| 非线性弦振动方程的相似约化 |
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| 引用本文： | 徐淑奖,郭玉翠.非线性弦振动方程的相似约化[J].工程数学学报,2007,24(3):494-502. |
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| 作者姓名： | 徐淑奖 郭玉翠 |
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| 作者单位： | 1. 山东省计算中心,济南,250014;北京邮电大学理学院,北京,100876
2. 山东省计算中心,济南,250014 |
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| 摘 要： | 应用经典无穷小Lie群方法和CK直接方法得到了非线性弦振动方程的新的相似约化和新的精确解。应用经典Lie群方法将非线性弦振动方程约化成了第三类和第四类椭圆方程,同时得到了非线性弦振动方程的显式类孤立波解。进而,应用不涉及群论的CK直接方法得到了非线性弦振动方程的更为一般的相似约化。
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| 关 键 词： | 非线性弦振动方程 经典相似约化方法 CK直接约化方法 类孤立波解 |
| 文章编号： | 1005-3085(2007)03-0494-09 |
| 修稿时间： | 2005-04-20 |
Similarity Reductions for the Nonlinear Vibrating String Equation |
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| XU Shu-jiang,GUO Yu-cui.Similarity Reductions for the Nonlinear Vibrating String Equation[J].Chinese Journal of Engineering Mathematics,2007,24(3):494-502. |
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| Authors: | XU Shu-jiang GUO Yu-cui |
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| Affiliation: | 1. Shandong Computer Science Center, Jinan 250014; 2. School of Science, Beijing University of Posts and Telecommunications, Beijing 100876 |
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| Abstract: | New explicit solutions and new similarity reductions are presented for the nonlinear vibrat- ing string equation,by means of both the classical Lie group method of infinitesimal transformation and the CK direct method.Using the classical Lie group method,the nonlinear vibrating string equation can be reduced to the third and fourth type elliptic equations,and the new explicit soliton-like solution is obtained at the same time.The more general similarity reductions are obtained by the CK direct method,this method does not require the Lie group theoretic techniques. |
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| Keywords: | nonlinear vibrating string equation similarity reduction Lie group method CK direct method soliton-like solution |
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