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Communications in Mathematical Physics

, Volume 285, Issue 2, pp 567–651 | Cite as

Travelling Waves for the Gross-Pitaevskii Equation II

  • Fabrice Béthuel
  • Philippe GravejatEmail author
  • Jean-Claude Saut
Article

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.

Keywords

Solitary Wave Vortex Ring Travel Wave Solution Universal Constant Energy Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Fabrice Béthuel
    • 1
  • Philippe Gravejat
    • 2
    Email author
  • Jean-Claude Saut
    • 3
  1. 1.Laboratoire Jacques-Louis LionsUniversité Pierre et Marie CurieParis Cedex 05France
  2. 2.Centre de Recherche en Mathématiques de la DécisionUniversité Paris DauphineParis Cedex 16France
  3. 3.Laboratoire de MathématiquesUniversité Paris SudOrsay CedexFrance

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