Multi-component Levi Hierarchy and Its Multi-component Integrable Coupling System

作     者：XIA Tie-Cheng YOU Fu-Cai ZHAO Wen-Ying 

作者机构：Department of Mathematics Shanghai University Shanghai 200444 China Department of Mathematics Bohai University Jinzhou 121000 China 

出 版 物：《Communications in Theoretical Physics》 (理论物理通讯（英文版）)

年 卷 期：2005年第44卷第6X期

页      面：990-996页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0704[理学-天文学] 0701[理学-数学] 0702[理学-物理学] 

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 

主　　题：多分量Levi层 多分量可积偶合系统 环代数 环论 

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.