  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.
