Homogenous balance method for solving exact solutions of the nonlinear Benny -luke equation and Vakhnenko-Parkes equation

  • Israa A. Ibrahim Department of Math., College Education for Pure Sciences, Tikrit University, Iraq
  • Wafaa M. Taha Department of Math., College Education for Pure Sciences, Tikrit University, Iraq
  • M. S. M. Noorani 1-Department of Math., College of Sciences, Kirkuk University, Iraq ,2-School of Math. Sciences, University Kebangsaan Malaysia UKM, Malaysia
Keywords: Application, Homogeneous balance method ,The Benny-Luke equation, The Vakhenko-Parkes equation

Abstract

      In this article, We apply the homogeneous balance method to construct the many families of exact solution of travelling wave solution of nonlinear equations, the Benny -Luke equation and vakhnenko-parkes equation. As the result, many solitary wave solution are obtained from the solution by hyperbolic function when the parameters were taken at special values and we compared the result with the solution of F-expansion method and -expansion method, we obtained the same results by certain hypotheses. Also we drew a 3D graph of exact solution  for the special Benny -luke equation and vakhnenko-parkes equation by help of the maple.  

References

Abazari, R., 2010. Application of (G′/G)-expansion method to travelling wave solutions of three nonlinear evolution equation, Computers and Fluids. Elsevier Ltd. https://doi.org/10.1016/j.compfluid.2010.06.024
Akbar, M.A., Shafiqul, I.M., Khan, K., 2017. Application of the improved F-expansion method with Riccati equation to find the exact solution of the nonlinear evolution equations, Journal of the Egyptian Mathematical Society. Elsevier B.V. https://doi.org/10.1016/j.joems.2016.03.008
El-Wakil, S.A., Abulwafa, E.M., Elhanbaly, A., Abdou, M.A., 2007. The extended homogeneous balance method and its applications for a class of nonlinear evolution equations. Chaos, Solitons & Fractals 33, 1512–1522. https://doi.org/10.1016/j.chaos.2006.03.010
Elwakil, S., El-labany, S.K., Zahran, M.A., Sabry, R., 2003. Exact travelling wave solutions for the generalized shallow water wave equation. Chaos, Solitons & Fractals 17, 121–126. https://doi.org/10.1016/S0960-0779(02)00414-9
Elwakil, S., El-labany, S.K., Zahran, M., Sabry, R., 2004. New exact solutions for a generalized variable coefficients 2D KdV equation. Chaos, Solitons & Fractals 19, 1083–1086. https://doi.org/10.1016/S0960-0779(03)00276-5
Fan, E., 2003. An algebraic method for finding a series of exact solutions to integrable and nonintegrable nonlinear evolution equations. Journal of Physics A: Mathematical and General 36, 7009–7026. https://doi.org/10.1088/0305-4470/36/25/308
Fan, E., 2000. Two new applications of the homogeneous balance method. Physics Letters A 265, 353–357. https://doi.org/10.1016/S0375-9601(00)00010-4
Khalfallah, M., 2009a. New exact traveling wave solutions of the (3+1) dimensional Kadomtsev–Petviashvili (KP) equation. Communications in Nonlinear Science and Numerical Simulation 14, 1169–1175. https://doi.org/10.1016/j.cnsns.2007.11.010
Khalfallah, M., 2009b. Exact traveling wave solutions of the Boussinesq–Burgers equation. Mathematical and Computer Modelling 49, 666–671. https://doi.org/10.1016/j.mcm.2008.08.004
Wang, M., Li, X., Zhang, J., 2008. The ()-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics. Physics Letters A 372, 417–423. https://doi.org/10.1016/j.physleta.2007.07.051
Wang, M., Zhou, Y., Li, Z., 1996. Application of a homogeneous balance method to exact solutions of nonlinear equations in mathematical physics. Physics Letters A 216, 67–75. https://doi.org/10.1016/0375-9601(96)00283-6
Wang M, 1995. Solitary wave solutions for variant Boussinesq equations. Phys. Lett. A 199, 169–172.
Zayed, E.M.E., Arnous, A.H., 2012. DNA Dynamics Studied Using the Homogeneous Balance Method 29, 10–12.https://doi.org/10.1088/0256-307X/29/8/080203
Zhao X, Wang, L., W.Sun, 2006. The repeated homogeneous balance method and its applications to nonlinear partial differential equations. Chaos, Solitons & Fractals 28, 448–453.
Published
2019-10-01
How to Cite
A. Ibrahim, I., W. M. Taha, and M. S. M. Noorani. “Homogenous Balance Method for Solving Exact Solutions of the Nonlinear Benny -Luke Equation and Vakhnenko-Parkes Equation”. ZANCO Journal of Pure and Applied Sciences, Vol. 31, no. s4, Oct. 2019, pp. 52-56, doi:10.21271/zjpas.31.s4.9.