An approach for generating enlarging integrable systems

By constructing a type of antisymmetric matrix Lie algebra, a way to generate enlarging integrable systems is presented. The such integrable hierarchies are not integrable couplings, specially, their corresponding Hamiltonian structure can be obtained by the trace identity. As an application example, the enlarging integrable system and the Hamiltonian structure of the AKNS hierarchy are given. Finally, the explicit relations expressed by the formulae among the solutions of the stationary zero curvature equations are obtained.