Integrable Couplings and Hamiltonian Structure of the AKNS-KN Soliton-Equation Hierarchy

By introducing a higher-dimensional loop algebra,a new integrable coupling of the AKNS-KN soliton hierarchy(called AKNS-KN-SH,for short)is obtained under the framework of zero curvature equations,whose Hamiltonian structure is worked out by using the quadratic-form identity.Finally we give a new Lie algebra A_4 so that its various loop algebras and its equivalent colummn-vector Lie algebra are introduced respectively for which multi-component integrable couplings and their Hamiltonian structure of the the AKNS-KN-SH could be generated.