The multi-component generalized Kaup-Newell hierarchy and its integrable couplings system with two arbitrary functions

Abstract:
We devise a new simple loop algebra $\tilde{G}_M$ and an isospectral problem. By making use of Tu scheme, the multi-component generalized Kaup-Newell
hierarchy is obtained. Furthermore, an expanding loop algebra $\tilde{F}_M$ of the loop algebra $\tilde{G}_M$ is presented. Based on $\tilde{F}_M$, the multi-component integrable couplings system with two arbitrary functions of the multi-component generalized Kaup-Newell hierarchy are worked out. The method can be applied to other nonlinear evolution equations hierarchy.