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

摘要

A general scheme for generating a multi-component integrable equation hierarchy is proposed.A simple 3Mdimensional loop algebra (X) is produced.By taking advantage of X,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) M of the loop algebra (X) is presented.Based on the FM,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.