Travelling Waves for the Gross-Pitaevskii Equation II

By F. Béthuel, Philippe Gravejat, Jean-Claude Saut. 2007

153 citations recorded by the source corpus.

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.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/4ae07990bf6d88dd8b8fe5ee13144b116fd40d80

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In Mathematical Physics

1. Boris Haspot
2. Frédéric Charve

In Statistical and Nonlinear Physics

1. Boris Haspot
2. Frédéric Charve

Citations in the corpus

• Existence of global strong solution and vanishing capillarity-viscosity limit in one dimension for the Korteweg system (2011, methodology): “Indeed, at least heuristically, the system is equivalent via the Madelung transform to the Gross-Pitaevskii equations which are globally well-posed for large initial data in dimension n = 1, 2, 3 (we refer to [4]).”