Dark-pulse solitons in nonlinear-optical fibers

We study analytically the generation and propagation of dark-pulse solitons in nonlinear-optical fibers in the normal dispersion regime. We demonstrate that dark-pulse solitons may be created as pairs by an arbitrary dark pulse with equal boundary conditions without a threshold. We also predict soliton generation by a step of an input pulse phase and obtain the parameters of the generated solitons. The case of soliton generation by a random input pulse is described, and probability of the generation for a Gaussian random pulse is calculated. We also consider the case when dark pulses are generated on a background of finite extent. This situation is related to experiments by Kr\"okel et al. [Phys. Rev. Lett. 60, 29 (1988)] and Weiner et al. [Phys. Rev. Lett. 61, 2445 (1988)], who produced dark pulses (e.g., \ensuremath{\sim}1 psec) on the long bright pulse (e.g., \ensuremath{\sim}${10}^{2}$ psec). We demonstrate that in this case dark pulses are not, strictly speaking, solitons, and in terms of the inverse scattering transform they correspond not to bound states (discrete spectrum) but to quasistationary ones lying in a continuous spectrum. We calculate the parameters of the pulses produced and study their dynamics. It is demonstrated that propagation of these dark pulses is similar to soliton motion. We also study the influence of small perturbations on dynamics of dark solitons, e.g., dispersive broadening of a background and dissipative losses.