plane-wave solutions of a dissipative generalization of the vector nonlinear schrödinger equation

the modulational instability of perturbed plane-wave solutions of the vector nonlinear schrödinger (vnls) equation is examined in the presence of multiple forms of dissipation. we establish that all constant-magnitude solutions of the dissipative vnls equation are less unstable than their counterparts in the conservative vnls equation. we also present three families of decreasing-in-magnitude plane-wave solutions to this dissipative vnls equation. we establish that if certain forms of dissipation are present, then all exponentially-decaying plane-wave solutions with spatial dependence are linearly unstable while those without spatial dependence are linearly stable.