Existence and Asymptotic Stability of Quasi-Periodic Solutions of Discrete NLS with Potential

We prove the existence of a two-parameter family of small quasi-periodic solutions of the discrete nonlinear Schrodinger equation (DNLS). We further show that all small solutions of DNLS decouple to one of these quasi-periodic solutions and dispersive wave. As a byproduct, we show that all small nonlinear bound states including excited states are stable.

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