Existence and properties of travelling waves for the Gross-Pitaevskii equation

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dc.creatorBéthuel, Fabrice
dc.creatorGravejat, Philippe
dc.creatorSaut, Jean-Claude
dc.date2009-02-22
dc.date.accessioned2026-07-07T12:45:32Z
dc.date.available2026-07-07T12:45:32Z
dc.descriptionThis 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.
dc.identifierhttps://arxiv.org/abs/0902.3804
dc.identifierhttp://arxiv.org/abs/0902.3804
dc.identifierStationary and time dependent Gross-Pitaevskii equations, A. Farina and J.-C. Saut (Ed.) (2008) 55-104
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/221113
dc.subjectAnalysis of PDEs
dc.subject35Q40 (Primary), 35Q53, 35Q55, 35A05 (Secondary), 35B40
dc.titleExistence and properties of travelling waves for the Gross-Pitaevskii equation
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