Asymptotics for the travelling waves in the Gross–Pitaevskii equation

Article type: Research Article

Authors: Gravejat, Philippe

Affiliations: Centre de Recherche en Mathématiques de la Décision, UMR CNRS 7534, Université Paris Dauphine (Paris 9), Place du Maréchal de Lattre de Tassigny, 75775 Paris cedex 16, France E-mail: gravejat@ceremade.dauphine.fr, Tel.: +33(0)144054872, Fax: +33(0)144054599

Abstract: We investigate the asymptotic behaviour of the subsonic travelling waves of finite energy in the Gross–Pitaevskii equation in dimension larger than two. In particular, we give their first-order asymptotics in the case they are axisymmetric, and link it to their energy and momentum.

Keywords: nonlinear Schrödinger equation, travelling waves, asymptotic behaviour

Journal: Asymptotic Analysis, vol. 45, no. 3-4, pp. 227-299, 2005