Tetsu Mizumachi and Dmitry Pelinovsky

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

Discrete and Continuous Dynamical Systems Series S 5, 971-987 (2012)

Abstract:
Asymptotic stability of localized modes in the discrete nonlinear Schrodinger (DNLS) equations was earlier established for septic and higher-order nonlinear functions by using Strichartz time-averaged estimates. We use here pointwise dispersive decay estimates to push down the lower bound for the exponent of the nonlinear functions.

Keywords:
discrete nonlinear Schrodinger equation, localized modes, dispersive decay estimates, asymptotic stability.