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

• 论文 • 上一篇    下一篇

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. 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 Yuan2,*(),Yonghong Wu3,4   

  1. 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:

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h,k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 h,k 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