Instability of bound states of nonlinear Schrödinger equations with Morse index equal to two

We prove that every bound state of the nonlinear Schrödinger equation (NLS) with Morse index equal to two, with d2dω2(E(ϕω)+ωQ(ϕω))>0, is orbitally unstable. We apply this result to two particular cases. One is the NLS equation with potential and the other is a system of three coupled NLS equations. In both the cases the linear instability is well known but the orbital instability results are new when the spatial dimension is high.