﻿ 应用F-展开法寻找KdV型方程精确解 Application of F-Expansion Method to Obtain Exact Solutions of KdV-Type Equation

Vol.05 No.03(2016), Article ID:18404,6 pages
10.12677/AAM.2016.53050

Application of F-Expansion Method to Obtain Exact Solutions of KdV-Type Equation

Ning Wang, Guofang Li, Yiyang Liu, Biqing Qiu

College of Sciences, North China University of Technology, Beijing

Received: Jul. 26th, 2016; accepted: Aug. 18th, 2016; published: Aug. 25th, 2016

ABSTRACT

F-expansion method is an effective method to construct exact solutions of nonlinear evolution equations. This paper applies F-expansion to study a class of KdV-type equation, and obtain affluent exact solutions of the equation. Moreover, the graphs of such solutions are depicted.

Keywords:F-Expansion, KdV-Type Equation, Exact Solutions

F-展开法是非线性发展方程精确解构造的一种行之有效的方法。本文利用F-展开法研究一类KdV型方程，获得了该方程新的精确解，并描绘出精确解对应的图像。

1. 引言

(1.1)

2. 方法概述

(2.1)

1) 假设方程(2.1)具有行波解：

(2.2)

(2.3)

2) 假设方程(2.3)可表达成如下形式：

(2.4)

(2.5)

3) 将(2.4)、(2.5)带入到方程(2.3)中，然后平衡方程(2.3)的非线性项和最高阶导数项即可确定表达式(2.4)中的

3. 方程求解

(3.1)

(3.2)

(3.3)

(3.3)的一阶导数为：

(3.4)

(3.3)的二阶导数为：

(3.5)

Table 1. Relations between the coefficients and corresponding in

(3.6)

(3.7)

(3.8)

(3.9)

(3.10)

(3.11)

Figure 1. Figure of solution (3.9)

Figure 2. Figure of solution (3.10)

Figure 3. Figure of solution (3.11)

4. 总结

Application of F-Expansion Method to Obtain Exact Solutions of KdV-Type Equation[J]. 应用数学进展, 2016, 05(03): 406-411. http://dx.doi.org/10.12677/AAM.2016.53050

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