Semiclassical Nonlinear Schrodinger equations with potential and focusing initial data

2002/12/31 by Remi Carles, Luc Miller
Mathematics · Physics and Astronomy · #math.AP #math-ph #math.MP #msc:35B40 #msc:35Q55 #msc:81Q20 #msc:35P25

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published as Osaka J. Math. 41 (2004), no. 3, 693-725. · Some typos fixed, final version to appear in Osaka J. Math

arxiv created 2003/07/03 · arxiv updated 2009/11/30

Abstract

We study the asymptotic behaviour of solutions to semi-classical nonlinear Schrodinger equations with a potential, for concentrating and oscillating initial data, when the nonlinearity is repulsive and the potential is a polynomial of degree at most two. We describe the separate roles of the nonlinearity and of the potential, with tools which seem to be specific to the class of potentials that we consider. We also discuss the case of more general subquadratic potentials.

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