%0 Journal Article
%T A Nonlinear Adiabatic Theorem for Coherent States
%A R¨Śmi Carles
%A Clotilde Fermanian Kammerer
%J Mathematics
%D 2010
%I arXiv
%R 10.1088/0951-7715/24/8/002
%X 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.
%U http://arxiv.org/abs/1010.5977v1