LINEAR VS. NONLINEAR EFFECTS FOR NONLINEAR SCHRÖDINGER EQUATIONS WITH POTENTIAL

Rémi Carles

Type: Article

Publication Date: 2005-08-01

Citations: 15

DOI: https://doi.org/10.1142/s0219199705001829

Abstract

We review some recent results on nonlinear Schrödinger 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 régimes, 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.

Locations

arXiv (Cornell University) - View - PDF
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Communications in Contemporary Mathematics - View

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+	On a class of nonlinear Schrödinger equations. II. Scattering theory, general case	1979	J. Ginibre G. Velo