Absorption and amplification of dark solitons

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Abstract
Propagation of dark solitons in nonlinear media that include gain and loss is investigated. Two-photon absorption is shown to lead to dark-soliton broadening and attenuation, whereas gain (such as that arising from stimulated Raman scattering) is shown to lead to their narrowing and amplification. The relations describing the adiabatic evolution of dark solitons in the weakly perturbed media are presented. In comparison with fundamental bright solitons, dark solitons are shown to be less sensitive to the perturbations. Stationary propagation of dark solitons is also found to be possible in the presence of both absorption and amplification, but it differs from that in the passive lossless nonlinear media.