The Exp-Function Method for Solving Two Dimensional Sine-Bratu Type Equations

In this paper, we apply Exp-function method to give traveling wave solutions of second order sine-Bratu type equations. This method is straightforward, concise and effective.

KEYWORDS

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Moradi, E. , Varasteh, H. , Abdollahzadeh, A. and Mostafaei-Malekshah, M. (2014) The Exp-Function Method for Solving Two Dimensional Sine-Bratu Type Equations. Applied Mathematics, 5, 1212-1217. doi: 10.4236/am.2014.58112.

 [1] Kutluay, S., Esen, A. and Tasbozan, O. (2010) The -Expansion Method for Some Nonlinear Evolution Equations. Applied Mathematics and Computation, 217, 384-391. http://dx.doi.org/10.1016/j.amc.2010.05.073 [2] Aslan, I. and Ozis, T. (2009) On the Validity and Reliability of the -Expansion Method by Using Higher-Order Nonlinear Equations. Applied Mathematics and Computation, 211, 531-536. http://dx.doi.org/10.1016/j.amc.2009.01.075 [3] Wang, M., Zhang, J. and Li, X. (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 [4] Wazwaz, A.M. (2006) The tanh and the sine-cosine Methods for a Reliable Treatment of the Modified Equal Width Equation and Its Variants. Communications in Nonlinear Science and Numerical Simulation, 11, 148-160.http://dx.doi.org/10.1016/j.cnsns.2004.07.001 [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] Parkes, E.J. (2010) Observations on the tanh-coth Expansion Method for Finding Solutions to Nonlinear Evolution Equations. Applied Mathematics and Computation, 217, 1749-1754. http://dx.doi.org/10.1016/j.amc.2009.11.037 [7] Wazwaz, A.M. (2005) The tanh Method: Exact Solutions of the Sine-Gordon and Sinh-Gordon Equations. Applied Mathematics and Computation, 167, 1196-1210. http://dx.doi.org/10.1016/j.amc.2004.08.005 [8] Biazar, J. and Ghazvini, H. (2007) Exact Solutions for Non-Linear Schrodinger Equations by He’s Homotopy Perturbation Method. Physics Letters A, 366, 79-84. http://dx.doi.org/10.1016/j.physleta.2007.01.060 [9] He, J.H. (2005) Application of Homotopy Perturbation Method to Nonlinear Wave Equations. Chaos, Solitons & Fractals, 26, 695-700. http://dx.doi.org/10.1016/j.chaos.2005.03.006 [10] Wang, M.L. and Li, X.Z. (2005) Extended F-Expansion Method and Periodic Wave Solutions for the Generalized Zakharov Equations. Physics Letters A, 343, 48-54. http://dx.doi.org/10.1016/j.physleta.2005.05.085 [11] Wang, M.L. and Li, X.Z. (2005) Applications of F-Expansion to Periodic Wave Solutions for a New Hamiltonian Amplitude Equation. Chaos, Solitons & Fractals, 24, 1257-1268. http://dx.doi.org/10.1016/j.chaos.2004.09.044 [12] Bekir, A. and Boz, A. (2008) Exact Solutions for Nonlinear Evolution Equations Using Exp-Function Method. Physics Letters A, 372, 1619-1625. http://dx.doi.org/10.1016/j.physleta.2007.10.018 [13] Ebaid, A. (2007) Exact Solitary Wave Solutions for Some Nonlinear Evolution Equations via Exp-Function Method. Physics Letters A, 365, 213-219. http://dx.doi.org/10.1016/j.physleta.2007.01.009 [14] Abdou, M.A., Solimanm, A.A. and El-Basyony, S.T. (2007) New Application of Exp-Function Method for Improved Boussinesq Equation. Physics Letters A, 369, 469-475. http://dx.doi.org/10.1016/j.physleta.2007.05.039 [15] Zhu, S.D. (2007) Exp-Function Method for the Discrete mKdV Lattice. International Journal of Nonlinear Sciences and Numerical Simulation, 8, 465-469.