On the asymptotic stability of localized modes in the discrete nonlinear Schrödinger equation
Tetsu Mizumachi - Faculty of Mathematics, Kyushu University, Fukuoka 819-0395, Japan (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.
Received: March 2011; Revised: June 2011; Published: January 2012.