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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

DOI: 10.12677/AAM.2013.21006, PP. 42-47

Keywords: 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

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Abstract:

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。
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.

References

[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 Schr?dinger 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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