A Lie algebra and corresponding integrable Hamiltonian system

How to construct a better integrable model in theory,especially the infinite dimensional Hamiltonian system,is one of the main contents of the integrable system. A Lie algebra and its loop algebra are established,from which an isospectral problem is defined. By using Tu-model,a nonlinear integrable hierarchy in the sense of Lax is obtained. Moreover,the trace identity over the corresponding loop algebra is used to furnish the Hamiltonian structure for the resulting nonlinear integrable system.