A Nonlinear Adiabatic Theorem for Coherent States

Details A Nonlinear Adiabatic Theorem for Coherent States A Nonlinear Adiabatic Theorem for Coherent States

2010-10-28

arxiv.org/abs/1010.5977v1

Nonlinearity 24, 8 (2011) 2143-2164

Mathematics

Analysis of PDEs

21 pages, no figure

Scientific paper

10.1088/0951-7715/24/8/002

We consider the propagation of wave packets for a one-dimensional nonlinear Schrodinger equation with a matrix-valued potential, in the semi-classical limit. For an initial coherent state polarized along some eigenvector, we prove that the nonlinear evolution preserves the separation of modes, in a scaling such that nonlinear effects are critical (the envelope equation is nonlinear). The proof relies on a fine geometric analysis of the role of spectral projectors, which is compatible with the treatment of nonlinearities. We also prove a nonlinear superposition principle for these adiabatic wave packets.

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