Travelling waves for the Gross-Pitaevskii equation II

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.

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

References in corpus (3)

• Travelling waves for the Gross-Pitaevskii equation II
• Global dispersive solutions for the Gross-Pitaevskii equation in two and three dimensions
• Scattering theory for the Gross-Pitaevskii equation in three dimensions

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