非线性微分方程不同形式椭圆函数解间的转换  

Conversion among the different forms of the elliptic functions solutions to nonlinear differential equations

作　　者：庞成群[1] 刘松红[1] 韩文娟[1] 

机构地区：[1]六盘水师范学院物理与电子科学系,贵州六盘水553004

出　　处：《安徽大学学报（自然科学版）》2013年第3期45-50,共6页Journal of Anhui University(Natural Science Edition)

基　　金：贵州省六盘水市科技基金资助项目(52020-2009-08-01)

摘　　要：在非线性微分方程的一个已知椭圆函数解的基础上,通过椭圆函数的变换,就可得到该方程丰富的其他形式的椭圆函数解,而无须对其进行求解.利用此方法从modified Korteweg-de Vries(mKdV)方程的两个椭圆函数解出发得到了它的多个其他形式的椭圆函数解,这些解不仅涵盖一些已知解,也包括一些新形式的椭圆函数解,且证明非线性微分方程的很多椭圆函数解之间可以通过椭圆函数的变换实现相互转换.Based on a known elliptic function solution to a nonlinear differential equation, through the transformation of the Jacobi elliptic functions, the equation＇ s more abundant Jacobi elliptic function solutions could be obtained without the equation solver. By means of this method, multiple Jacobi elliptic function form solutions were obtained from two elliptic function solutions to the modified Korteweg-de Vries （mKdV） equation. These solutions not only covered a number of known solutions, but also included some new form of elliptic function solutions. By the transformation of the elliptic functions, the mutual conversion of many elliptic function solutions to nonlinear differential equations was proved.

关 键 词：JACOBI椭圆函数 椭圆函数变换 MKDV方程 

分 类 号：O411.1[理学—理论物理] O175.29[理学—物理]