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.
External document linkhttp://hal.archives-ouvertes.fr/hal-00363329/en/
Book titleStationary and time dependent Gross-Pitaevskii equations
Book authorA. Farina and J.-C. Saut
Series titleContemporary Mathematics
Number of pages55-104
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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 / KeywordsGross-Pitaevskii equation; travelling wave; Kadomtsev-Petviashvili equation
Showing items related by title and author.
Smets, Didier; Saut, Jean-Claude; Gravejat, Philippe; Béthuel, Fabrice (2009) Article accepté pour publication ou publié
Béthuel, Fabrice; Gravejat, Philippe; Saut, Jean-Claude; Smets, Didier (2010) Article accepté pour publication ou publié