(1+1)维修正Broer-Kaup-Kupershmidt方程的G′/G展开和精确解  

G′/G Expansion and Exact Solutions of(1+1)-Dimensional Modified Broer-Kaup-Kupershmidt Equation

作　　者：陈南 朱鸿翔 CHEN Nan;ZHU Hongxiang(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》2024年第10期6-9,共4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分析与可积性研究”(JAT190958);厦门工学院校级中青年科研基金项目“非线性偏微分方程的达布变换与精确解研究”(KYT2022002)。

摘　　要：使用G′/G展开方法对(1+1)维修正Broer-Kaup-Kupershmidt方程进行研究.对该方程进行行波变换,将非线性微分方程转变成常微分方程,并假设具有u(ξ)=∑n i=0 a i(G′/G)i形式的解,通过平衡线性最高阶导数项与最高阶非线性项的幂次来确定正整数n,将确定n的拟设形式的解代入方程中,令同次幂项的系数为零,得到一个代数方程组并求解,最终得到非线性微分方程的拟设形式的精确解.The G′/G expansion method is used to solve the(1+1)-dimensional Modified Broer-Kaup-Kuperschmidt equation.Firstly,a traveling wave transformation is performed on the equation to transform the nonlinear differential equation into an ordinary differential equation.Let s assum a formal solution exists of u(ξ)=∑n i=0 a i(G′/G)i,and then,a positive integer is determined by balancing the power of the linear highest order derivative term and the highest order nonlinear term.The proposed solution of n is substituted into the equation.Then,let us make the coefficient of the same power term zero,resulting in an algebraic equation system and it is solved.Finally,we obtain exact solutions in the assumed form of the nonlinear differential equation.

关 键 词：(1+1)维修正Broer-Kaup-Kupershmidt方程 G′/G展开法 精确解 

分 类 号：O174.55[理学—数学]