Dark Optical Solitons on Influence of the Self-steepening Term

Essential difficulties caused by the nonvanishing boundary condition greatly hinder the development of the systematic perturbation theory for dark solitons. Recently a direct perturbation method for dark one-soliton is developed by the authors with rigorous proof of the completeness of squared Jost solutions. In this letter, influence of the self-steepening term is discussed analytically with the method.