广义超弹性杆波方程的行波解  

Traveling Wave Solutions of the Generalized Hyperelastic-Rod Wave Equation

作　　者：古勇毅 袁文俊[2] 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)

机构地区：[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

出　　处：《数学物理学报（A辑）》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)~~

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.

关 键 词：广义超弹性杆波方程 微分方程 椭圆函数 亚纯函数 

分 类 号：O174.52[理学—数学]