A NEW HIERARCHY OF LAX AND LIOUVILLE INTEGRABLE EVOLUTION EQUATIONS ASSOCIATED WITH AN ISOSPECTRAL PROBLEM IN THE LOOP ALGEBRA■  

作　　者：Zhenya YAN 

机构地区：[1]Key Laboratory of Mathematics Mechanization, Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China.

出　　处：《Journal of Systems Science & Complexity》2006年第3期301-306,共6页系统科学与复杂性学报（英文版）

基　　金：This work was supported by the National Natural Science Foundation of China(No.10401039);the National Key Basic Research Project of China(No. 2004CB318000)

摘　　要：In this paper, an isospectral problem with five potentials is investigated in loop algebra A2 such that a new hierarchy of evolution equations with five arbitrary functions is obtained. And then by fixing the five arbitrary functions to be certain flmctions and using the trace identity, the generalized Hamiltonian structure of the hierarchy of evolution equations is given, it is shown that this hierarchy of equations is Liouville integrable. Finally some special cases of the isospectral problem are also given.

关 键 词：Isospectral problem loop algebra Lax integrable Liouville integrable Hamiltonian structure. 

分 类 号：O15[理学—数学]