AKNS Type Reduced Integrable Hierarchies with Hamiltonian Formulations

"The aim of this paper is to generate a kind of integrable hierarchies of four-component evolution equations with Hamiltonian structures, from a kind of reduced Ablowitz-Kaup-Newell-Segur (AKNS) matrix spectral problems. The zero curvature formulation is the basic tool and the trace identity is the key to establishing Hamiltonian structures. Two examples of Hamiltonian equations in the resulting inte- grable hierarchies are added to the category of coupled integrable nonlinear Schr¨odinger equations and coupled integable modified Korteweg-de Vries equations."