| 两个高维loop代数及应用 |
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| 引用本文： | 张玉峰,张鸿庆.两个高维loop代数及应用[J].数学学报,2006,49(6):1287-129. |
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| 作者姓名： | 张玉峰 张鸿庆 |
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| 作者单位： | [1]辽宁师范大学数学学院,大连116029 [2]大连理工大学应用数学系,大连116024 |
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| 基金项目： | 国家自然科学基金资助项目（10471139） |
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| 摘 要： | 借助于循环数,构造了维数分别是5(s+1)和4(s+1)的两个高维loop代数．为了计算方便,本文只考虑s=1时的应用．利用第一个loop代数■_1~*得到了具有4-Hamilton结构的一个广义AKNS族,该方程族可约化为著名的AKNS族．利用第二个loop代数■_2~*,得到了具有4个分量位势函数的4-Hamilton结构方程族,该族可约化为一个非线性耦合Burgers方程和一个耦合的KdV方程．
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| 关 键 词： | 循环数 loop代数 Hamilton结构 |
| 文章编号： | 0583-1431（2006）06-1287-10 |
| 收稿时间： | 2005-01-26 |
| 修稿时间： | 2005-01-262005-09-15 |
Two Higher-Dimensional loop Algebras and Their Applications |
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| Yu Feng ZHANG,Hong Qing ZHANG.Two Higher-Dimensional loop Algebras and Their Applications[J].Acta Mathematica Sinica,2006,49(6):1287-129. |
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| Authors: | Yu Feng ZHANG Hong Qing ZHANG |
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| Institution: | Mathematical School, Liaoning Normal University, Dalian 116029, P. R. China Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, P. R. China |
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| Abstract: | With the help of the cycled numbers,two higher-dimensional loop algebras are constructed,whose dimension numbers are 5(s+1) and 4(s+1),respectively.For the sake of simple calculation,we only take s=1 in the paper for illustrating their applications.By employing the first loop algebra ■,a generalized AKNS hierarchy is obtained,possessing 4-Hamiltonian structure,which is also reduced to the well-known AKNS hierarchy.By making use of the second loop algebra ■,a new integrable hier- archy with 4-potential functions is generated,also possessing 4-Hamiltonian structure, which is redued to a nonlinear couled Burgers equation and a coupled KdV equation, respectively. |
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| Keywords: | cycled number loop algebra Hamiltonian structure |
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