Journal of Ocean Engineering and Science

Volume 2, Issue 2

(7) Solitary wave solutions for the generalized Zakharov–Kuznetsov–Benjamin–Bona–Mahony nonlinear evolution equation

Aly R. Seadawy^a , Dianchen Lu ^b , Mostafa M.A. Khater ^{b , c , ∗}
a Department of Mathematics, Faculty of Science, Taibah University, Al-Ula, Saudi Arabia

b Department of Mathematics, Faculty of Science, Jiangsu University, China

c Department of Mathematics, Faculty of Science, Mansoura University, 35516 Mansoura, Egypt

Received 8 March 2017; received in revised form 29 April 2017; accepted 8 May 2017
Available online 19 May 2017

Abstract
In this paper, we utilize the exp( −ϕ( ξ ))-expansion method to find exact and solitary wave solutions of the generalized Zakharov–Kuznetsov–Benjamin–Bona–Mahony nonlinear evolution equation. The generalized Zakharov–Kuznetsov–Benjamin–Bona–Mahony nonlinear evolution equation describes the model for the propagation of long waves that mingle with nonlinear and dissipative impact. This model is used in the analysis of the surface waves of long wavelength in hydro magnetic waves in cold plasma, liquids, acoustic waves in harmonic crystals and acoustic–gravity waves in compressible fluids. By using this method, seven different kinds of traveling wave solutions are successfully obtained for this model. The considered method and transformation techniques are efficient and consistent for solving nonlinear evolution equations and obtain exact solutions that are applied to the science and engineering fields.
© 2017 Shanghai Jiaotong University. Published by Elsevier B.V.
This is an open access article under the CC BY-NC-ND license. ( http://creativecommons.org/licenses/by-nc-nd/4.0/ )

Keywords: The exp( −ϕ( ξ ))-expansion method; The generalized Zakharov–Kuznetsov–Benjamin–Bona–Mahony nonlinear evolution equation; Traveling wave solutions; Solitary wave solutions.

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