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Article Dans Une Revue Annales de l'Institut Henri Poincaré C, Analyse non linéaire Année : 2009

WKB analysis for the Gross-Pitaevskii equation with non-trivial boundary conditions at infinity

Résumé

We consider the semi-classical limit for the Gross-Pitaevskii equation. In order to consider non-trivial boundary conditions at infinity, we work in Zhidkov spaces rather than in Sobolev spaces. For the usual cubic nonlinearity, we obtain a point-wise description of the wave function as the Planck constant goes to zero, so long as no singularity appears in the limit system. For a cubic-quintic nonlinearity, we show that working with analytic data may be necessary and sufficient to obtain a similar result.
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Dates et versions

hal-00176524 , version 1 (03-10-2007)

Identifiants

Citer

Thomas Alazard, Rémi Carles. WKB analysis for the Gross-Pitaevskii equation with non-trivial boundary conditions at infinity. Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 2009, 26 (3), pp.959-977. ⟨10.1016/j.anihpc.2008.02.006⟩. ⟨hal-00176524⟩
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