Multi-speed solitary wave solutions for nonlinear Schrödinger systems

Abstract. We prove the existence of a new type of solutions to a nonlinear Schrödinger system. These solutions, which we callmulti-speeds solitary waves, are behaving at large time as a couple of scalar solitary waves traveling at different speeds. The proof relies on the construction of approximations of the multi-speeds solitary waves by solving the system backwards in time and using energy methods to obtain uniform estimates.