Inverse Scattering Transform of the Coupled Sasa–Satsuma Equation by Riemann–Hilbert Approach**Supported by the National Natural Science Foundation of China under Project Nos. 11331008 and 11171312 and the Collaborative Innovation Center for Aviation Economy Development of Henan Province

Abstract

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 Riemann–Hilbert 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.