Dark solitonic interactions for the (3 + 1)-dimensional coupled nonlinear Schrödinger equations in nonlinear optical fibers

Abstract

In this paper, the (3 + 1)-dimensional coupled nonlinear Schrödinger equations are investigated, which describe the transverse effects in the nonlinear optical system and arise in the study of the transmission of coupled wave packets and optical solitons in nonlinear optical fibers. Bilinear forms, dark one-, two- and three-soliton solutions are obtained by virtue of the Hirota method. Propagations and interactions of the dark solitons are analyzed graphically: Soliton amplitudes and velocities are determined by the variables related to the wave numbers. Stationary dark solitons are also depicted. Interactions between/among the two/three parallel dark solitons are presented, and soliton amplitudes remain unchanged after each interaction, which signifies that the interactions are elastic.