一个广义变系数KdV方程新的精确解
New Exact Solutions of a Generalized KdV Equation with Variable Coefficients

作者: 张佳梅 , 马 超 , 叶彩儿 :浙江农林大学理学院,临安;

关键词: 广义变系数KdV方程指数函数方法精确解 Generalized KdV Equation with Variable Coefficients Exp-Function Method Exact Solutions

摘要:

本文我们利用指数函数方法求解一个广义变系数KdV方程,结果我们求出了许多类型的解,这些解包括孤立波解,爆破解和周期波解。

Abstract: In this paper, we use the exp-function method to solve a generalized KdV equation with variable coefficients. As a result, several types of solutions are obtained which contain solitary wave solutions, blow-up solutions and periodic solutions.

文章引用: 张佳梅 , 马 超 , 叶彩儿 (2013) 一个广义变系数KdV方程新的精确解。 应用数学进展, 2, 42-47. doi: 10.12677/AAM.2013.21006

参考文献

[1] M. J. Ablowitz, P. A. Clarkson. Soliton, nonlinear evolution equations and inverse scattering. New York: Cambridge University Press, 1991.

[2] C. S. Gardner, J. M. Greene and M. D. Kruskal. Method for solving the Korteweg-deVries equation. Physical Review Letters, 1967, 19(19): 1095-1097.

[3] J. Lin. On solution of the Dullin-Gottwald-Holm equation. International Journal of Nonlinear Science, 2006, 1(1): 43-48.

[4] V. B. Matveev, M. A. Salle. Darboux transformations and solitons. Berlin: Springer, 1991.

[5] R. Hirota, J. Satsuma. Soliton solutions for a coupled KdV equation. Physics Letters A, 1981, 85: 407-408.

[6] M. L. Wang, Y. B. Zhou and Z. B. Li. Application of a homogeneous balance method to exact solution of nonlinear equations in mathematical physics. Physics Letters A, 1996, 216(1-5): 67-75.

[7] E. J. Parkes, B. R. Duffy. An automated tanh-function method for finding solitary wave solutions to non-linear evolution equations. Computer Physics Communications, 1996, 98(3): 288-300.

[8] C. T. Yan. A simple transformation for nonlinear waves. Physics Letters A, 1996, 224(1-2): 77-84.

[9] W. H. Huang, Y. L. Liu. Jacobi elliptic function solutions of the Ablowitz-Ladik discrete nonlinear Schrödinger system. Chaos, Solitons & Fractals, 2009, 40: 786-792.

[10] Sirendaoreji. Auxiliary equation method and new solutions of Klein-Gordon equations. Chaos, Solitons & Fractals, 2007, 31(4): 943-950.

[11] J.H. He, X.H. Wu. Exp-function method for nonlinear wave equations. Chaos, Solitons & Fractals, 2006, 30(3): 700-708.

[12] X. H. Wu, J. H. He. Solitary solutions periodic solutions and compacton-like solutions using the exp-function method. Computers & Mathematics with Applications, 2007, 54(7-8): 966-986.

[13] J. H. He. An elementary introduction to recently developed asymptotic methods and nanomechanics in textile engineering. International Journal of Modern Physics B (IJMPB), 2008, 22(21): 3487-3578.

[14] D. Q. Xian, Z. D. Dai. Application of exp-function method to potential Kadomtsev-Petviashvili equation. Chaos, Solitons & Fractals, 2009, 42(5): 2653-2659.

[15] S. Zhang. Application of exp-function method to a KdV equation with variable coefficients. Physics Letters A, 2007, 365(5-6): 448-453.

[16] M. L. Wang, Y. M. Wang and Y. B. Zhou. An auto-Backlund transformation and exact solutions to a generalized KdV equation with variable coefficients and their applications. Physics Letters A, 2002, 303(1): 45-51.

[17] C. Tian. Symmetries and a hierarchy of the general KdV equation. Journal of Physics A: Mathematical and General, 1987, 20(2): 359-366.

[18] Z. T. Fu, S. D. Liu and S. K. Liu. New exact solutions to KdV equations with variable coefficients or forcing. Applied Mathematics and Mechanics (English Edition), 2004, 25(1): 73-79.

[19] E. G. Fan, H. Q. Zhang. A note on the homogeneous balance method. Physics Letters A, 1998, 246(5): 403-406.

[20] G.Q. Xu, Z. B. Li. Mixing exponential method and its application to the solitary wave solution of the nonlinear evolution equation. Acta Physica Sinica, 2002, 51: 946-950 (in Chinese).

[21] G. Q. Xu, Z. B. Li. Explicit solutions to the coupled KdV equations with variable coefficients. Applied Mathematics and Mechanics, 2005, 26(1): 101-107.

[22] P. A. Clarkson, E. L. Mansfield. Symmetry reductions and exact solutions of a class of nonlinear heat equations. Physica D: Nonlinear Phenomena, 1993, 70(3): 250-288.

[23] N. A. Kudryashov, E. D. Zargaryan. Solitary waves in active-dissipative dispersive media. Journal of Physics A: Mathematical and General, 1996, 29(24): 8067-8077.

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