利用通用F-展开法求解ZK-BBM方程  

UsingGeneral F-expansion Method Solve the Exact Solutions of ZK-BBM Equation

作　　者：陈南 CHEN Nan(Xiamen Institute of Technology,Xiamen 361021,China)

机构地区：[1]厦门工学院,福建厦门361021

出　　处：《长春师范大学学报》2023年第8期15-19,共5页Journal of Changchun Normal University

基　　金：福建省中青年教师教育科研项目“非线性系统的Painlevé分析和可积性研究”(JAT190958);厦门工学院校级科研基金项目“非线性系统的Painlevé分析与可积性”(KYT2019021)。

摘　　要：利用通用F-展开法对ZK-BBM方程进行求解,作行波变换,将偏微分方程转化为常微分方程.假设方程具有洛朗级数形式的解,其中φ满足一般椭圆方程.通过齐次平衡法,确定参数n.通过比较同次幂项的系数,将非线性方程的求解问题转化为代数方程组求解.运用扩展的椭圆方程方法,求解ZK-BBM方程的孤子解、三角函数解、有理解和Jacobi椭圆函数解.The general F-expansion method is used to solve the ZK-BBM equation.Firstly,the partial differential equation is transformed into ordinary differential equation by traveling wave transformation.It is assumed that the equation has a solution in the form of Laurent series,where the general elliptic equation is satisfied byφ.The parameters n are determined by homogeneous balance method.By comparing the coefficients of the same power term,the problem of solving nonlinear equations is transformed into solving algebraic equations.By using the extended elliptic equation method,the soliton solutions,trigonometric function solutions,understandable and Jacobi elliptic function solutions are obtained.

关 键 词：ZK-BBM方程 通用F-展开法 行波变换 JACOBI椭圆函数 

分 类 号：O174.55[理学—数学]