几种广义的函数展开法在构建偏微分方程精确解中的文献综述与应用(G^′/G²)-展开法、(exp)-展开法构建(2 + 1)维Boiti-Leon-Pempinelli方程精确解  

A Literature Review and Application of Sev Eral Generalized Function Expansion Methods in Constructing Exact Solutions of Partial Differential Equations(G′/G2)-Expansion Method,(exp)-Expansion Method Construction (2 + 1) Exact Solution of the Dimensional Boiti-Leon-Pempinelli Equation

作　　者：吴大山 孙峪怀 杜玲禧 

机构地区：[1]四川师范大学,数学科学学院,四川成都

出　　处：《应用数学进展》2019年第10期1659-1674,共16页Advances in Applied Mathematics

基　　金：National Natural Science Foundation of China (国家自然科学基金,11371267);Natural Science Foundation of Sichuan Province of China (四川省自然科学基金,2012ZA135).

摘　　要：首先,系统给出(G′/G2)-展开法、F-展开法、(exp)-展开法、改进的Kudryashov方法、直接截断法,构建偏微分方程的精确解的起源与研究现状的文献综述。接下来,采用对比方式给出上述五种广义的函数展开法在构建偏微分方程精确解的步骤。最后,通过上述五种广义的函数展开法中的(G′/G2)-展开法、(exp)-展开法构建(2 + 1)维Boiti-Leon-Pempinelli方程的精确解,并使用控制变量法进行数学实验分析了(2 + 1)维Boiti-Leon-Pempinelli方程中三个变量对于精确解的影响。First, the system gives(G′/G2)-expansion method, F-expansion method, (exp)-expansion method, improved Kudryashov method, direct truncation method, to construct the literature review of the origin and research status of the exact solutions of partial differential equations. Next, the steps of constructing the exact solutions of the partial differential equations by the above five generalized function expansion methods are given in comparison. Finally, through the above five generalized (G′/G2)-expansion method, (exp)-expansion method in the function expansion method constructs the exact solution of the (2 + 1)-dimensional Boiti-Leon-Pempinelli equation. The control variable method is used to analyze the influence of three variables on the exact solution in the (2 + 1)-dimensional Boiti-Leon-Pempinelli equation.

关 键 词：(G^′ /G²)-展开法 F-展开法 (exp)-展开法 改进的Kudryashov方法 直接截断法 (2 + 1)维Boiti-Leon-Pempinelli方程 精确解 数学实验 

分 类 号：G63[文化科学—教育学]