| 热方程的非古典势对称群与不变解 |
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| 引用本文： | 秦茂昌,梅凤翔,许学军.热方程的非古典势对称群与不变解[J].应用数学和力学,2006,27(2):217-222. |
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| 作者姓名： | 秦茂昌 梅凤翔 许学军 |
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| 作者单位： | 重庆工商大学 理学院,重庆 400067;2.北京理工大学 理学院,北京 100081 |
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| 摘 要： | 主要研究了热方程与波方程的非古典势对称群生成元及相应的群不变解．研究表明对于守恒形式的偏微分方程，可通过其伴随系统求得的非古典势对称群生成元来构造其显式解．这些显式解不能由方程本身的Lie对称群生成元或Lie-B?cklund对称群生成元构造得到．
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| 关 键 词： | 非古典势对称群生成元 热方程 波方程 显式解 |
| 文章编号： | 1000-0887（2006）02-0217-06 |
| 收稿时间： | 2004-03-19 |
| 修稿时间： | 2005-10-30 |
Nonclassical Potential Symmetries and Invariant Solutions of Heat Equation |
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| QIN Mao-chang,MEI Feng-xiang,XU Xue-jun.Nonclassical Potential Symmetries and Invariant Solutions of Heat Equation[J].Applied Mathematics and Mechanics,2006,27(2):217-222. |
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| Authors: | QIN Mao-chang MEI Feng-xiang XU Xue-jun |
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| Institution: | School of Science, Chongqing Technology and Business University, Chongqing 400067, P. R. China; |
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| Abstract: | Some nonclassical potential symmetry generators and group-invariant of heat equation and wave equation were determined. It is shown that new explicit solutions of conserved equations can be constructed by using the nonclassical potential symmetry generators which are derived from their adjoit system. These explicit solutions cannot be obtained by using the Lie or Lie-Backlund symmetry group generators of differential equations. |
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| Keywords: | nonclassical potential symmetry generators heat equation wave equation explicit solution |
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