Semi-classical Schrodinger equations with harmonic potential and nonlinear perturbation
Analysis of PDEs
2016-08-14 v1
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.
Cite
@article{arxiv.math/0702656,
title = {Semi-classical Schrodinger equations with harmonic potential and nonlinear perturbation},
author = {Rémi Carles},
journal= {arXiv preprint arXiv:math/0702656},
year = {2016}
}
Comments
32 pages. Published version with a few typos fixed