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Exact Solutions to the Generalized Benjamin Equation

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Based on the -expansion method, a series of exact solutions of the generalized Benjamin equation have been obtained. The travelling wave solutions are expressed by the hyperbolic functions, the trigonometric functions and the rational functions. It is shown that the -expansion method is concise, and its applications are promising.
Cite this paper
Gao, H. and Di, G. (2014) Exact Solutions to the Generalized Benjamin Equation. Journal of Applied Mathematics and Physics, 2, 671-676. doi: 10.4236/jamp.2014.27074
 

[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
[2] Hirota, R. (2004) The Direct Method in Soliton Theory. Cambridge University Press, New York.
http://dx.doi.org/10.1017/CBO9780511543043
[3] Parkes, E.J. and Duffy, B.R. (1996) An Automated tanh-Function Method for Finding Solitary Wave Solutions to Nonlinear Evolution Equations. Computer Physics Communications, 98, 288-300.
http://dx.doi.org/10.1016/0010-4655(96)00104-X
[4] Fan, E.G. (2000) Extended tanh-Function Method and Its Applications to Nonlinear Equations. Physics Letters A, 277, 212-218. http://dx.doi.org/10.1016/S0375-9601(00)00725-8
[5] Yan, C.T. (1996) A Simple Transformation for Nonlinear Waves. Physics Letters A, 224, 77-84.
http://dx.doi.org/10.1016/S0375-9601(96)00770-0
[6] Wazwaz, A.M. (2003) A Study on Nonlinear Dispersive Partial Differential Equations of Compact and Noncompact Solutions. Applied Mathematics and Computation, 135, 399-409.
http://dx.doi.org/10.1016/S0096-3003(02)00005-X
[7] Wang, M.L. (1995) Solitary Wave Solutions for Variant Boussinesq Equations. Physics Letters A, 199, 169-172.
http://dx.doi.org/10.1016/0375-9601(95)00092-H
[8] Wang, M.L., Zhou, Y.B. and Li, Z.B. (1996) Applications of a Homogeneous Balance Method to Exact Solutions of Nonlinear Equations in Mathematical Physics. Physics Letters A, 216, 67-75.
http://dx.doi.org/10.1016/0375-9601(96)00283-6
[9] Liu, S.K., Fu, Z.T. and Liu, S.D. (2001) Jacobi Elliptic Function Expansion Method and Periodic Wave Solutions of Nonlinear Wave Equations. Physics Letters A, 289, 69-74. http://dx.doi.org/10.1016/S0375-9601(01)00580-1
[10] Fu, Z.T., Liu, S.K. and Liu, S.D. (2001) New Jacobi Elliptic Function Expansion and New Periodic Wave Solutions of Nonlinear Wave Equations. Physics Letters A, 290, 72-76. http://dx.doi.org/10.1016/S0375-9601(01)00644-2
[11] Feng, Z.S. (2002) On Explicit Exact Solutions to the Compound Burgers-KdV Equation. Physics Letters A, 293, 57-66.
http://dx.doi.org/10.1016/S0375-9601(01)00825-8
[12] Feng, Z.S. (2002) Exact Solution to an Approximate Sine-Gordon Equation in (n + 1)-Dimensional Space. Physics Letters A, 302, 64-76. http://dx.doi.org/10.1016/S0375-9601(02)01114-3
[13] Chen, Y. and Yan, Z.Y. (2005) New Exact Solutions of (2 + 1)-Dimensional Gardner Equation via the New Sine-Gordon Equation Expansion Method. Chaos, Solitons & Fractals, 26, 399-406.
http://dx.doi.org/10.1016/j.chaos.2005.01.004
[14] He, J.H. and Wu, X.H. (2006) Exp-Function Method for Nonlinear Wave Equations. Chaos, Solitons & Fractals, 30, 700-708. http://dx.doi.org/10.1016/j.chaos.2006.03.020
