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

International audienceWe 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