Effect of self-steepening on optical solitons in a continuous wave background

We present an analytic method to generate solutions for the optical fiber soliton system that reveals self-steepening effects on solitons coupled to a continuous wave. Exact soliton solutions are obtained by adopting a universal Lax pair technique that solves simultaneously the nonlinear Schrödinger (NLS) equation and the derivative NLS equation. We find that, in the presence of a self-steepening term, the bright type NLS equation with abnormal group velocity dispersion is related to the dark type NLS equation with normal group velocity dispersion and, accordingly, exact soliton solutions of the bright type NLS equation describe both bright and dark solitons depending on the strength of the continuous wave. The self-steepening effect on solitons and possible applications of a continuous wave for the control of solitons are explained.