Nonautonomous soliton, controllable interaction and numerical simulation for generalized coupled cubic–quintic nonlinear Schrödinger equations

Abstract

The study of soliton interactions is a significance for improving pulse qualities in nonlinear optics. In this paper, a generalized coupled cubic–quintic nonlinear Schrodinger (GCCQNLS) equation with the group-velocity dispersion, fiber gain-or-loss and nonlinearity coefficient functions is studied, which describes the evolution of a slowly varying wave packet envelope in the inhomogeneous optical fiber. In particular, based on the similarity transformation, we report several families of nonautonomous wave solutions of the GCCQNLS equation. It is reported that there are possibilities to manipulate the interactions of nonautonomous wave solution through manipulating nonlinear and gain/loss functions. Interactions between the different-type bright two solitons have been asymptotically analyzed and presented. And, the two parabolic-type bright solitons propagating with the opposite directions both change their directions after the interaction. Interactions between the linear-, parabolic- and periodic-type bright two solitons are elastic. At last, the numerical simulations on the evolution and collision of two soliton solutions are performed to verify the prediction of the analytical formulations. We present the general approach can provide many possibilities to manipulate soliton waves experimentally and consider the potential applications for the optical self-routing, non-Kerr media and Bose–Einstein condensates (BEC).