Sasa–Satsuma type matrix integrable hierarchies and their Riemann–Hilbert problems and soliton solutions

Abstract

Sasa–Satsuma type matrix integrable hierarchies are generated from taking two group reductions of replacing the spectral parameter with its complex conjugate and its negative in the matrix AKNS spectral problems. Based on the Lax pairs and the adjoint lax pairs, Riemann–Hilbert problems and thus inverse scattering transforms are formulated for the resulting Sasa–Satsuma type matrix integrable hierarchies, and their soliton solutions are generated from the associated reflectionless Riemann–Hilbert problems.