Travelling waves for the Gross-Pitaevskii equation II

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Date
2009
Notes
Final version accepted for publication in Communications in Mathematical Physics with a few minor corrections and added remarks
Link to item file
http://hal.archives-ouvertes.fr/hal-00187672/en/
Dewey
Probabilités et Mathématiques appliquées
Sujet
Gross-Pitaevksii equation; Travelling waves.
Journal issue
Communications in Mathematical Physics
Volume
285
Number
2
Publication date
01-2009
Article pages
567-651
Publisher
Springer
DOI
http://dx.doi.org/10.1007/s00220-008-0614-2
URI
https://basepub.dauphine.fr/handle/123456789/704
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Author
Béthuel, Fabrice
Gravejat, Philippe
Saut, Jean-Claude
Type
Article accepté pour publication ou publié
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.