展开方法及Fitzhugh-Nagumo方程新的孤波解

周建荣

(佛山科学技术学院 理学院数学系, 广东 佛山 528000)

周建荣

(佛山科学技术学院 理学院数学系, 广东 佛山 528000)

应用展开方法导出了Fitzhugh-Nagumo非线性方程新的孤波解.

孤波解;展开方法; Fitzhugh-Nagumo方程

近年来, 寻求非线性方程的行波解已引起人们的极大兴趣. 目前, 求解非线性方程比较成功的方法有齐次平衡法[5], 逆散射方法[2], Hopf-Cole变换法[12], Exp函数展开法[13], 双曲正切函数展开法[3,11], Sine-Cosine方法[15], 辅助方程法[14], 双曲函数法[4], 第一积分法[1,9]和双线性法[6], 等等.

新的孤波解, 其中δ为实常数.

这里的求导是关于波变量ξ.

应用方程(4), 从(3)式可得

应用数学软件Maple解此方程组得三组解:

(6)～(13)式是在文[11]中通过Tanh-Coth方法已经得到的孤波解.

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ZHOU Jian-rong
(Department of Mathematics, Foshan University, Foshan 528000, China)

The-expansion method is used to construct new solitary wave solutions of Fitzhugh-Nagumo equation.

solitary wave solutions;-expansion method; Fitzhugh-Nagumo equation

O175.29

A

1672-5298(2010)03-0021-03

2010-01-15

广东高校优秀青年创新人才培育项目(LYM08101)

周建荣(1978- ), 男, 湖南永州人, 博士, 佛山科学技术学院理学院数学系讲师. 主要研究方向: 渐近分析及非线性问题