The N-soliton solution to the higher-order nonlinear Schrödinger–Maxwell–Bloch system via the Riemann–Hilbert approach

Abstract

In this paper, we study the N-soliton solution of the high-order nonlinear Schrödinger–Maxwell–Bloch system via the Riemann–Hilbert approach. Based on a Lax pair of the system, we carry out a spectral analysis and construct the corresponding Riemann–Hilbert problem. By solving the Riemann–Hilbert problem without reflection, we obtain the N-soliton solution of the system, especially the explicit expression of the single-soliton solution and the expression of the two-soliton solution. The partial three-dimensional diagrams of single-soliton and two-soliton solutions are also given. By comparing the diagrams, we also discuss the relationship between the parameters of the system and the soliton direction.