Multi-speed solitary wave solutions for nonlinear Schrödinger systems

We prove the existence of a new type of solutions to a nonlinear Schrödinger system. These solutions, which we call multi-speeds solitary waves, behave 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 backward in time and using energy methods to obtain uniform estimates.