广义超弹性杆波方程的行波解

数学物理学报 ›› 2019, Vol. 39 ›› Issue (6): 1342-1351.

广义超弹性杆波方程的行波解

古勇毅¹,袁文俊^2,*(),吴永洪^3,⁴

¹ 广东财经大学统计与数学学院广州 510320
² 广州大学数学与信息科学学院广州 510006
³ Curtin 大学数学和统计系西澳珀斯 6845
⁴ 中南财经政法大学统计与数学学院武汉 430073

收稿日期:2018-08-15 出版日期:2019-12-26 发布日期:2019-12-28
通讯作者: 袁文俊 E-mail:wjyuan1957@126.com
基金资助:
国家自然科学基金(11901111);国家自然科学基金(11271090)

Traveling Wave Solutions of the Generalized Hyperelastic-Rod Wave Equation

Yongyi Gu¹,Wenjun Yuan^2,*(),Yonghong Wu^3,⁴

¹ School of Statistics and Mathematics, Guangdong University of Finance and Economics, Guangzhou 510320
² School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006
³ Department of Mathematics and Statistics, Curtin University, Perth WA 6845, Australia
⁴ Department of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan 430073

Received:2018-08-15 Online:2019-12-26 Published:2019-12-28
Contact: Wenjun Yuan E-mail:wjyuan1957@126.com
Supported by:
the NSFC(11901111);the NSFC(11271090)

摘要/Abstract

摘要：

该文研究了广义超弹性杆波方程.利用行波变换将广义超弹性杆波方程转化为一个复微分方程，并通过弱 $\left\langle {h, k} \right\rangle$ 条件和Fuchs指数证明了该复微分方程的亚纯解属于W类.进一步求出了该复微分方程的所有亚纯解，从而得到了广义超弹性杆波方程的行波解.可将该文的方法应用到一些相关的数学物理方程.

关键词: 广义超弹性杆波方程, 微分方程, 椭圆函数, 亚纯函数

Abstract:

In this paper, we study the generalized hyperelastic-rod wave equation. We changed the generalized hyperelastic-rod wave equation into a complex differential equation by using traveling wave transform and show that meromorphic solutions of the complex differential equation belong to the class W by the weak $\left\langle {h, k} \right\rangle$ condition and the Fuchs index. Furthermore, we find out all meromorphic solutions of the complex differential equation, then we obtain the traveling wave solutions of the generalized hyperelastic-rod wave equation. We can apply the idea of this study to some related mathematical physics equations.

Key words: Generalized hyperelastic-rod wave equation, Differential equation, Elliptic function, Meromorphic function

中图分类号:

O174.52

古勇毅,袁文俊,吴永洪. 广义超弹性杆波方程的行波解[J]. 数学物理学报, 2019, 39(6): 1342-1351.

Yongyi Gu,Wenjun Yuan,Yonghong Wu. Traveling Wave Solutions of the Generalized Hyperelastic-Rod Wave Equation[J]. Acta mathematica scientia,Series A, 2019, 39(6): 1342-1351.

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