Multi-component Dirac equation hierarchy and its multi-component integrable couplings system

A general scheme for generating a multi-component integrable equation hierarchy is proposed. A simple 3M-dimensional loop algebra (X) over tilde is produced. By taking advantage of (X) over tilde, a new isospectral problem is established and then by making use of the Tu scheme the multi- component Dirac equation hierarchy is obtained. Finally, an expanding loop algebra (F) over tilde (M) of the loop algebra (X) over tilde is presented. Based on the (F) over tilde (M), the multi- component integrable coupling system of the multi- component Dirac equation hierarchy is investigated. The method in this paper can be applied to other nonlinear evolution equation hierarchies.