An unified form of the AKNS and BPT hierarchies with two arbitrary parameters

We present a new basis of the loop algebra A˜1 which is devote to setting up a new isospectral problem. By using Tu scheme, a new Liouville integrable hierarchy of soliton equations with two arbitrary parameters, which possesses the bi-Hamiltonian structure, is worked out. As reduction cases, it is shown that the hierarchy can be decomposed into the well-known AKNS hierarchy and the BPT hierarchy by taking different values of the parameters respectively. We call the hierarchy as an unified expression of the AKNS and the BPT hierarchies.