广义超弹性杆波方程的行波解

Acta mathematica scientia,Series A ›› 2019, Vol. 39 ›› Issue (6): 1342-1351.

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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)

Abstract

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

CLC Number:

O174.52

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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Traveling Wave Solutions of the Generalized Hyperelastic-Rod Wave Equation

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