Vol. 8, No. 6, 2015

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On small energy stabilization in the NLS with a trapping potential

Scipio Cuccagna and Masaya Maeda

Vol. 8 (2015), No. 6, 1289–1349
DOI: 10.2140/apde.2015.8.1289
Abstract

We describe the asymptotic behavior of small energy solutions of an NLS with a trapping potential, generalizing work of Soffer and Weinstein, and of Tsai and Yau. The novelty is that we allow generic spectra associated to the potential. This is a new application of the idea of interpreting the nonlinear Fermi golden rule as a consequence of the Hamiltonian structure.

Keywords
nonlinear Schroedinger equation, asymptotic stability
Mathematical Subject Classification 2010
Primary: 35Q55
Milestones
Received: 3 September 2013
Revised: 11 January 2015
Accepted: 14 May 2015
Published: 5 September 2015
Authors
Scipio Cuccagna
Department of Mathematics and Geosciences
University of Trieste
via Valerio 12/1
I-34127 Trieste
Italy
Masaya Maeda
Department of Mathematics and Informatics
Chiba University
Faculty of Science
Chiba 263 8522
Japan