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Travelling waves for the Gross-Pitaevskii equation II

Béthuel, Fabrice; Gravejat, Philippe; Saut, Jean-Claude (2009), Travelling waves for the Gross-Pitaevskii equation II, Communications in Mathematical Physics, 285, 2, p. 567-651. http://dx.doi.org/10.1007/s00220-008-0614-2

Type
Article accepté pour publication ou publié
External document link
http://hal.archives-ouvertes.fr/hal-00187672/en/
Date
2009
Journal name
Communications in Mathematical Physics
Volume
285
Number
2
Publisher
Springer
Pages
567-651
Publication identifier
Metadata
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Author(s)
Béthuel, Fabrice
Gravejat, Philippe
Saut, Jean-Claude
Abstract (EN)
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.
Subjects / Keywords
Gross-Pitaevksii equation; Travelling waves.