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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.
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Submitted on : Tuesday, August 26, 2008 - 5:31:15 PM
Last modification on : Tuesday, January 18, 2022 - 3:24:22 PM
Long-term archiving on: : Tuesday, September 21, 2010 - 5:41:05 PM

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Fabrice Bethuel, Philippe Gravejat, Jean-Claude Saut. Travelling waves for the Gross-Pitaevskii equation II. Communications in Mathematical Physics, Springer Verlag, 2009, 285 (2), pp.567-651. ⟨10.1007/s00220-008-0614-2⟩. ⟨hal-00187672v2⟩

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