分数阶Burgers-Kdv方程的新精确解  

New exact solutions to the fractional Burgers-Kdv equation

作　　者：陈兆蕙[1] 张燕 邓胜忠 CHEN Zhaohui;ZHANG Yan;DENG Shengzhong(Zhujiang College,South China Agricultural University,Guangzhou 510900,China;Guangzhou College of Technology and Business,Guangzhou 510850,China)

机构地区：[1]华南农业大学珠江学院,广东广州510900 [2]广州工商学院,广东广州510850

出　　处：《南昌大学学报（理科版）》2020年第1期6-9,15,共5页Journal of Nanchang University(Natural Science)

基　　金：广东省普通高校特色创新类项目(2018KTSCX269);2019广州工商学院质量工程高等教育学改革项目(ZL20191120)。

摘　　要：本文考虑了一类分数阶Burgers-Kdv方程,采用了扩展的Riccati展开法。首先使用分数阶复变换将分数阶Burgers-Kdv方程转化为常微分方程;其次使用扩展的Riccati展开法得到方程的许多精确解;最后根据其中一个精确解,对变量给出特殊值,描绘出了α取不同值时的图形。结果表明:扩展的Riccati展开法对于求解非线性分数阶Burgers-Kdv方程作用很大,具有简单便捷等优点。The fractional Burgers-Kdv equation is explicitly discussed in this paper by the expansion Riccati method.Firstly,the fractional Burgers-Kdv equation is converted into an non-fractional ordinary differential equation by fractional complex transformation.Then some exact solutions of the fractional Burgers-Kdv equation are obtained through the expansion Riccati method.Also,some specific values are assigned to the variables by choosing one of the exact solutions.Furthermore,some following graphs are drawn with different values ofα.The results show that the expansion Riccati method plays an effective role in solving the nonlinear fractional Burgers-Kdv equations due to its advantages of simplicity and convenience.

关 键 词：分数阶Burgers-Kdv方程 Riccati展开法 精确解 

分 类 号：O175.29[理学—数学]