Dark broad-band solitons and opposite self-frequency shift

In the present paper the nonlinear propagation of ultra-short dark solitons in dispersive optical fibers, described in the frames of the nonparaxial nonlinear amplitude equation is investigated. The nonparaxial equation governs the evolution of narrow-band, as well as broad-band laser pulses with few oscillations under the envelope. We are looking for a solution of that equation, describing the propagation of broad-band laser pulses in single mode optical fibers with normal dispersion. Analytical solutions in the form of dark solitons are found.In the present paper the nonlinear propagation of ultra-short dark solitons in dispersive optical fibers, described in the frames of the nonparaxial nonlinear amplitude equation is investigated. The nonparaxial equation governs the evolution of narrow-band, as well as broad-band laser pulses with few oscillations under the envelope. We are looking for a solution of that equation, describing the propagation of broad-band laser pulses in single mode optical fibers with normal dispersion. Analytical solutions in the form of dark solitons are found.