The Multi-component Bpt Hierarchy And Their Integrable Coupling System

In this paper, A matrix Lie algebra A_3M and its corresponding loop algebra (A|⁾_3M are presented firstly. By introducing a new spectral problem , the multi-component BPT equation hierachy is obtained. It follows that the Hamiltonian structure of the above system is presented by use of trace identity. Morever, expanding matrix loop algebra and the integrable coupling of the obtained system are worked out. Finally, taking M=1, the Liouville integrability and Hamiltonian stuctrue of equation hierarchy could be successfully estabilished by making use of the quadratic-form identity.