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.