywave,shockwaveandellipticfunctionwaveandchaos.Thebifurcationphenomenonexistsinbothsteadyandnon-steadysolutions.Thechaoticandperiodicmotionscancoexistinacertainparametricspaceregion.

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简介：Itisshowninthispaperthatifparametersβ1,β2andβ3ofanonlinearSchrodingerequationwithhigherorderdispersionterms(HNLS)satisfythecondition:6β1-β2-2β3(1-6β1k)=0,karealconstant,thenthefundamentalsolitonsolutionsoftheHNLSequationexist.Theexactsolitonsolutionsaregivenandtherelationbetweenthisconditionandtheknownresultsintheliteratureisalsodiscussed.

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简介：NonlinearSchrodingerequation(NSE)arisesinmanyphysicalproblems.Itisaveryimportantequation.Alotofworksstudiedthewellposed,theexistenceofsolutionofNSEetc.Andtherearemanyworksstudiedthenumericalmethodsforit.Recently,sincethedevelopmentofinfinitedimensionaldynamicsystemthedynamicalbehaviorofNSEhasbeeninvestigated.Thepaper[1]studiedthelongtimewellposedness,theexistenceofuniversalattractorandtheestimateofLyapunovexponentforNSEwithweaklydamped.Atthesametimeitwasneedtostudythelargetimenewcomputationalmethodsandtodiscussitsconvergenceerrorestimate,theexistenceofapproximateattractorsetc.InthispapewestudytheNSEwithweaklydamped(1.1).Weassume,where0<λ<2isaconstant.Ifwewishtoconstructthehigheraccuracycomputationalscheme,itwillbedifficultthatstaighfromtheequation(1.1).Thereforewestartwith(1.4)andusefullydiscreteFourierspectralmethodwithtimedifferencetodisscus

简介：在这篇论文，我们扩大印射的途径到N顺序Schroedingerequation。以扩大印射的途径，有一些任意的函数的可变分离解决方案的新家庭被导出。

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简介：Inthispaper,weconsidertheevolutionofasolitonwhendissipativeloseexists.Bymeansofnon-perturbedmethod,anexactenvelopewavesolutionofnonlimearSchroedingerequationwithdissipativetermisobtained.ItisshownthatwhenГ=γ0/(1+2γot),thesolutiongivenherestillmaintainsthehyperbolicsecantprofile.