A combined generalized Kaup–Newell soliton hierarchy and its hereditary recursion operator and bi-Hamiltonian structure

On the basis of a specific matrix Lie algebra, we propose a Kaup–Newell-type matrix eigenvalue problem with four potentials and compute an associated soliton hierarchy within the zero-curvature formulation. A hereditary recursion operator and a bi-Hamiltonian structure are presented to show the Liouville integrability of the resulting soliton hierarchy. An illustrative example is a novel model consisting of combined derivative nonlinear Schrödinger equations with two arbitrary constants.