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.