Orbital stability for schrödinger systems with nonautonomous coupled nonlinearities

We prove the existence and the orbital stability of standing waves for the nonautonomous Schrödinger system {iut+Δu-a(x)u+(|u|2p+b(x)|u|p-1|v|p+1)u=0,x∈ℝN,ivt+Δv-a(x)v+(|v|2p+b(x)|v|p-1|u|p+1)v=0,x∈ℝNunder suitable conditions on the coefficient functions a and b. We follow the idea of analyzing the compactness of minimizing sequence of the constrained minimization problems.