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Travelling waves for the Gross-Pitaevskii equation. II. (English) Zbl 1190.35196
Authors’ 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 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.
[For part I, cf. Ann. Inst. Henri Poincaré, Phys. Théor. 70, No. 2, 147–238 (1999, Zbl 0933.35177)].
Reviewer: Ma Wen-Xiu (Tampa)

MSC:
35Q53 KdV equations (Korteweg-de Vries equations)
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
82D55 Statistical mechanics of superconductors
35C07 Traveling wave solutions
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