| 一类四阶偏微分方程的对称分析及级数解 |
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| 引用本文： | 杨春艳,李小青. 一类四阶偏微分方程的对称分析及级数解[J]. 纯粹数学与应用数学, 2016, 32(4): 432-440. DOI: 10.3969/j.issn.1008-5513.2016.04.011 |
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| 作者姓名： | 杨春艳 李小青 |
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| 作者单位： | 西北大学数学系,陕西 西安,710127;西北大学数学系,陕西 西安,710127 |
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| 基金项目： | 国家自然科学基金(11201371)，陕西省自然科学基金(2012JQ1013)，陕西省教育厅专项科研基金(11JK0482) |
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| 摘 要： | 研究了一类四阶偏微分方程的李对称,构造了方程所容许的李对称的优化系统,进行了对称约化,得到了精确解.进一步,基于幂级数理论,得到了这类四阶偏微分方程的幂级数解.
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| 关 键 词： | 四阶偏微分方程 李对称 优化系统 幂级数法 精确解 |
The symmetry and series solutions of a class of fourth-order partial differential equation |
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| Yang Chunyan,Li Xiaoqing. The symmetry and series solutions of a class of fourth-order partial differential equation[J]. Pure and Applied Mathematics, 2016, 32(4): 432-440. DOI: 10.3969/j.issn.1008-5513.2016.04.011 |
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| Authors: | Yang Chunyan Li Xiaoqing |
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| Abstract: | In the paper, Lie symmetry analysis of a fourth-order partial differential equation is performed. The one dimension optimal system of the Lie symmetries admitted by the equation in consideration is constructed. In addition, all exact solutions or the reduced equations corresponding to the optimal system are presented. Furthermore, based on the power series theory, a kind of explicit power series solutions for the equation is well constructed with a detailed derivation. |
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| Keywords: | fourth-order partial differential equation Lie symmetry optimal system power series method exact solutions |
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