Riemann–Hilbert problems of a six-component fourth-order AKNS system and its soliton solutions

Associated with a 4×4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$4\times 4$$\end{document} matrix spectral problem, a six-component AKNS soliton hierarchy is presented, together with the first three nonlinear soliton systems. From an equivalent spectral problem, a kind of Riemann–Hilbert problems is formulated for a six-component system of fourth-order AKNS equations in the resulting AKNS hierarchy. Soliton solutions to the considered system of coupled fourth-order AKNS equations are worked out from a reduced Riemann–Hilbert problem where an identity jump matrix is taken.