Linear vs. nonlinear effects for nonlinear Schrodinger equations with potential
偏微分方程分析
2007-05-23 v1 数学物理
math.MP
摘要
We review some recent results on nonlinear Schrodinger equations with potential, with emphasis on the case where the potential is a second order polynomial, for which the interaction between the linear dynamics caused by the potential, and the nonlinear effects, can be described quite precisely. This includes semi-classical regimes, as well as finite time blow-up and scattering issues. We present the tools used for these problems, as well as their limitations, and outline the arguments of the proofs.
引用
@article{arxiv.math/0405411,
title = {Linear vs. nonlinear effects for nonlinear Schrodinger equations with potential},
author = {Remi Carles},
journal= {arXiv preprint arXiv:math/0405411},
year = {2007}
}
备注
20 pages; survey of previous results