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.