简介:Theusual(1+1)-dimensionalSchwartzBoussinesqequationisextendedtothe(1+1)-dimensionalspace-timesym-metricformandthegeneral(n+1)-dimensionalspace-timesymmetricform.TheseextensionsarePainlevintegrableinthesensethattheypossessthePainlevproperty.Thesinglesolitonsolutionsandtheperiodictravellingwavesolutionsforarbitrarydimensionalspace-timesymmetricformareobtainedbythePainlev-Bcklundtransformation.
简介:UsingthestandardPainlevéanalysisandtheperturbativemethod,thePainlevétestforthelogarithmicbranchisinvestigated.NinearbitraryfunctionsareobtainedandtheBacklundtransformationofthelogarithmicbranchisgiven.UsingthenewtypeBacklundtransformation,manyexactsolutionsareobtained.
简介:WeinvestigatethePainlevéintegrabilityofnonautonomousnonlinearSchrdinger(NLS)equationswithbothspace-andtime-dependentdispersion,nonlinearity,andexternalpotentials.ThePainlevéanalysisiscarriedoutwithoutusingtheKruskal'ssimplification,whichresultsinmoregeneralizedformofinhomogeneousequations.TheobtainedequationsareshowntobereducibletothestandardNLSequationbyusingapointtransformation.WealsoconstructthecorrespondingLaxpairandcarryoutitsKundu-typereductiontothestandardLaxpair.SpecialcasesofequationsfromchoosinglimitedformofcoefficientscoincidewiththeequationsfromthepreviousPainlevéanalysesand/orbecomeunknownnewequations.
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