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.

Automated summary

The main focus of this paper is to investigate the soliton solutions and asymptotic behavior of the integrable reverse space-time nonlocal Sasa-Satsuma equation, derived from a coupled two-component Sasa-Satsuma system with a specific constraint. The soliton solutions are obtained by solving the inverse scattering problems using the Riemann-Hilbert method. The reverse space-time nonlocal Sasa-Satsuma equation exhibits novel symmetries and constraints in the discrete eigenvalues and eigenvectors, compared to local systems. The obtained results on the soliton solutions and their dynamics, as well as the asymptotic behaviors, contribute to a better understanding of nonlocal nonlinear systems.