| Hunter-Saxton方程的对称约化与群不变解 |
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| 引用本文： | 檀美英,胡恒春.Hunter-Saxton方程的对称约化与群不变解[J].上海理工大学学报,2016,38(4):313-317. |
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| 作者姓名： | 檀美英 胡恒春 |
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| 作者单位： | 上海理工大学 理学院, 上海 200093;上海理工大学 理学院, 上海 200093 |
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| 基金项目： | 国家自然科学基金资助项目（110711640）；国家自然科学基金青年基金资助项目（11201302）；上海市自然科学基金资助项目（10ZR1420800）；上海市重点学科建设资助项目（XTKX2012） |
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| 摘 要： | 借助符号计算软件Maple,根据微分方程单参数不变群和群不变解的概念,利用李群对称的待定系数法,得到Hunter-Saxton方程的包含5个任意常数和一个任意函数的一般形式的对称.通过该对称中任意的函数和常数的不同选取,将Hunter-Saxton方程约化为不同形式的常微分方程.最后对约化后的常微分方程进行变换求解,进一步得出Hunter-Saxton方程的一些群不变解和精确解.
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| 关 键 词： | Hunter-Saxton方程 李群对称 群不变解 |
| 收稿时间： | 2015/12/24 0:00:00 |
Symmetry Reduction and Group Invariant Solutions of Hunter-Saxton Equations |
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| TAN Meiying and HU Hengchun.Symmetry Reduction and Group Invariant Solutions of Hunter-Saxton Equations[J].Journal of University of Shanghai For Science and Technology,2016,38(4):313-317. |
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| Authors: | TAN Meiying and HU Hengchun |
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| Institution: | College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China;College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China |
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| Abstract: | By using the symbolic computation software Maple,according to the concepts of single parameter invariant groups and group invariant solutions of differential equations,the general symmetry of the Hunter-Saxton equation was obtained with the help of its symmetry equation,which included five arbitrary constants and one arbitrary function.The Hunter-Saxton equation was reduced to some types of different ordinary differential equations by selecting different constants and function.Finally,with the transformational solving of the ordinary differential equations,group invariant solutions and exact solutions of the Hunter-Saxton equation were obtained directly. |
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| Keywords: | Hunter-Saxton equation Lie symmetry group group-invariant solutions |
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