[15] He, J.H. and Abdou, M.A. (2007) New Periodic Solutions for Nonlinear Evolutions Using Exp-Function Method, Chaos, Solitons & Fractals, 34, 1421-1429. http://dx.doi.org/10.1016/j.chaos.2006.05.072
[16] Gao, H. and Zhao, R.X. (2010) New Exact Solutions to the Generalized Burgers-Huxley Equation. Applied Mathematics and Computation, 217, 1598-1603. http://dx.doi.org/10.1016/j.amc.2009.07.020
[17] Wang, M.L., Li, X.Z. and Zhang, J.L. (2008) The -Expansion Method and Travelling Wave Solutions of Nonlinear Evolution Equations in Mathematical Physics. Physics Letters A, 372, 417-423.
http://dx.doi.org/10.1016/j.physleta.2007.07.051
[18] Bekir, A. (2008) Application of the -Expansion Method for Nonlinear Evolution Equations. Physics Letters A, 372, 3400-3406. http://dx.doi.org/10.1016/j.physleta.2008.01.057
[19] Wang, M.L., Zhang, J.L. and Li, X.Z. (2008) Application of the -Expansion to Travelling Wave Solutions of the Broer-Kaup and the Approximate Long Water Wave Equations. Applied Mathematics and Computation, 206, 321-326.
http://dx.doi.org/10.1016/j.amc.2008.08.045
[20] Zhang, J., Wei, X. and Lu, Y. (2008) A generalized -Expansion Method and Its Applications. Physics Letters A, 372, 3653-3658. http://dx.doi.org/10.1016/j.physleta.2008.02.027
[21] Zhang, S., Tong, J.L. and Wang, W. (2008) A Generalized -Expansion Method for the mKdV Equation with Variable Coefficients. Physics Letters A, 372, 2254-2257.
http://dx.doi.org/10.1016/j.physleta.2007.11.026
[22] Zhang, S., Dong, L., Ba, J.M. and Sun, Y.N. (2009) The -Expansion Method for Nonlinear Differential-Difference Equations. Physics Letters A, 373, 905-910. http://dx.doi.org/10.1016/j.physleta.2009.01.018
[23] Zhang, H.Q. (2009) New Application of the -Expansion Method. Communications in Nonlinear Science and Numerical Simulation, 14, 3220-3225. http://dx.doi.org/10.1016/j.cnsns.2009.01.006
[24] Aslan, I. and Ozis, T. (2009) Analytic Study on Two Nonlinear Evolution Equations by Using the (G’/G)-Expansion Method. Applied Mathematics and Computation, 209, 425-429.
http://dx.doi.org/10.1016/j.amc.2008.12.064
[25] Ozis, T. and Aslan, I. (2009) Symbolic Computation and Construction of New Exact Traveling Wave Solutions to Fitzhugh-Nagumo and Klein-Gordon Equations. Zeitschrift für Naturforschung, 64a, 15-20.
[26] Ozis, T. and Aslan, I. (2009) Symbolic Computations and Exact and Explicit Solutions of Some Nonlinear Evolution Equations in Mathematical Physics. Communications in Theoretical Physics, 51, 577-580.
http://dx.doi.org/10.1088/0253-6102/51/4/01
[27] Gao, H. and Zhao, R.X. (2009) New Application of the (G’/G)-Expansion Method to Higher-Order Nonliear Equations. Applied Mathematics and Computation, 215, 2781-2786.
http://dx.doi.org/10.1016/j.amc.2009.08.041
[28] Hereman, W., Banerjee, P.P. and Korpel, A. (1986) Exact Solitary Wave Solutions of Nonliear Evolution and Wave Equations Using a Direct Algebraic Method. Journal of Physics A: Mathematical and General, 19, 607-628.
http://dx.doi.org/10.1088/0305-4470/19/5/016
[29] Taghizadeh, N., Mirzazadeh, M. and Moosavi Noori, S.R. (2012) Exact Solutions of the Generalized Benjamin Equation and (3 + 1)-Dimensional Gkp Equation by the Extended tanh Method. Applications & Applied Mathematics, 7, 175-187.                                                    eww141112lx

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