一类四阶偏微分方程的李对称分析、Bäcklund变换及其精确解

代慧菊; 李连忠; 王琪; 沙安

doi:10.3969/j.issn.1000-5641.2019.01.003

一类四阶偏微分方程的李对称分析、Bäcklund变换及其精确解

doi: 10.3969/j.issn.1000-5641.2019.01.003

江南大学理学院, 江苏无锡 214122

基金项目:

江苏省自然科学基金青年基金 BK20170171

详细信息

作者简介:
代慧菊, 女, 硕士研究生, 研究方向为数学物理方程.E-mail:923649959@qq.com

通讯作者:
李连忠, 男, 教授, 研究方向为数学物理方程.E-mail:lilianjn@jiangnan.edu.cn

中图分类号: O175.29
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- 被引次数: 0
出版历程
- 收稿日期: 2017-09-20
- 刊出日期: 2019-01-25

Lie symmetry analysis, Bäcklund transformation and exact solutions for a class of fourth-order partial differential equations

School of Science, Jiangnan University, Wuxi Jiangsu 214122, China

摘要

摘要: 利用齐次平衡法获得了一类四阶偏微分方程的Bäcklund变换，进而得到方程的几组精确解；然后运用李对称分析方法，获得该方程的向量场，利用相似变换，把难于求解的非线性偏微分方程转化为易于求解的常微分方程，并通过求解所得到的约化方程，结合幂级数展开法，得到原方程的一系列精确解.
- Bäcklund变换法 /
- 四阶偏微分方程 /
- 李对称分析 /
- 幂级数展开法 /
- 精确解
Abstract: This paper investigates a class of variable coefficient partial differential equations. By using the homogeneous balance method, the Bäcklund transformation is obtained, which leads to exact solutions for the equation. By applying Lie symmetry analysis, the symmetries and vector field of the equation are obtained. Then, by means of a similarity transformation, the partial differential equations are reduced to ordinary differential equations. Solving the reduced equations, we investigate the exact solutions to the equations concisely using the power series expansion method.
- Bäcklund transformation /
- fourth-order partial differential equation /
- Lie symmetry analysis /
- power series expansion method /
- exact solution

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参考文献(15)

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