Perturbation theory for dark solitons: inverse scattering transform approach and radiative effects

A perturbation theory for dark solitons of the nonlinear Schrödinger equation is developed. The theory is based on the inverse scattering transform method. Equations describing dynamics discrete (solitonic) and continuous (radiative) scattering data in the presence of perturbations are derived for N-soliton case. Adiabatic equations for soliton parameters and the perturbation-induced radiative field are obtained. The problem of the absence of a threshold for the creation of dark solitons under the action of a perturbation is discussed. A temporal one-soliton pulse with random initial perturbation and a spatial soliton with linear gain and two-photon absorption are considered as examples of application of the developed theory.