Optical Solitons for a Five-component Coupled Sasa-Satsuma Equation with Riemann-Hilbert Approach

Abstract In this study, a five-component coupled Sasa-Satsuma system under the zero boundary condition is investigated with the Riemann-Hilbert approach. To begin with, we give its Lax pair and perform the normalization. Based on the normalized Lax pair, we then analyze the analyticity and symmetry of the eigenfunctions and the scattering matrix, which enables the successful establishment of the Riemann- Hilbert problem corresponding to the system. Furthermore, solving the re ectionless Riemann-Hilbert problem, we obtain the N-soliton solutions of the equation. Deducing three special cases of the system's solutions for N = 1, 2, and 3, we perform graphical analysis of the local structures and dynamic behaviors of solitons. It can be observed that the amplitude, velocity, and shape of the solitons remain unchanged before and after their interaction, resembling an elastic collision. However, near the collision point, the mutual interaction between the solitons causes a temporary deformation of their profiles, and they superimpose into a single peak at the meeting point. This collision behavior is distinct from that of ordinary linear waves.