Perturbation-induced dynamics of dark solitons

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Abstract
We study analytically and numerically the effect of perturbations on (spatial and temporal) dark optical solitons. Our purpose is to elaborate a general analytical approach to describe the dynamics of dark solitons in the presence of physically important effects which break integrability of the primary nonlinear Schrödinger equation. We show that the corresponding perturbation theory differs for the cases of constant and varying backgrounds which support the dark solitons. We present a general formalism describing the perturbation-induced dynamics for both cases and also analyze the influence of several physically important effects, such as linear and two-photon absorption, Raman self-induced scattering, gain with saturation, on the propagation of the dark soliton. As we show, the perturbation-induced dynamics of a dark soliton may be treated as a result of the combined effect of the background evolution and internal soliton dynamics, the latter being characterized by the soliton phase angle. A similar approach is applied to the problem of the dark-soliton propagation on a finite-width background. We analyze adiabatic modification of a dark pulse propagating on a dispersively spreading finite-width background, and we prove analytically that a frequency chirp of the background does not affect the soliton motion. As a matter of fact, the results obtained describe the perturbation-induced dynamics of dark solitons in the so-called adiabatic approximation and, as we show for all the cases analyzed, they are in excellent agreement with direct numerical simulations of the corresponding perturbed nonlinear Schrödinger equation, provided the effects produced by the emitted radiation are small.