Travelling Waves for the Gross-Pitaevskii Equation II |
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| Authors: | Fabrice Béthuel Philippe Gravejat Jean-Claude Saut |
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| Affiliation: | 1.Laboratoire Jacques-Louis Lions,Université Pierre et Marie Curie,Paris Cedex 05,France;2.Centre de Recherche en Mathématiques de la Décision,Université Paris Dauphine,Paris Cedex 16,France;3.Laboratoire de Mathématiques,Université Paris Sud,Orsay Cedex,France |
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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 (see [3,4,8]) 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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