KdV-Burgers-Kuramoto方程的多种类型新精确解及其分析  

Multiple Types New Exact Solutions of KdV-Burgers-Kuramoto Equation and Its Analysis

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,China)

机构地区：[1]贵州财经大学数统学院,贵州贵阳550025

出　　处：《数学的实践与认识》2022年第4期196-205,共10页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11761018,11361012);贵州省科技计划基金项目(黔科合基础-ZK[2022]一般021);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);贵州财经大学创新探索及学术新苗项目(黔科合平台人才[2017]5736-020)。

摘　　要：首先采用Riccati方程的解的性质和试探函数法找到了Riccati方程的八种类型的显式新精确解.其次运用李群分析法获得了KdV-Burgers-Kuramoto方程的约化方程和群不变解.然后利用Riccati方程的八种类型的显式新精确解和广义Tanh函数法给出了约化方程的多种类型的显式新精确解.最后将Riccati方程的八种类型的显式新精确解与李群分析法和广义Tanh函数法相结合,得到了KdV-Burgers-Kuramoto方程的多种类型的显式新行波解.这些技巧和方法可以用于求解其它一些非线性偏微分方程或方程组的显式新精确解.Firstly,8 types new explicit exact solutions of Riccati equation are presented by the properties of solutions of the Riccati equation and trial function method.Secondly,the reduced equations and invariant solutions of KdV-Burgers-Kuramoto equation are given by the Lie group analysis method.Thirdly,multiple types new explicit exact solutions of the reduced equation are presented by 8 types new explicit exact solutions of the Riccati equation and extended tanh-function method.Finally,multiple types new explicit travelling wave solutions of KdV-Burgers-Kuramoto equation are obtained by use of 8 types new explicit exact solutions of the Riccati equation,the Lie group analysis method and extended tanh-function method.These techniques and methods can be applied to find new explicit exact solutions of other nonliner partial differential equations.

关 键 词：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]