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

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.