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

Pages: 971 - 987, Volume 5, Issue 5, October 2012

doi:10.3934/dcdss.2012.5.971       Abstract        References        Full Text (421.5K)       Related Articles

Tetsu Mizumachi - Faculty of Mathematics, Kyushu University, Fukuoka 819-0395, Japan (email)
Dmitry Pelinovsky - Department of Mathematics, McMaster University, Hamilton, Ontario L8S 4K1, Canada (email)

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.

Received: March 2011;      Revised: June 2011;      Published: January 2012.

 References