Orbital stability of standing waves for a system of nonlinear Schr\"{o}dinger equations with three wave interaction

We study the existence and stability of standing waves solutions of a three-coupled nonlinear Schr"{o}dinger system related to the Raman amplification in a plasma. By means of the concentration-compacteness method, we provide a characterization of the standing waves solutions as minimizers of an energy functional subject to three independent $L^2$ mass constraints. As a consequence, we establish existence and orbital stability of solitary waves.