Stable solitary waves with prescribed L2-mass for the cubic Schrodinger system with trapping potentials

For the cubic Schrödinger system with trapping potentials in RN, N≤3, or in bounded domains, we investigate the existence and the orbital stability of standing waves having components with prescribed L²-mass. We provide a variational characterization of such solutions, which gives information on the stability through a condition of Grillakis-Shatah-Strauss type. As an application, we show existence of conditionally orbitally stable solitary waves when: a) the masses are small, for almost every scattering lengths, and b) in the defocusing, weakly interacting case, for any masses.