LINEAR VS. NONLINEAR EFFECTS FOR NONLINEAR SCHRÖDINGER EQUATIONS WITH POTENTIAL
- 1 August 2005
- journal article
- Published by World Scientific Pub Co Pte Ltd in Communications in Contemporary Mathematics
- Vol. 7 (4) , 483-508
- 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.Keywords
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