Travelling waves for the Gross-Pitaevskii equation II

Details Travelling waves for the Gross-Pitaevskii equation II Travelling waves for the Gross-Pitaevskii equation II

2007-11-15

arxiv.org/abs/0711.2408v2

Communications in Mathematical Physics 285, 2 (2009) 567-651

Mathematics

Analysis of PDEs

Final version accepted for publication in Communications in Mathematical Physics with a few minor corrections and added remark

Scientific paper

10.1007/s00220-008-0614-2

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.

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