Semiclassical asymptotics for weakly nonlinear Bloch waves
arXiv:math-ph/0401053 · doi:10.1023/B:JOSS.0000044070.34410.17
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.
References added; more explanations; inaccuracy concerning the initial data fixed
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Cited by in corpus (8)
- Mathematical theory and numerical methods for Bose-Einstein condensation
- Multiphase weakly nonlinear geometric optics for Schrodinger equations
- Semiclassical wave packet dynamics in Schrodinger equations with periodic potentials
- Characterization of edge states in perturbed honeycomb structures
- From power law to Anderson localization in nonlinear Schrödinger equation with nonlinear randomness
- Nonlinear dynamics of semiclassical coherent states in periodic potentials
- A Bloch decomposition based split-step pseudo spectral method for quantum dynamics with periodic potentials
- Bloch dynamics with second order Berry phase correction