用Riccati方程求KdV-Burgers-Kuramoto方程的显式新行波解  

Solving explicit new travelling wave solutions of KdV-Burgers-Kuramoto equation by Riccati equation

作　　者：林府标 张千宏 LIN Fu-biao;ZHANG Qian-hong(School of Mathematics and Statistics,Guizhou University of Finance and Economics,Guiyang 550025,Guizhou,China)

机构地区：[1]贵州财经大学数统学院

出　　处：《山东大学学报（理学版）》2019年第12期24-31,共8页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(11761018);贵州省科技计划基金项目(黔科合基础[2019]1051);贵州省教育厅青年科技人才成长项目(黔教合KY字[2017]150);2018年度贵州财经大学校级科研基金项目资助(2018XYB04)

摘　　要：首先利用Riccati方程解的相关性质和试探函数法获得了Riccati方程的8种类型的显式新解析解,其次运用李群分析法得到了KdV-Burgers-Kuramoto(KBK)方程的约化方程和群不变解。最后将广义tanh函数法结合Riccati方程的8种新解析解用于KBK方程的约化方程,找到了KBK方程的多种类型的显式新行波解。另外,把Riccati方程的这8种类型的显式新解析解结合广义tanh函数法与李群分析法可获得属于这一类方程中的其他非线性偏微分方程(组)的周期性型、幂指函数和三角函数的有理型显式新行波解。Firstly, 8 types explicit new analytical solutions of the Riccati equation are presented by the trial function method combing with the related properties of solutions for the Riccati equation. Secondly, the reduced equations and invariant solutions of KdV-Burgers-Kuramoto(KBK) equation are given by the Lie group analysis method. Finally, the extended tanh-function method and 8 types explicit new analytical solutions of the Riccati equation are used to solve the reduced equation of KBK equation, moreover, many types explicit new travelling wave solutions of KBK equation are found. In addition, periodic types, rational types of exponential function and trigonometric function of explicit new travelling wave solutions of other similar nonlinear partial differential equations can be obtained by use of the extended tanh-function method, 8 types explicit new analytical solutions of the Riccati equation and the Lie group analysis method.

关 键 词：RICCATI方程 KdV-Burgers-Kuramoto方程 李群分析法 广义tanh函数法 行波解 

分 类 号：O175.29[理学—数学]