On the asymptotic stability of localized modes in the discrete nonlinear Schrödinger equation

Tetsu Mizumachi; Dmitry Pelinovsky

doi:10.3934/dcdss.2012.5.971

Article Contents

2012, Volume 5, Issue 5: 971-987. Doi: 10.3934/dcdss.2012.5.971

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On the asymptotic stability of localized modes in the discrete nonlinear Schrödinger equation

Tetsu Mizumachi^1, and
Dmitry Pelinovsky^2,

1.
Faculty of Mathematics, Kyushu University, Fukuoka 819-0395
2.
Department of Mathematics, McMaster University, Hamilton, Ontario L8S 4K1

Received: March 2011

Revised: June 2011

Published: October 2012

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Abstract

Asymptotic stability of localized modes in the discrete nonlinear Schrödinger equation was earlier established for septic and higher-order nonlinear terms by using Strichartz estimate. We use here pointwise dispersive decay estimates to push down the lower bound for the exponent of the nonlinear terms.

Keywords:

Discrete nonlinear Schrödinger equation,
localized modes,
dispersive decay estimates,
asymptotic stability.

Mathematics Subject Classification: Primary: 37K60; Secondary: 35Q55, 37K40.

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