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dc.contributor.authorBéthuel, Fabrice
dc.contributor.authorGravejat, Philippe
HAL ID: 812
dc.contributor.authorSaut, Jean-Claude
dc.subjectGross-Pitaevskii equationen
dc.subjecttravelling waveen
dc.subjectKadomtsev-Petviashvili equationen
dc.titleExistence and properties of travelling waves for the Gross-Pitaevskii equationen
dc.typeChapitre d'ouvrage
dc.contributor.editoruniversityotherUniversité d'Orsay, Paris XI;France
dc.contributor.editoruniversityotherUniversité Pierre et Marie Curie, Paris;France
dc.description.abstractenThis paper presents recent results concerning the existence and qualitative properties of travelling wave solutions to the Gross-Pitaevskii equation posed on the whole space R^N. Unlike the defocusing nonlinear Schrödinger equations with null condition at infinity, the presence of non-zero conditions at infinity yields a rather rich and delicate dynamics. We focus on the case N = 2 and N = 3, and also briefly review some classical results on the one-dimensional case. The works we survey provide rigorous justifications to the impressive series of results which Jones, Putterman and Roberts established by formal and numerical arguments.en
dc.relation.ispartofseriestitleContemporary Mathematicsen_US
dc.relation.ispartoftitleStationary and time dependent Gross-Pitaevskii equationsen
dc.relation.ispartofeditorA. Farina and J.-C. Saut
dc.relation.ispartofpublnameAmerican Mathematical Societyen
dc.relation.ispartofpublcityProvidence, R.I.en
dc.subject.ddclabelProbabilités et mathématiques appliquéesen

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