应用指数函数方法求解KdV型方程
Application of Exp-Function Method to Solve KdV-Type Equation
DOI: 10.12677/AAM.2015.44046, PDF,    科研立项经费支持
作者: 张赛, 李国放, 王宁：北方工业大学理学院，北京
关键词: 指数函数方法；KdV型方程；精确解；Exp-Function Method； KdV-Type Equation； Exact Solution
摘要: 指数函数方法是求解数学物理领域中偏微分方程的一种十分有效的方法。本文利用指数函数方法获得了KdV型方程新的精确解，并描绘出精确解对应的图像,以便更好地理解解的性质。
Abstract: Exp-function method is an effective way to construct exact solutions of partial differential equations in mathematics and physics. This paper applies Exp-function method to obtain the new exact solutions of KdV-type equation, and depicts the figures of the solutions respectively in order to better understand the properties of the solutions.
文章引用：张赛, 李国放, 王宁. 应用指数函数方法求解KdV型方程[J]. 应用数学进展, 2015, 4(4): 369-375. https://dx.doi.org/10.12677/AAM.2015.44046

参考文献

[1] Ablowitz, M.J. and Clarkson, P.A. (1991) Solitons, Nonlinear Evolution Equations and Inverse Scattering. Cambridge University Press, New York. http://dx.doi.org/10.1017/CBO9780511623998 [Google Scholar] [CrossRef] 
[2] 闫振亚. 复杂非线性波的构造性理论及其应用[M]. 北京: 科学出版社, 2007.
[3] 范恩贵, 张鸿庆. 非线性孤子方程的齐次平衡法[J]. 物理学报, 1998(47): 333-361.
[4] 李志斌, 张善卿. 非线性波动方程准确孤立波解的符号计算[J]. 数学物理学报, 1997(17): 81-89.
[5] 楼森岳, 唐晓艳. 非线性数学物理方程[M]. 北京: 科学出版社, 2006.
[6] He, J.-H. and Wu, X.-H. (2006) Exp-Function Method for Nonlinear Wave Equations. Chaos, Solitons and Fractals, 30, 700-708. http://dx.doi.org/10.1016/j.chaos.2006.03.020 [Google Scholar] [CrossRef] 
[7] Bluman, G.W. and Anco, S.C. (2002) Symmetry and Integration Methods for Differential Equations. Springer, New York.
[8] Dey, B. (1985) Domain Wall Solution of KdV like Eq-uation with Higher Order Nonlinearity. Journal of Physics A: Mathematical and General, 19, L9-L12. http://dx.doi.org/10.1088/0305-4470/19/1/003 [Google Scholar] [CrossRef] 
[9] Zhang, W.G., Chang, Q.S. and Jiang, B.G. (2002) Explicit Exact Solitary-Wave Solutions for the Compound KdV- Type and Compound KdV-Burgers-Type Equations with Nonlinear Terms of Any Order. Chaos, Solitons and Fractals, 13, 311-319. http://dx.doi.org/10.1016/S0960-0779(00)00272-1 [Google Scholar] [CrossRef] 

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