Travelling waves for the Gross-Pitaevskii equation II
Analysis of PDEs
2009-02-09 v2
Abstract
The purpose of this paper is to provide a rigorous mathematical proof of the existence of travelling wave solutions to the Gross-Pitaevskii equation in dimensions two and three. Our arguments, based on minimization under constraints, yield a full branch of solutions, and extend earlier results, where only a part of the branch was built. In dimension three, we also show that there are no travelling wave solutions of small energy.
Keywords
Cite
@article{arxiv.0711.2408,
title = {Travelling waves for the Gross-Pitaevskii equation II},
author = {Fabrice Bethuel and Philippe Gravejat and Jean-Claude Saut},
journal= {arXiv preprint arXiv:0711.2408},
year = {2009}
}
Comments
Final version accepted for publication in Communications in Mathematical Physics with a few minor corrections and added remarks