On the asymptotic stability of bound states in 2D cubic Schrödinger equation

Kirr, E and Zarnescu, A (2009) On the asymptotic stability of bound states in 2D cubic Schrödinger equation. Communications in Mathematical Physics, 272 (2). pp. 443-468. ISSN 0010-3616

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Abstract

We consider the cubic nonlinear Schrödinger equation in two space dimensions with an attractive potential. We study the asymptotic stability of the nonlinear bound states, i.e. periodic in time localized in space solutions. Our result shows that all solutions with small, localized in space initial data, converge to the set of bound states. Therefore, the center manifold in this problem is a global attractor. The proof hinges on dispersive estimates that we obtain for the non-autonomous, non-Hamiltonian, linearized dynamics around the bound states.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QA Mathematics > QA0299 Analysis. Including analytical methods connected with physical problems
Depositing User: Arghir Zarnescu
Date Deposited: 18 May 2014 10:07
Last Modified: 18 May 2014 10:07
URI: http://sro.sussex.ac.uk/id/eprint/48725
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