WKB analysis for the Gross-Pitaevskii equation with non-trivial boundary conditions at infinity
arXiv:0710.0816 · doi:10.1016/j.anihpc.2008.02.006
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.
arXiv comment20 pages
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Cited by in corpus (4)
- Madelung, Gross-Pitaevskii and Korteweg
- An asymptotic preserving approach for nonlinear Schrodinger equation in the semiclassical limit
- WKB analysis of the Logarithmic Nonlinear Schrodinger Equation in an analytic framework
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