﻿ 分数阶广义KDV方程的精确解 Travelling Wave Solution of the Generalized KDV Equation

Pure Mathematics
Vol.07 No.05(2017), Article ID:21950,8 pages
10.12677/PM.2017.75049

Travelling Wave Solution of the Generalized KDV Equation

Xiaojiao Wang*, Xianlin Zhou, Fangqi Wei

College of Mathematics and Software Science, Sichuan Normal University, Chengdu Sichuan

*通讯作者。

Received: Aug. 17th, 2017; accepted: Aug. 31st, 2017; published: Sep. 6th, 2017

ABSTRACT

By combining the fractional transform with Cn-expansion method, we give the improved elliptic expansion method to solve the generalized fraction KDV equations, and obtain some new periodic solution and solitary wave solutions.

Keywords:Complex-Transform-Cn Expansion Method, Modified Riemann-Liouville Derivative, Fractional Generalized KDV Equation

1. 引言

(1)

(2)

(3)

Jumarie的修正Riemann-Liouville导数有如下性质：

(4)

2. 复变换-Cn函数展开法

(5)

(6)

(7)

(8)

，由椭圆函数的导数公式有：

(9)

(10)

(11)

(12)

3. 分数阶广义KDV方程

(13)

(14)

(15)

(16)

(17)

(18)

(19)

，代入到(19)中得到

(20)

(21)

(22)

(23)

(24)

(25)

(26)

(27)

(28)

(29)

(30)

(31)

，代入到(31)得到

(32)

(33)

(34)

(35)

(36)

(37)

(38)

(39)

4. 结语

Travelling Wave Solution of the Generalized KDV Equation[J]. 理论数学, 2017, 07(05): 378-385. http://dx.doi.org/10.12677/PM.2017.75049

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