Inverse scattering perturbation theory for the nonlinear Schrödinger equation with non-vanishing background

In this paper, a perturbation theory for the nonlinear Schrödinger equation with non-vanishing boundary conditions based on the inverse scattering transform is presented. It is applied to study the stability of the soliton propagation on a continuous-wave background. It is shown that the soliton is rather robust with respect to dispersive perturbations but it can be strongly affected by damping. In particular, it is shown that adiabatic approaches can underestimate the decay of the soliton energy.