Reverse-time type nonlocal Sasa–Satsuma equation and its soliton solutions

Abstract

In this work, we study the Riemann–Hilbert problem and the soliton solutions for a nonlocal Sasa–Satsuma equation with reverse-time type, which is deduced from a reduction of the coupled Sasa–Satsuma system. Since the coupled Sasa–Satsuma system can describe the dynamic behaviors of two ultrashort pulse envelopes in birefringent fiber, our equation presented here has great physical applications. The classification of soliton solutions is studied in this nonlocal model by considering an inverse scattering transform to the Riemann–Hilbert problem. Simultaneously, we find that the symmetry relations of discrete data in the special nonlocal model are very complicated. Especially, the eigenvectors in the scattering data are determined by the number and location of eigenvalues. Furthermore, multi-soliton solutions are not a simple nonlinear superposition of multiple single-solitons. They exhibit some novel dynamics of solitons, including meandering and sudden position shifts. Also, they have the bound state of multi-soliton entanglement and its interaction with solitons.