Multi-component SC Lax Integrable Hierarchy of Soliton Equations and Its Multi-component Integrable Coupling System with Two Arbitrary Functions

A new simple loop algebra (?)M is constructed,which is devoted to establishing an isospectral problem.By making use of generalized Tu scheme,the multi-component SC hierarchy is obtained.Furthermore,an expandingloop algebra (?)M of the loop algebra (?)M is presented.Based on (?)M,the multi-component integrable coupling systemof the multi-component SC hierarchy of soliton equations is worked out.How to design isospectral problem of mulit-component hierarchy of soliton equations is a technique and interesting topic.The method can be applied to othernonlinear evolution equations hierarchy.