# 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

• 全文下载: PDF(477KB)    PP.406-411   DOI: 10.12677/AAM.2016.53050
• 下载量: 697  浏览量: 1,605   科研立项经费支持

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。

F-expansion method is an effective method to construct exact solutions of nonlinear evolution eq-uations. 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.

 [1] Wang, M.L., Zhou, Y.B. and Li, Z.B. (1996) Application of a Homogeneous Balance Method to Exact Solution of Nonlinear Equations in Mathematical Physics. Physics Letters A, 216, 67-75. http://dx.doi.org/10.1016/0375-9601(96)00283-6 [2] Parkes, E.J. and Duffy, B.R. (1996) An Automated tanh-Function Method for Finding Solitary Wave Solutions to Non-Linear Evolution Equations. Computer Physics Communications, 98, 288-300. http://dx.doi.org/10.1016/0010-4655(96)00104-X [3] Tam, H.W., Ma, W.X., Hu, X.B., et al. (2000) The Hirota-Satsuma Coupled KdV Equation and a Coupled Ito System Revisited. Journal of the Physical Society of Japan, 69, 45-52. http://dx.doi.org/10.1143/JPSJ.69.45 [4] 屠规彰. Boussinesq方程的Bäcklund变换与守恒律[J]. 应用数学学报, 1981, 4(1): 63-68. [5] Zedan, H.A. (2011) Exact Solutions for the Generalized KdV Equation by Using Bäcklund Transformations. Journal of the Franklin Institute, 348, 1751-1768. http://dx.doi.org/10.1016/j.jfranklin.2011.04.013 [6] 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 [7] Matveev, V.B. and Salle, M.A. (1991) Darbooux Transformation and So-liton. Springer, Berlin. http://dx.doi.org/10.1007/978-3-662-00922-2 [8] 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.