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A KAM theorem for the defocusing NLS equation


Kappeler, T; Liang, Z (2012). A KAM theorem for the defocusing NLS equation. Journal of Differential Equations, 252(6):4068-4113.

Abstract

In this paper we prove a KAM theorem for the defocusing NLS equation in one space dimension with periodic boundary conditions. The novelty of our result is that it is valid not only near the zero solution, but on the entire Sobolev space H-N(T,C) with N is an element of Z(>= 1). In particular, the invariant tori which persist under small Hamiltonian perturbations might be far away from the zero potential. (C) 2011 Elsevier Inc. All rights reserved.

Abstract

In this paper we prove a KAM theorem for the defocusing NLS equation in one space dimension with periodic boundary conditions. The novelty of our result is that it is valid not only near the zero solution, but on the entire Sobolev space H-N(T,C) with N is an element of Z(>= 1). In particular, the invariant tori which persist under small Hamiltonian perturbations might be far away from the zero potential. (C) 2011 Elsevier Inc. All rights reserved.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:15 March 2012
Deposited On:22 Jan 2013 13:26
Last Modified:05 Apr 2016 16:18
Publisher:Elsevier
ISSN:0022-0396
Publisher DOI:https://doi.org/10.1016/j.jde.2011.11.028

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