Asymptotic stability of soliton for discrete nonlinear Schr\"odinger equation on one-dimensional lattice

Abstract

In this paper we give a simple and short proof of asymptotic stability of soliton for discrete nonlinear Schr\"odinger equation near anti-continuous limit. Our novel insight is that the analysis of linearized operator, usually non-symmetric, can be reduced to a study of simple self-adjoint operator almost like the free discrete Laplacian restricted on odd functions.