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 Schrodinger 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 Schrodinger 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 Schrodinger 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.