Semiclassical asymptotics for weakly nonlinear Bloch waves

Carles, Remi; Markowich, Peter A.; Sparber, Christof

Semiclassical asymptotics for weakly nonlinear Bloch waves

Authors

Carles, Remi

Markowich, Peter A.

Sparber, Christof

Description

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