摘要
A simple 3M-dimensional loop algebra X is produced, whose commutation operation defined by us is as simple and straightforward as that in the loop algebra A1. It follows that a general scheme for generating multicomponent integrable hierarchy is proposed. By taking advantage of X, a new isospectral problem is established, and then by making use of the Tu scheme the well-known multi-component Levi hierarchy is obtained. Finally, an expanding loop algebra FM of the loop algebra X is presented, based on the FM, the multi-component integrable coupling system of the multi-component Levi hierarchy is worked out. The method in this paper can be applied to other nonlinear evolution equation hierarchies.
A simple 3M-dimensional loop algebra X is produced, whose commutation operation defined by us is A1 as simple and straightforward as that in the loop algebra A1. It follows that a general scheme for generating multi-component integrable hierarchy is proposed. By taking advantage of X, a new isospectral problem is established, and then by making use of the Tu scheme the well-known multi-component Levi hierarchy is obtained. Finally, an expanding loop algebra FM of the loop algebra .X is presented, based on the FM, the multi-component integrable coupling system of the multi-component Levi hierarchy is worked out. The method in this paper can be applied to other nonlinear evolution equation hierarchies.
基金
the National Natural Science Foundation of China under,南开大学-天津大学合作项目,天津大学校科研和教改项目,the Educational Committee of Liaoning Province of China under Gant
关键词
多分量Levi层
多分量可积偶合系统
环代数
环论
loop algebra, multi-component Levi hierarchy, multi-component integrable coupling system