Multi-speed solitary wave solutions for a coherently coupled nonlinear Schrödinger system

Existence of multi-speed solitary wave solutions for a coherently coupled system of nonlinear Schrödinger equations is proved. Such solutions behave at large time as a couple of scalar solitary waves traveling at different speeds. Compared to incoherently coupled nonlinear Schrödinger systems which have enjoyed a lot of research during the past several decades, coherently coupled nonlinear Schrödinger systems have a significant different feature that their component masses are not conserved but only the total mass is conserved. Some restriction upon the phases and velocities of the two component solitary waves is therefore imposed to fit this situation.