Linear vs. nonlinear effects for nonlinear Schrödinger equations with potential.
Linear vs. nonlinear effects for nonlinear Schrödinger equations with potential.
复制标题
DOI：
10.1142/s0219199705001829
复制
发表时间：
2004-05
影响因子：
1.6
通讯作者：
R. Carles
中科院分区：
文献类型：
--
作者：
R. Carles
本文综述了近年来关于带势的非线性Schrodinger方程的一些结果，重点讨论了势为二阶多项式的情形，在这种情形下，由势引起的线性动力学与非线性效应之间的相互作用可以得到相当精确的描述.这包括半经典制度，以及有限时间爆破和散射问题。我们提出了用于这些问题的工具，以及它们的局限性，并概述了证据的论点。
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.