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Article Dans Une Revue Nonlinearity Année : 2011

A Nonlinear Adiabatic Theorem for Coherent States

Résumé

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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Dates et versions

hal-00530175 , version 1 (27-10-2010)

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Rémi Carles, Clotilde Fermanian Kammerer. A Nonlinear Adiabatic Theorem for Coherent States. Nonlinearity, 2011, 24 (8), pp.2143-2164. ⟨10.1088/0951-7715/24/8/002⟩. ⟨hal-00530175⟩
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