Fabrice Bethuel, Philippe Gravejat, Jean-Claude Saut
Published 2007-11-15, updated 2008-08-26Version 2
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.
Comments: Final version accepted for publication in Communications in Mathematical Physics with a few minor corrections and added remarks
Journal: Communications in Mathematical Physics 285, 2 (2009) 567-651
Scattering for the Gross-Pitaevskii equation
On the linear wave regime of the Gross-Pitaevskii equation
Scattering theory for the Gross-Pitaevskii equation in three dimensions
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