Skip to Main content Skip to Navigation
Journal articles

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

Abstract : 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.
Complete list of metadata

Cited literature [27 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-00176524
Contributor : Rémi Carles Connect in order to contact the contributor
Submitted on : Wednesday, October 3, 2007 - 5:30:57 PM
Last modification on : Monday, October 11, 2021 - 1:22:31 PM
Long-term archiving on: : Thursday, September 27, 2012 - 1:15:37 PM

Files

gp.pdf
Files produced by the author(s)

Identifiers

Citation

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) Non Linear Analysis, Elsevier, 2009, 26 (3), pp.959-977. ⟨10.1016/j.anihpc.2008.02.006⟩. ⟨hal-00176524⟩

Share

Metrics

Record views

215

Files downloads

293