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

Béthuel, Fabrice; Gravejat, Philippe; Saut, Jean-Claude (2008), Existence and properties of travelling waves for the Gross-Pitaevskii equation, in A. Farina and J.-C. Saut, Stationary and time dependent Gross-Pitaevskii equations, American Mathematical Society : Providence, R.I.

Type
Chapitre d'ouvrage
External document link
http://hal.archives-ouvertes.fr/hal-00363329/en/
Date
2008
Book title
Stationary and time dependent Gross-Pitaevskii equations
Book author
A. Farina and J.-C. Saut
Publisher
American Mathematical Society
Series title
Contemporary Mathematics
Published in
Providence, R.I.
ISBN
978-0-8218-4357-4
Number of pages
55-104
Metadata
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Author(s)
Béthuel, Fabrice
Gravejat, Philippe
Saut, Jean-Claude
Abstract (EN)
This 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.
Subjects / Keywords
Gross-Pitaevskii equation; travelling wave; Kadomtsev-Petviashvili equation