Semiclassical asymptotics for weakly nonlinear Bloch waves
  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. 
Remi Carles, Peter A. Markowich, Christof Sparber