| Lie Reduction and Conditional Symmetries of Some Variable Coefficient Nonlinear Wave Equations＊ |
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| 引用本文： | 黄定江,周水庚,梅建琴,张鸿庆.Lie Reduction and Conditional Symmetries of Some Variable Coefficient Nonlinear Wave Equations＊[J].理论物理通讯,2010,53(1):1-5. |
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| 作者姓名： | 黄定江 周水庚 梅建琴 张鸿庆 |
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| 基金项目： | Supported by the National Key Basic Research Project of China under Grant No. 2010CB126600, the National Natural Science Foundation of China under Grant No. 60873070, Shanghai Leading Academic Discipline Project No. B114, the Postdoctoral Science Foundation of China under Grant No. 20090450067 and Shanghai Postdoctoral Science Foundation under Grant No. 09R21410600 |
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| 摘 要： | Lie symmetry reduction of some truly ＂variable coefficient＂ wave equations which are singled out from a class of （1 ＋ 1）-dimensional variable coefficient nonlinear wave equations with respect to one and two-dimensional algebras is carried out. Some classes of exact solutions of the investigated equations are found by means of both the reductions and some modern techniques such as additional equivalent transformations and hidden symmetries and so on. Conditional symmetries are also discussed.
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| 关 键 词： | 非线性波动方程 可变系数 条件对称 李群 对称性 现代技术 等效变换 精确解 |
| 收稿时间： | 2009-02-04 |
Lie Reduction and Conditional Symmetries of Some Variable Coefficient Nonlinear Wave Equations |
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| HUANG Ding-Jiang,ZHOU Shui-Geng,MEI Jian-Qin,ZHANG Hong-Qing.Lie Reduction and Conditional Symmetries of Some Variable Coefficient Nonlinear Wave Equations[J].Communications in Theoretical Physics,2010,53(1):1-5. |
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| Authors: | HUANG Ding-Jiang ZHOU Shui-Geng MEI Jian-Qin ZHANG Hong-Qing |
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| Institution: | .
;1.School of Computer Science, Fudan University, Shanghai 200433, China
;2.Shanghai Key Lab of Intelligent Information Processing, Fudan University, Shanghai 200433, China
;3.Department of Mathematics, East China University of Science and Technology, Shanghai 200237, China
;4.Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China |
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| Abstract: | Lie symmetry reduction of some truly ``variable coefficient' wave equations which are singled out from a class of (1 + 1)-dimensional variable coefficient nonlinear wave equations with respect to one and two-dimensional algebras is carried out. Some classes of exact solutions of the investigated equations are found by means of both the reductions and some modern techniques such as additional equivalent transformations and hidden symmetries and so on. Conditional symmetries are also discussed. |
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| Keywords: | symmetry reduction conditional symmetry exact solutions variable-coefficient nonlinear wave equations |
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