| 一个新的Lie代数和它的应用 |
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| 引用本文： | 常双领.一个新的Lie代数和它的应用[J].纯粹数学与应用数学,2013(6):627-633. |
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| 作者姓名： | 常双领 |
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| 作者单位： | 北京物资学院信息学院,北京101149 |
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| 摘 要： | 通过构造一个新的Lie代数，利用它相应的Loop代数设计等谱Lax对，根据其相容性条件，得到了一族Lax可积方程族，其一种约化形式为著名的AKNS族．根据迹恒等式得到该方程族的Hamilton结构．利用该可积方程族可以进一步研究它的达布变换、对称、代数几何解等相关性质．
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| 关 键 词： | Lie代数 可积方程族 迹恒等式 Hamilton结构 |
A new Lie algebra and its applications |
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| Chang Shuangling.A new Lie algebra and its applications[J].Pure and Applied Mathematics,2013(6):627-633. |
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| Authors: | Chang Shuangling |
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| Institution: | Chang Shuangling (School of Information, Beijing Wuzi University, Beijing 101149, China) |
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| Abstract: | By constructing a new Lie algebra and its corresponding Loop algebra, an isospectral Lax pair is established whose compatibility condition gives rise to a Lax integrable hierarcy, whose reduced form is the well-known AKNS hierarchy. Its Hamilton structure is obtained by the use of the trace identity. Then, its Darboux transformations, symmetry, algebro-geometric solutions, and so on will be investigated further. |
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| Keywords: | Lie algebra trace identity integrable hierarchy Hamilton structure |
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