Semiclassical asymptotics for weakly nonlinear Bloch waves
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🧮 math-ph
math.APmath.MP
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nonlinearasymptoticspotentialweaklyadiabaticberryblochclass
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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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