Geometric optics and instability for semi-classical Schrodinger equations
Analysis of PDEs
2007-05-23 v4 Mathematical Physics
math.MP
Abstract
We prove some instability phenomena for semi-classical (linear or) nonlinear Schrodinger equations. For some perturbations of the data, we show that for very small times, we can neglect the Laplacian, and the mechanism is the same as for the corresponding ordinary differential equation. Our approach allows smaller perturbations of the data, where the instability occurs for times such that the problem cannot be reduced to the study of an o.d.e.
Cite
@article{arxiv.math/0505468,
title = {Geometric optics and instability for semi-classical Schrodinger equations},
author = {Remi Carles},
journal= {arXiv preprint arXiv:math/0505468},
year = {2007}
}
Comments
22 pages. Corollary 1.7 added