| A NEW HIERARCHY OF LAX AND LIOUVILLE INTEGRABLE EVOLUTION EQUATIONS ASSOCIATED WITH AN ISOSPECTRAL PROBLEM IN THE LOOP ALGEBRA A2 |
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| 引用本文： | Zhenya YAN. A NEW HIERARCHY OF LAX AND LIOUVILLE INTEGRABLE EVOLUTION EQUATIONS ASSOCIATED WITH AN ISOSPECTRAL PROBLEM IN THE LOOP ALGEBRA A2[J]. 系统科学与复杂性, 2006, 19(3): 301-306. DOI: 10.1007/s11424-006-0301-3 |
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| 作者姓名： | Zhenya YAN |
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| 作者单位： | Key Laboratory of Mathematics Mechanization, Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China. |
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| 基金项目： | This work was supported by the National Natural Science Foundation of China （No. 10401039） and the National Key Basic Research Project of China （No. 2004CB318000）. |
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| 摘 要： |
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| 关 键 词： | 哈密尔敦函数结构 积分 环代数 等光谱问题 |
| 收稿时间： | 2006-06-09 |
| 修稿时间： | 2006-06-09 |
A New Hierarchy of Lax and Liouville Integrable Evolution Equations Associated with an Isospectral Problem in the Loop Algebra Ã2 |
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| Zhenya Yan. A New Hierarchy of Lax and Liouville Integrable Evolution Equations Associated with an Isospectral Problem in the Loop Algebra Ã2[J]. Journal of Systems Science and Complexity, 2006, 19(3): 301-306. DOI: 10.1007/s11424-006-0301-3 |
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| Authors: | Zhenya Yan |
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| Affiliation: | (1) Key Laboratory of Mathematics Mechanization, Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100080, China |
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| Abstract: | 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. |
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| Keywords: | Isospectral problem loop algebra Lax integrable Liouville integrable Hamiltonian structure. |
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