Multi-speed solitary waves of nonlinear Schr "odinger systems:\n theoretical and numerical analysis

2015/04/20 by Fanny Delebecque, Delebecque, Fanny, Stefan Le Coz +3
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1504.04976

openalex publication_date 2015/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a system of coupled nonlinear Schr "odinger equations in one\nspace dimension. First, we prove the existence of multi-speed solitary waves,\ni.e solutions to the system with each component behaving at large times as a\nsolitary wave. Then, we investigate numerically the interaction of two solitary\nwaves supported each on one component. Among the possible outcomes, we find\nelastic and inelastic interactions, collision with mass extraction and\nreflexion.\n

Citations

• Orbital stability of standing waves for some nonlinear Schr�dinger equations

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