Asymptotic Stability of Small Bound States in the Discrete Nonlinear Schrdinger Equation

Asymptotic stability of small bound states in one dimension is proved in the framework of a discrete nonlinear Schrdinger equation with septic and higher power-law nonlinearities and an external potential supporting a simple isolated eigenvalue. The analysis relies on the dispersive decay estimates from Pelinovsky and Stefanov [J. Math. Phys., 49 (2008), 113501] and the arguments of Mizumachi [J. Math. Kyoto Univ., 48 (2008), pp. 471497] for a …