The propagation of bright and dark solitons in lossy optical fibers

An analytic perturbation solution to the nonlinear Schrodinger equation with loss Γ for both normal and anomalous dispersion is developed. Explicit results are obtained through second order in the perturbation Γ. The results show that the dark pulse spreads less rapidly than the bright one and that total spreading as well as the difference in spreading rate for the two types of pulses decreases with loss. Comparisons are made with a zeroth-order perturbation theory and with numerical simulations, which are found to bracket the second-order results