Painlevé方法构造Hirota-Satsuma方程组的精确解  

Exact Solution of Hirota-Satsuma Equations by Constructing Painlevé Method

作　　者：唐晓苓 刘汉泽[1] TANG Xiao-ling;LIU Han-ze(School of Mathematical Sciences,Liaocheng University,Liaocheng Shandong 252059,China)

机构地区：[1]聊城大学数学科学学院,山东聊城252059

出　　处：《菏泽学院学报》2018年第5期1-5,共5页Journal of Heze University

基　　金：国家自然科学基金项目(11171041)

摘　　要：用Painlevé分析的WTC方法求解非线性偏微分方程组,当选择同一个奇异流形时,此方法在方程组中的运用得以实现.首先对Hirota-Satsuma方程组进行Painlevé分析,确定Painlevé展开式,确定共振点,验证共振点,再到相容性分析,得到方程的Painlevé性质,对方程进行对称分析,最后借助于Backlund变换得到方程组的精确解.This paper uses the WTC method of Painlev analysis to solve the nonlinear partial differential equations, and the application of this method in the equations can be realized when the same singular manifold is chosen. First of all, the Hirota-Satsuma equation group is analyzed by Painlev to determine the open mode of Painlev and the resonance point to be verified. Then, the compatibility analysis is taken to obtain the Painlev property of the equation, with the symmetry of the equation analyzed. Finally, the exact solution of the equations is obtained by means of transform.

关 键 词：PAINLEVE分析 Bacldhnd变换 Hirota-Satsuma方程组 精确解 

分 类 号：O175.2[理学—数学]