推广的(G′/G^2)展开法求Gardner方程的新精确解  

Generalized(G′/G^2)-expansion Method for New Exact Solutions of Gardner Equation

作　　者：曾娇 崔泽建[2] ZENG Jiao;CUI Zejian(College of Mathematic,YiBin University,Yibin Sichuan 644000,China;College of Mathematics and Information,China West Normal University,Nanchong Sichuan 637009,China)

机构地区：[1]宜宾学院数学学院,四川宜宾644000 [2]西华师范大学数学与信息学院,四川南充637009

出　　处：《西华师范大学学报（自然科学版）》2020年第4期359-363,共5页Journal of China West Normal University(Natural Sciences)

基　　金：四川省教育厅自然科学重点项目基金项目(09ZA119);四川省宜宾学院校级项目(02180196)。

摘　　要：应用(G′/G^2)展开法求Gardner方程的新精确解,讨论了λμ在三种不同情形下的通解,分别得出了该方程的双曲函数通解、三角函数通解以及有理函数通解。实践证明,推广的(G′/G^2)展开法不仅能直接有效地求出Gardner方程的精确解,而且与之前已有的Gardner方程精确解的求解方法相比,此方法扩充了Gardner方程的解系,因此,(G′/G^2)展开法对求解偏微分方程具有十分重要意义。Generalized(G′/G^2)-expansion method is used to obtain the new exact solutions of Gardner equation and the general solutions ofλμin three different cases are discussed.The general hyperbolic functions,trigonometric functions and rational functions of the equation are obtained.It is found that the method is not only capable of solving Gardner equation more directly and effectively but also extending its exact solutions when compared with other existing solving methods.Therefore,generalized(G′/G^2)-expansion method is of great significance for partial differential equation.

关 键 词：(G′/G^2)展开法 Gardner方程 齐次平衡法 行波解 精确解 

分 类 号：O29[理学—应用数学]