一类组合sinh-cosh-Gordon方程的对称约化、动力学性质与精确解（英文）  

Symmetry Reductions,Dynamical Behavior and Exact Explicit Solutions to the Combined sinh-cosh-Gordon Equation

作　　者：代慧菊 李连忠 王宇航 何芳琴 DAI Huiju;LI Lianzhong;WANG Yuhang;HE Fangqin(School of Science,Jiangnan University,Wuxi,Jiangsu,214122,P.R.China)

机构地区：[1]江南大学理学院,无锡江苏214122

出　　处：《数学进展》2018年第6期844-854,共11页Advances in Mathematics（China）

基　　金：supported by the Natural Science Foundation of Jiangsu Province(No.BK20170171)

摘　　要：文章综合运用李对称分析、幂级数解法和动力系统法来求解组合sinh-cosh-Cordon方程的精确解.利用李对称分析得到了组合sinh-cosh-Cordon方程的向量场和相似变换,把难以求解的偏微分问题约化为常微分方程,利用幂级数解法求得了方程的精确解析解.然后用MATLAB画出了约化后方程的相图,最后利用动力系统法分析研究了解的动力学行为,并得到了方程的行波解.In this paper, we employ Lie symmetry analysis along with the analytic power series method and dynamical method to investigate the exact solutions of the combined sinh- cosh-Gordon equation. Through the Lie symmetry analysis, the geometric vector fields and the symmetry reductions of the combined sinh-cosh-Gordon equation are presented, and the difficult problem of partial differential equation is reduced to ordinary differential equation＇s. We get the exact explicit solutions of the combined sinh-cosh-Gordon equation by the analytic power series method. Especially, the bifurcations of the combined sinh-cosh-Gordon equation are obtained through MATLAB. The dynamical behavior and the exact explicit traveling wave solutions are investigated by the dynamical system method.

关 键 词：李对称分析 向量场 动力系统法 行波解 组合sinh-cosh-Gordon方程 

分 类 号：O175.29[理学—数学]