The Study on the Soliton Solution of the Generalized Burgers-Fisher System


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By introducing the (G'/G)-expansion method, the exact soliton solution is constructed for generalized burgers-fisher system. The two classes of soliton, namely, kink-like soliton and anti-kink-like soliton are studied for the system.



Edited by:

Honghua Tan




Y. L. Ma and B. Q. Li, "The Study on the Soliton Solution of the Generalized Burgers-Fisher System", Applied Mechanics and Materials, Vols. 29-32, pp. 768-773, 2010

Online since:

August 2010




[1] M.L. Wang, Solitary wave solutions for variant Boussinesq equations, Phys. Lett. A Vol. 199(1995), pp.169-172.

[2] M.L. Wang, Y.B. Zhou, Z.B. Li, Application of a homogeneous balance method to exact solutions of nonlinear equations in mathematical physics, Phys. Lett. A Vol. 216(1996), pp.67-75.


[3] E.J. Parkes, B.R. Duffy, An automated tanh-function method for finding solitary wave solutions to non-linear evolution equations, Comput. Phys. Commum. Vol. 98(1996), pp.288-300.


[4] E.G. Fan, Auto-Baklund transformation and similarity reductions for general variable coefficient KdV equations, Phys. Lett. A Vol. 294(2002), pp.26-30.


[5] S.A. Ei-Wakil, New exact travelling wave solutions using modified extended tanh-function method, Chaos Solitons Fractals Vol. 31(2001), pp.840-852.


[6] Y.T. Gao, B. Tian, Generalized hyperbolic-function method with computerized symbolic computation to construct the solitonic solutions to nonlinear equations of mathematical physics, Comput. Phys. Commun. Vol. 133(2001), pp.158-164.


[7] Y.D. Shang, H. Huang, W.J. Yuan, The extended hyperbolic functions method and new exact solutions to the Zakharov equations, Appl. Math. Comput. Vol. 200(2008), pp.110-122.


[8] S. Liu, Z. Fu, S. Liu, Q. Zhao, Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations, Phys. Lett. A Vol. 289(2001), pp.69-74.


[9] G.T. Liu, T.Y. Fan, New applications of developed Jacobi elliptic function expansion methods, Phys. Lett. A Vol. 345(2005), pp.161-166.

[10] A. Ebaid, Exact solitary wave solutions for some nonlinear evolution equations via Exp-function method, Phys. Lett. A Vol. 365(2007), pp.213-219.


[11] Y.B. Zhou, M.L. Wang, Y.M. Wang, Periodic wave solutions to a coupled KdV equations with variable coefficients, Phys. Lett. A Vol. 308(2003), pp.31-36.


[12] Sirendaoreji, A new auxiliary equation and exact travelling wave solutions of nonlinear equations, Phys. Lett. A Vol. 356(2006), pp.124-130.


[13] Y.L. Ma, B.Q. Li, A series of abundant exact travelling wave solutions for a modified generalized Vakhnenko equation using auxiliary equation method, Appl. Math. Comput. Vol. 201(2009), pp.102-107.


[14] M.L. Wang, X.Z. Li, J.L. Zhang, The (G'/G)-expansion method and traveling wave solutions of nonlinear evolution equations in mathematical physics, Phys. Lett. A Vol. 372(2008), pp.417-423.


[15] M.L. Wang, J.L. Zhang, X.Z. Li, Application of the (G'/G)-expansion to travelling wave solutions of the Broer-Kaup and the approximate long water wave equations, Appl. Math. Comput. Vol. 206(2008), pp.321-326.


[16] L.X. Li, M.L. Wang, The (G'/G)-expansion method and travelling wave solutions for a higher-order nonlinear schrodinger equation, Appl. Math. Comput. Vol. 208(2009), pp.440-445.


[17] Ismail Aslan, Turgut Ozisb, Analytic study on two nonlinear evolution equations by using the (G'/G)-expansion method, Appl. Math. Comput. 209(2009), pp.425-429.


[18] Y.B. Zhou, C. Li, Application of Modified G'/G-Expansion Method to Traveling Wave Solutions for Whitham-Broer-Kaup-Like Equations, Commun. Theor. Phys. (Beijing) 51(2009) pp.664-670.


[19] B.Q. Li, Y.L. Ma, (G'/G)-expansion method and new exact solutions for (2+1)-dimensional asymmetrical Nizhnik-Novikov-Veselov system, Acta Phys. Sin. 58(2009), pp.4373-4378.

[20] Y.L. Ma, B.Q. Li, J.Z. Sun, New application of (G'/G)-expansion method for high dimensional nonlinear physical equations, Acta Phys. Sin. Vol. 58(2009), pp.7402-7408.

[21] B.Q. Li, Y.L. Ma, M.P. Xu, (G'/G)-expansion method and novel fractal structure for high-dimensional nonlinear physical equation, Acta Phys. Sin. Vol. 59(2010), pp.1409-1415.

[22] B.Q. Li, Y.L. Ma, Exact solutions for coupled mKdV equations by a new symbolic computation method, Appl. Mech. Mater. Vol. 20-23(2010), pp.184-189.


[23] B.Q. Li, M.P. Xu, Y.L. Ma, New exact solutions of (2+1)-dimensional generalization of shallow water wave equation by (G'/G)-expansion method, Appl. Mech. Mater. Vol. 20-23(2010), pp.1516-1521.


[24] Y. Kametaka, On the nonlinear diffusion equation of Kolmogorov-Petrovskii-Piskunov type, Osaka J. Math, Vol. 13(1976), pp.11-66.

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