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

Associated with a 4 x 4 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.