Dynamics of Nonautonomous Dark Solitons

We solve a generalized nonautonomous nonlinear Schrödinger equation analytically by performing the Hirota's bilinearization method. The precise expression of a parameter ∈, which provides a compatibility condition and dark soliton management, is obtained. Comparing with nonautonomous bright soliton, we find that the gain parameter affects both the background and the valley of dark soliton (∈²≠1) while it has no effects on the wave central position. Moreover, the precise expressions of a nonautonomous black soliton's (∈²=1) width, background and the trajectory of its wave central, which describe the dynamic behavior of soliton's evolution, are investigated analytically. Finally, the stability of the dark soliton solution is demonstrated numerically. It is shown that the main characteristic of the dark solitons keeps unchanged under a slight perturbation in the compatibility condition.