Dynamics of Spatial Dark Solitons Trapped in the Media with Gain and TPA

The propagation of dark solitons in nonlinear media that include gain and loss described by a nonlinear Schrödinger equation is investigated. Based on the direct approach of perturbation theory, the width, height and other related quantities of dark solitons are obtained. It is shown that stationary propagation of dark solitons is found to be possible in the presence of both gain and absorption. The results obtained by means of our analytic method are in excellent agreement with numerical simulations. Our results are helpful for the research into the optical soliton transmission system.