Binary Darboux transformation and interactions of solitons for a higher-order matrix nonlinear Schrödinger equation

Abstract

In this paper, we present two- and three-soliton solutions for a higher-order matrix nonlinear Schrödinger equation based on the binary Darboux transform constructed, and analyze various types of interaction properties of solitons. For the two solitons, our analytical results reveal four major features that are associated to interaction dynamics: breather-like solitons, bound-state solitons, bound states of the solitons with one/two peaks and bound states of one soliton and another soliton with breather-like structure. In addition, we graphically analyze the related properties with regard to interactions of three solitons, and seven different types of interesting appearances about soliton interactions are obtained, including shape-changing and shape-preserving interactions.

Keywords

• Higher-order matrix nonlinear Schrödinger equation
• Bound-state solitons
• Binary Darboux transformation