Vector solitons for the (2 + 1)‐dimensional coupled nonlinear Schrödinger system in the Kerr nonlinear optical fiber

Abstract

AbstractInvestigated in this paper is the (2 + 1)‐dimensional coupled nonlinear Schrödinger system, which describes the propagation of the optical soliton through the Kerr nonlinear fiber in which each component diffracts in two transverse dimensions. By virtue of the Kadomtsev‐Petviashvili hierarchy reduction, we obtain the bright, dark and mixed vector soliton solutions in terms of the Gramian. We investigate the vector solitons graphically: (1) Bright‐dark one solitons with one of the components being gray or black are shown. Bouncing, beating, oscillating and breathing effects which appear during the interactions between the bright‐dark two solitons are discussed, and those interactions are shape‐preserving; (2) Degenerate and non‐degenerate dark‐dark one solitons are presented. Interaction of the dark‐dark two solitons is discussed and the two solitons keep their amplitudes and velocities invariant except for some phase shifts during the interaction; (3) Bound‐state and complexes of the bright‐bright solitons are presented.