简介：<正>Inthispaper,westudythebifurcationproblemsofroughheteroclinicloupscormectingthrecsaddlepointsforahigher-dimensionalsystem.Undersometransversalconditionsandthenontwistedcondition.theexistence.uniqueness.ndincoexistenccofthcl-heteroclinicloopwiththrecortwosaddlepomts.l-homoclinicorbitandl-periodicorbitnearTareobtained.Nleanwhile,thebifurcationsurfacesandexistenceregionsarealsogiven.Moreover.theabovebifurcationresultsareextendedtothecaseforheteroclinicloopwithlsaddlepoints.

简介：

简介：ThefollowingcoupledSchrdingersystemwithasmallperturbationuxx+u-u3+βuv2+f(,u,ux,v,vx)=0inR,vxx-v+v3+βu2v+g(,u,ux,v,vx)=0inRisconsidered,whereβandaresmallparameters.ThewholesystemhasaperiodicsolutionwiththeaidofaFourierseriesexpansiontechnique,anditsdominantsystemhasaheteroclinicsolution.Thenadjustingsomeappropriateconstantsandapplyingthefixedpointtheoremandtheperturbationmethodyieldthatthisheteroclinicsolutiondeformstoaheteroclinicsolutionexponentiallyapproachingtheobtainedperiodicsolution(calledthegeneralizedheteroclinicsolutionthereafter).