Existence and asymptotic stability of quasi-periodic solution of discrete NLS with potential in $\mathbb{Z}$

Abstract

We prove the existence of a 2-parameter family of small quasi-periodic in time solutions of discrete nonlinear Schrödinger equation (DNLS). We further show that all small solutions of DNLS decouples to this quasi-periodic solution and dispersive wave.

31 pages

References in corpus (2)

• On the spectral theory and dispersive estimates for a discrete Schrödinger equation in one dimension
• On asymptotic stability of standing waves of discrete Schrödinger equation in $\mathbb{Z}$

Cited by in corpus (2)

• On orbital instability of spectrally stable vortices of the NLS in the plane
• A note on small periodic solutions of discrete nonlinear Klein-Gordon equations