Asymptotic stability of soliton for discrete nonlinear Schrödinger equation on one-dimensional lattice

2021/12/02 by Masaya Maeda, Maeda, Masaya, Masafumi Yoneda +1
Mathematics · Physics and Astronomy · #35Q55 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Photonic Systems #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.2112.00998

openalex publication_date 2021/12/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we give a simple and short proof of asymptotic stability of soliton for discrete nonlinear Schrödinger 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.

Citations

• On asymptotic stability of standing waves of discrete Schrödinger equation in \Bbb Z

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