Semi-classical Schrodinger equations with harmonic potential and nonlinear perturbation

Details Semi-classical Schrodinger equations with harmonic potential and nonlinear perturbation Semi-classical Schrodinger equations with harmonic potential and nonlinear perturbation

2007-02-22

arxiv.org/abs/math/0702656v1

Annales I.H.P., Analyse non lin\'{e}aire 20 (2003) no. 3, 501-542

Mathematics

Analysis of PDEs

32 pages. Published version with a few typos fixed

Scientific paper

10.1016/S0294-1449%2802%2900027-

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.

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