Existence and orbital stability of standing waves for nonlinear Schrödinger systems

In this paper we investigate the existence of solutions in H1(RN)×H1(RN)H1(RN)×H1(RN) for nonlinear Schrödinger systems of the form {−Δu1=λ1u1+μ1|u1|p1−2u1+r1β|u1|r1−2u1|u2|r2,−Δu2=λ2u2+μ2|u2|p2−2u2+r2β|u1|r1|u2|r2−2u2, under the constraints ∫RN|u1|2dx=a1>0,∫RN|u2|2dx=a2>0. Here N≥1,β>0,μi>0,ri>1,2