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.
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.
作者
古勇毅
袁文俊
吴永洪
Gu Yongyi;Yuan Wenjun;Wu Yonghong(School of Statistics and Mathematics,Guangdong University of Finance and Economics,Cuangzhou 510320;School of Mathematics and Information Science,Guangzhou University,Guangzhou 510006;Department of Mathematics and Statistics,Gurtin University,Perth WA6845,Australia;Department of Statistics and Mathematics,Zhongnan University of Economics and Law,Wuhan 430073)
出处
《数学物理学报（A辑）》
CSCD
北大核心
2019年第6期1342-1351,共10页
Acta Mathematica Scientia
基金
国家自然科学基金(11901111,11271090)~~
关键词
广义超弹性杆波方程
微分方程
椭圆函数
亚纯函数
Generalized hyperelastic-rod wave equation
Differential equation
Elliptic func-tion
Meromorphic function
