Black and gray soliton interactions and cascade compression in the variable coefficient nonlinear Schrödinger equation

We present the theoretical study of dark soliton dynamics in inhomogeneous fiber system by means of a variable coefficient nonlinear Schrödinger equation (Vc-NLSE). The dark soliton interaction in the dispersion-managed system with gain/loss and cascade compression of solitons by the nonlinear tunneling phenomena are studied in detail. Numerically, we study the dark soliton propagation in the continuous wave background, and the obtained soliton solution is found to be robust against perturbations. The elastic collision behavior of the dark solitons are observed by means of asymptotic analysis. For better insight, we study the impact of the blackness factor in the phase profile and also on the interaction dynamics of the different dark soliton settings, such as black and gray soliton. Additionally, we extend the study to the investigation of tunneling of the dark soliton across the barrier/well with a particular emphasize on the role of blackness parameter in the nonlinear tunneling phenomena, and demonstrated a cascaded compression of soliton in the inhomogeneous system.