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arXiv · 0711.2408

Travelling waves for the Gross-Pitaevskii equation II

Fabrice Bethuel·Philippe Gravejat·Jean-Claude Saut
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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.

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Fabrice Bethuel, Philippe Gravejat, Jean-Claude Saut. 2008-08-26. Travelling waves for the Gross-Pitaevskii equation II. https://doi.org/10.1007/s00220-008-0614-2

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