Two types of multicomponent matrix loop algebras and its application

Abstract

Two types of multicomponent matrix Lie algebras are constructed, which are devoted to obtain two types of new loop algebras ÃM−1. By making use of Tu scheme, integrable multicomponent Levi hierarchy and multicomponent Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy are generated, which contain an arbitrary positive integer M. Furthermore, we expanded the multicomponent matrix loop algebra into a large one and work out integrable coupling of Levi hierarchy and AKNS hierarchy. This method proposed in this paper can be used generally.