Stability of dark soliton solutions of the quintic complex Ginzburg--Landau equation inthe case of normal dispersion

Dark soliton solutions of the one-dimensional complex Ginzburg--Landau equation (CGLE) are analysed for the case of normal group-velocity dispersion. The CGLE can be transformed to the nonlinear Schr?dinger equation (NLSE) with perturbation terms under some practical conditions. The main properties of dark solitons are analysed by applying the direct perturbation theory of the NLSE. The results obtained may be helpful for the research on the optical soliton transmission system.