Multi-speed solitary waves of nonlinear Schr{\"o}dinger systems: theoretical and numerical analysis

TL;DR

This paper proves the existence of multi-speed solitary waves in coupled nonlinear Schrödinger systems and numerically explores their interactions, revealing elastic and inelastic collision behaviors.

Contribution

It introduces the first proof of multi-speed solitary waves in such systems and provides numerical analysis of their complex interactions.

Findings

Existence of multi-speed solitary waves proven mathematically.

Numerical simulations show elastic and inelastic collisions.

Collision outcomes include mass extraction and reflection.

Abstract

We consider a system of coupled nonlinear Schr{\"o}dinger 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.