Riemann–Hilbert Approach and N-Soliton Solutions for a Higher-Order Coupled Nonlinear Schrödinger System

In this paper, the main work is to study the N-soliton solutions for a higher-order coupled nonlinear Schrödinger system by using the method of Riemann–Hilbert. In the process of research, starting with the spectral analysis for the x-part of the Lax pair, we formulate the Riemann–Hilbert problem for the higher-order coupled nonlinear Schrödinger system. Then we infer the symmetric relation of the potential matrix and scattering data, from which we can find the zero structure of the Riemann–Hilbert problem. Moreover, we can obtain the unified formulas of the N-soliton solutions for the higher-order coupled nonlinear Schrödinger system by solving the non-regular Riemann–Hilbert problem. In addition, the dynamical behaviors of the single-soliton solution, the two-soliton solutions and the three-soliton solutions are analyzed by choosing appropriate parameters.