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Asymptotic evolution for the semiclassical nonlinear Schrödinger equation in presence of electric and magnetic fields

TitleAsymptotic evolution for the semiclassical nonlinear Schrödinger equation in presence of electric and magnetic fields
Publication TypeJournal Article
Year of Publication2008
AuthorsSelvitella, A
JournalJournal of Differential Equations
Volume245
Pagination2566 - 2584
ISSN0022-0396
Abstract

In this paper we study the semiclassical limit for the solutions of a subcritical focusing NLS with electric and magnetic potentials. We consider in particular the Cauchy problem for initial data close to solitons and show that, when the Planck constant goes to zero, the motion shadows that of a classical particle. Several works were devoted to the case of standing waves: differently from these we show that, in the dynamic version, the Lorentz force appears crucially.

URLhttp://www.sciencedirect.com/science/article/pii/S002203960800243X
DOI10.1016/j.jde.2008.05.012

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