A Class of Multi-Component Non-Isospectral TD Hierarchies and Their Bi-Hamiltonian Structures

By using the classical Lie algebra, the stationary zero curvature equation, and the Lenard recursion equations, we obtain the non-isospectral TD hierarchy. Two kinds of expanding higher-dimensional Lie algebras are presented by extending the classical Lie algebra. By solving the expanded non-isospectral zero curvature equations, the multi-component non-isospectral TD hierarchies are derived. The Hamiltonian structure for one of them is obtained by using the trace identity.