Semi-classical Schrodinger equations with harmonic potential and nonlinear perturbationReport as inadecuate




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1 IMB - Institut de Mathématiques de Bordeaux 2 ICP - Institut CNRS-PAULI 3 I3M - Institut de Mathématiques et de Modélisation de Montpellier

Abstract : Solutions of semi-classical Schrodinger equation with isotropic harmonic potential focus periodically in time. We study the perturbation of this equation by a nonlinear term. If the scaling of this perturbation is critical, each focus crossing is described by a nonlinear scattering operator, which is therefore iterated as many times as the solution passes through a focus. The study of this nonlinear problem is made possible by the introduction of two operators well adapted to Schrodinger equations with harmonic potential, and by suitable Strichartz inequalities.

Keywords : Harmonic oscillator nonlinear Schrodinger equation scattering theory Maslov index





Author: Rémi Carles -

Source: https://hal.archives-ouvertes.fr/



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