Inverse Scattering Transform of the Coupled Sasa-Satsuma Equation by Riemann-Hilbert Approach

The inverse scattering transform of a coupled Sasa Satsuma equation is studied via Riemann Hilbert approach. Firstly, the spectral analysis is performed for the coupled Sasa Satsuma equation, from which a RiemannHilbert problem is formulated. Then the Riemann Hilbert problem corresponding to the reflection-less case is solved. As applications, multi-soliton solutions are obtained for the coupled Sasa Satsuma equation. Moreover, some figures are given to describe the soliton behaviors, including breather types, single-hump solitons, double-hump solitons, and two-bell solitons.