Asymptotic stability of multi-soliton solutions for nonlinear Schroedinger eqations

2003/09/09 by Galina Perelman, G. Perelman, Perelman, G.
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Numerical methods for differential equations #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.math-ph/0309021

30 pages

arxiv created 2003/09/09 · openalex publication_date 2003/09/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the Cauchy problem for the nonlinear Schroedinger eqiation with initial data close to a sum of N decoupled solitons. Under some suitable assumptions on the spectral structure of the one soliton linearizations we prove that for large time the asymptotics of the solution is given by a sum of solitons with slightly modified parameters and a small dispersive term.

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