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Semiclassical asymptotics for weakly nonlinear Bloch waves

Remi Carles·Peter A. Markowich·Christof Sparber
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Abstract

We study the simultaneous semi-classical and adiabatic asymptotics for a class of (weakly) nonlinear Schroedinger equations with a fast periodic potential and a slowly varying confinement potential. A rigorous two-scale WKB-analysis, locally in time, is performed. The main nonlinear phenomenon is a modification of the Berry phase.

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Remi Carles, Peter A. Markowich, Christof Sparber. 2004-04-19. Semiclassical asymptotics for weakly nonlinear Bloch waves. https://doi.org/10.1023/b%3Ajoss.0000044070.34410.17

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