| 一类孤立子系统的Hamilton结构及Liouville可积性 |
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| 引用本文： | 王燕,吕芳. 一类孤立子系统的Hamilton结构及Liouville可积性[J]. 数学学报, 2011, 54(1): 15-22 |
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| 作者姓名： | 王燕 吕芳 |
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| 作者单位： | 洛阳师范学院数学科学学院 洛阳 471000 |
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| 基金项目： | 河南省基础与前沿技术研究计划项目(092300410187),河南省教育厅自然科学基金研究项目(2009B110014,2008B110010);洛阳师范学院青年自然科学基金项目(qnjj-2009-12) |
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| 摘 要： | 本文给出了一个2×2谱问题及其相应的孤子族,并利用此孤子族的Lenard算子对的性质,证明了该系统是具有Bi-Hamilton结构和Multi-Hamilton结构的广义Hamilton系统,进一步给出其Liouville可积性的证明.此外,值得提出的是此系统可约化为广义TD族、TD族和广义C-KdV族、C-KdV族等,并得到了该孤子族的Hamilton泛函与守恒密度之问的一一对应关系.
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| 关 键 词： | Hamilton算子 Hamilton结构 Liouville可积 |
| 收稿时间： | 2009-04-24 |
| 修稿时间： | 2010-07-23 |
Hamiltonian Structure and Liouville Integrability of a Kind of Soliton Hierarchy |
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| Affiliation: | Department of Science and Mathematics, Luoyang Normal University, Luoyang 471000, P. R. China |
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| Abstract: | Based on a 2 × 2 spectral problem, the corresponding hierarchy of evolution equations is derived. According to the property of its 2 × 2 Lenard pair of operators, it can be checked that the hierarchy is a generalized Hamilton system and possesses Bi-Hamilton structure and Multi-Hamilton structure. Furthermore, its Liouville integrability is also evidenced. What's more, this hierarchy, in special cases, can reduce to the general TD hierarchy, TD hierarchy, general C-KdV hierarchy, C-KdV hierarchy, etc. In the end, the one to one relation between the Hamilton functionals and the conservation densities are provided too. |
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| Keywords: | Hamiltonian operator Hamiltonian structure Liouville integrability |
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