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

The main work of this paper is to study the soliton solutions and asymptotic behavior of the integrable reverse space-time nonlocal Sasa-Satsuma equation, which is derived from the coupled two-component Sasa-Satsuma system with a specific constraint. The soliton solutions of the nonlocal Sasa-Satsuma equation are constructed through solving the inverse scattering problems by Riemann-Hilbert method. Compared with local systems, discrete eigenvalues and eigenvectors of the reverse space-time nonlocal Sasa-Satsuma equation have novel symmetries and constraints. On the basis of these symmetry relations of eigenvalues and eigenvectors, the one-soliton and two-soliton solutions are obtained and the dynamic properties of these solitons are shown graphically. Furthermore, the asymptotic behaviors of two-soliton solutions are analyzed. All these results about physical features and mathematical properties may be helpful to comprehend nonlocal nonlinear system better.