Semiclassical asymptotics for weakly nonlinear Bloch waves

Details Semiclassical asymptotics for weakly nonlinear Bloch waves Semiclassical asymptotics for weakly nonlinear Bloch waves

2004-01-29

arxiv.org/abs/math-ph/0401053v4

J. Stat. Phys., 117 (2004), nos. 1-2, 343-375.

Physics

Mathematical Physics

References added; more explanations; inaccuracy concerning the initial data fixed

Scientific paper

10.1023/B:JOSS.0000044070.34410.

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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