Communications in Mathematical Sciences

Volume 14 (2016)

Number 6

Multi-speed solitary waves of nonlinear Schrödinger systems: Theoretical and numerical analysis

Pages: 1599 – 1624

DOI: http://dx.doi.org/10.4310/CMS.2016.v14.n6.a7

Authors

Fanny Delebecque (Institut de Mathématiques de Toulouse, Université Paul Sabatier, Toulouse, France)

Stefan le Coz (Institut de Mathématiques de Toulouse, Université Paul Sabatier, Toulouse, France)

Rada M. Weishäupl (Faculty of Mathematics, University of Vienna, Austria)

Abstract

We consider a system of coupled nonlinear Schrödinger equations in one space dimension. First, we prove the existence of multi-speed solitary waves, i.e., solutions to the system with each component behaving at large times as a solitary wave. Then, we investigate numerically the interaction of two solitary waves supported each on one component. Among the possible outcomes, we find elastic and inelastic interactions, collision with mass extraction and reflexion.

Keywords

solitons, solitary waves, nonlinear Schrödinger systems

2010 Mathematics Subject Classification

35C08, 35Q51, 35Q55, 37K40

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