Riemann–Hilbert problems and soliton solutions for the reverse space-time nonlocal Sasa–Satsuma equation

Abstract

In this paper, the reverse space-time nonlocal Sasa-Satsuma equation is introduced from the coupled Sasa-Satsuma system via the specific solution constraint. Soliton and multisolitons solutions of the reverse spacetime nonlocal Sasa-Satsuma equation are derived through the following steps: 1) The inverse scattering transform method of the coupled Sasa-Satsuma system is carried out, and then the solutions for the system are obtained through solving the established Riemann-Hilbert problems; 2) The symmetry relations of discrete eigenvalues and eigenvectors for the reverse space-time nonlocal Sasa-Satsuma equation are analyzed under the specific solution constraint; 3) Based on the symmetry constraints, the one-soliton and two-soliton solutions are derived, and their dynamics is investigated. Finally, asymptotic analysis of two-soliton solutions for the reverse space-time nonlocal Sasa-Satsuma equation is used to study. The results shown some interesting physical feature and mathematical properties, which might be useful to comprehend nonlocal nonlinear system.