Stability and instability of standing waves to a system of Schrödinger equations with combined power-type nonlinearities

We obtain the existence of standing wave solutions to a coupled nonlinear Schrödinger system{−iu1t=Δu1+(μ|u1|p+∑k=1mαk|u1|pk−2|u2|qk)u1in RN×(0,T),−iu2t=Δu2+(γ|u2|p+∑k=1mβk|u1|pk|u2|qk−2)u2in RN×(0,T),u1(x,0)=u10(x),u2(x,0)=u20(x)in RN, where 0