On asymptotic stability of solitons for nonlinear Schödinger equation

2008/07/11 by Alexander Komech, Elena Kopylova, Komech, A. I. +3
Mathematics · Physics and Astronomy · #35B41 #35L #35P25 #35Q #37K #81 #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.0807.1878

openalex publication_date 2008/07/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The long-time asymptotics is analyzed for finite energy solutions of the 1D Schrödinger equation coupled to a nonlinear oscillator; mathematically the system under study is a nonlinear Schrödinger equation, whose nonlinear term includes a Dirac delta. The coupled system is invariant with respect to the phase rotation group U(1). This article, which extends the results of a previous one, provides a proof of asymptotic stability of solitary wave solutions in the case that the linearization contains a single discrete oscillatory mode satisfying a non-degeneracy assumption of the type known as the Fermi Golden Rule.

Citations

• Spectral properties of Schrödinger operators and time-decay of the wave functions
• Resonances, radiation damping and instabilitym in Hamiltonian nonlinear wave equations
• SELECTION OF THE GROUND STATE FOR NONLINEAR SCHRÖDINGER EQUATIONS

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