Linear vs. nonlinear effects for nonlinear Schrodinger equations with potential

Preprint

21 May 2004

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.math/0405411

Abstract

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.

Keywords

NONLINEAR SCHRODINGER EQUATIONS
EQUATIONS WITH POTENTIAL
SCHRODINGER EQUATIONS
NONLINEAR EFFECTS
RECENT RESULTS
SCATTERING

All Related Versions

Version 1, 2004-05-21, ArXiv
Published version: Communications in Contemporary Mathematics, 7 (4), 483.

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