Numerical study of bright-bright-dark soliton dynamics in the mixed coupled nonlinear Schrödinger system

Abstract

An efficient, accurate numerical method is developed to study the mixed (bright-bright-dark) solitons in a three component mixed coupled nonlinear Schrödinger system, arising in nonlinear optics. For this purpose, a compact finite difference method involving different boundary conditions for the bright and dark solitons is employed to derive an implicit nonlinear numerical scheme of fourth order in space and second order in time. Particularly, the scheme is shown to be unconditionally stable by von Neumann stability method. Also, the exact soliton solutions and the conserved quantities are used to assess the proposed method. Propagation dynamics as well as the standard elastic and the fascinating energy-sharing collisions of multicomponent mixed solitons are studied in this framework. Significantly, the energy-sharing collision scenario of solitons is found to be robust against small perturbations.