摘要
用经典李群分析法给出了Dodd-Bullough-Mikhailov方程的约化变换方程和群不变解,用广义tanh函数法分别找到了Dodd-Bullough-Mikhailov方程的行波解及约化变换方程的显式精确解.用该方程的约化变换方程及精确解构造了一种求解非线性偏微分方程的φ(ξ)展式法,用该方法获得了七阶KdV方程、五阶Kawahara方程和Caudrey-Dodd-Gibbon方程的双曲型、三角型、有理函数型和周期型的显式行波解,并分析了解的动力学行为及性态.
The reduced transformation equations and group invariant solutions of Dodd-Bullough-Mikhailov(DBM)were given by using Lie group analysing method.The travelling wave solutions of the DBM equation and exact solutions of the reduced transformation equation of the DBM equation were found by using the method of extended tanh-function,respectively.Theφ(ξ)-expansion method was proposed by using the reduced transformation equation of the DBM equation and its explicit exact solutions.The hyperbolic,trigonometric,rational function and periodic type explicit travelling solutions of seventh order KdV equation,fifth order Kawahara and Caudrey-Dodd-Gibbon equation were presented byφ(ξ)-expansion method.The dynamic behavior of some travelling wave solutions were also analyzed.Moreover,theφ(ξ)-expansion method can be used to solve some other nonlinear evolution equations.
作者
林府标
马丽荣
杨洋
LIN Fu-biao;MA Li-rong;YANG Yang(School of Mathematics and Statistics,Guizhou University of Finance and Economics,Guiyang 550025,China;School of Accounting,Shijiazhuang Posts and Telecommunications Technical College,Shijiazhuang 050000,China)
出处
《东北师大学报（自然科学版）》
CAS
北大核心
2024年第4期11-19,共9页
Journal of Northeast Normal University(Natural Science Edition)
基金
贵州省科技计划基金资助项目(黔科合基础-ZK[2022]一般021)
贵州财经大学2023年度在校学生科研资助项目(2022BZXS143)。
