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

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

2009-02-22

arxiv.org/abs/0902.3804v1

Stationary and time dependent Gross-Pitaevskii equations, A. Farina and J.-C. Saut (Ed.) (2008) 55-104

Mathematics

Analysis of PDEs

Scientific paper

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 Schr\"odinger 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.

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