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Abstract: We consider the propagation of wave packets for the nonlinear Schrodingerequation, in the semi-classical limit. We establish the existence of a criticalsize for the initial data, in terms of the Planck constant: if the initial dataare too small, the nonlinearity is negligible up to the Ehrenfest time. If theinitial data have the critical size, then at leading order the wave functionpropagates like a coherent state whose envelope is given by a nonlinearequation, up to a time of the same order as the Ehrenfest time. We also prove anonlinear superposition principle for these nonlinear wave packets.



Autor: Rémi Carles I3M, Clotilde Fermanian Kammerer LAMA

Fuente: https://arxiv.org/







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