| 带幂非线性项变系数非线性波动方程的李对称分类与等价性变换 |
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| 引用本文： | 黄定江,杨勤民,周水庚.带幂非线性项变系数非线性波动方程的李对称分类与等价性变换[J].数学年刊A辑(中文版),2012,33(4):389-398. |
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| 作者姓名： | 黄定江 杨勤民 周水庚 |
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| 作者单位： | 华东理工大学数学系;复旦大学计算机科学技术学院;复旦大学上海市智能信息处理重点实验室 |
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| 基金项目： | 国家重点基础研究发展计划项目(No.2010CB126600);国家自然科学基金(No.60873070);中国博士后科学基金特别资助(No.201104247),中国博士后科学基金(No.20090450067);中央高校基本业务费(No.WM0911004);上海博士后科学基金(No.09R21410600)资助的项目 |
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| 摘 要： | 从微分方程群理论分析角度,研究了一类含有3个任意函数和2个幂非线性项的变系数非线性波动方程.由于方程具有很强的任意性和非线性项,可通过等价性变换寻找方程的不变对称分类.首先给出了等价性变换的一般结果,其中包括一些包含任意元的非局部变换.然后对所研究的方程,利用广义扩展等价群和条件等价群给出了方程的完全对称分类.最后获得并分析了方程的特殊类相似解.
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| 关 键 词： | 对称分类 等价性变换 波动方程 不变解 李代数 |
Lie Symmetry Classification and Equivalence Transformation of Variable Coefficient Nonlinear Wave Equations with Power Nonlinearities |
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| HUANG Dingjiang,YANG Qinmin and ZHOU Shuigeng.Lie Symmetry Classification and Equivalence Transformation of Variable Coefficient Nonlinear Wave Equations with Power Nonlinearities[J].Chinese Annals of Mathematics,2012,33(4):389-398. |
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| Authors: | HUANG Dingjiang YANG Qinmin and ZHOU Shuigeng |
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| Institution: | 1 Department of Mathematics,East China University of Science and Technology, Shanghai 200237,China;School of Computer Science,Fudan University,Shanghai 200433;Shanghai Key Lab of Intelligent Information Processing,Fudan University, Shanghai,200433,China. 2 East China University of Science and Technology,Shanghai 200237,China. 3School of Computer Science,Fundan University,Shanghai 200433;Shanghai Key Lab of Intelligent Information Processing,Fudan University,Shanghai,200433, China. |
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| Abstract: | A class of variable coefficient nonlinear wave equations containing three arbitrary
functions and two power nonlinearities is investigated within the framework of group theo-
retical analysis of differential equations. Because of the strong arbitrariness and nonlinearity
of the model, the authors look for an invariant symmetry classification via equivalence trans-
formations. Some general results concerned with the equivalence transformations are shown
including ones with transformations which are nonlocal with respect to arbitrary elements.
For the class, the complete symmetry classification is performed by means of generalized
extended equivalence groups and conditional equivalence groups. Special classes of similar
solutions for the equation are also obtained and analyzed. |
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| Keywords: | Symmetry classification Equivalence transformation Wave equation Invariant solution Lie algebra |
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