构造非线性偏微分方程精确解的(1/G)-展开法  

The(1/G)-Expansion Method of Constructing Exact Solutions to Nonlinear Partial Differential Equations

作　　者：马志民[1] 孙峪怀[2] MA Zhimin;SUN Yuhuai(College of Engineering and Technical,Chengdu University of Technology,Leshan 614000,China;College of Mathematics and Software Science,Sichuan Normal University,Chengdu 610066,China)

机构地区：[1]成都理工大学工程技术学院,四川乐山614000 [2]四川师范大学数学与软件科学学院,成都610066

出　　处：《重庆理工大学学报（自然科学）》2020年第3期240-243,共4页Journal of Chongqing University of Technology：Natural Science

基　　金：成都理工大学工程技术学院科学基金项目(C122019028);四川省教育厅科研基金项目(15ZB0326)。

摘　　要：精确解是研究非线性偏微分方程的重要课题。许多自然现象都可以由非线性偏微分方程的精确解描述。利用(1/G)-展开法,并借助符号计算系统Maple,获得了Sharma-Tasso-Olver方程和Ablowitz-Kaup-Newell-Segur水波方程的精确解,其中包括一些新的结果。未来这一方法也可用来构造其他非线性偏微分方程的精确解。Exact solutionsis the backbone to study nonlinear partial differential equations.Many significant natural science can be described by exact solutions of nonlinear partial differential equation.(1/G)-expansion method is given here.With the help of Maple,theexact solutions of Sharma-Tasso-Olver equation and Ablowitz-Kaup-Newell-Segur water equation are presented.As a result,many new exact solutions are obtained.This method also can be used for many other nonlinear partial differential equations.

关 键 词：Sharma-Tasso-Olver方程 Ablowitz-Kaup-Newell-Segur水波方程 (1/G)-展开法 精确解 

分 类 号：O175.2[理学—数学]