Title: The exp(−Φ(ξ))-expansion method for finding travelling wave solutions of Vakhnenko-Parkes equation

Authors: Kamruzzaman Khan; M. Ali Akbar

Addresses: Department of Mathematics, Pabna University of Science and Technology, Pabna 6600, Bangladesh ' Department of Applied Mathematics, University of Rajshahi, Rajshahi 6205, Bangladesh

Abstract: The paper employs the exp(−Φ(ξ))-expansion method for finding exact solutions of the Vakhnenko-Parkes (VP) equation. Each of the obtained solutions, namely hyperbolic function solutions, trigonometric function solutions, exponential function solutions and rational function solutions, contain an explicit function of the variables in the considered equation. It has been shown that the method provides a powerful mathematical tool for solving non-linear wave equations in mathematical physics and engineering problems.

Keywords: exp(-Phi(xi))-expansion method; Vakhnenko-Parkes equation; exact solution; NLEEs; nonlinear evolution equations; hyperbolic function; trigonometric function; exponential function; rational function; nonlinear wave equations.

DOI: 10.1504/IJDSDE.2014.067119

International Journal of Dynamical Systems and Differential Equations, 2014 Vol.5 No.1, pp.72 - 83

Received: 01 Feb 2014
Accepted: 07 Oct 2014
Published online: 29 Apr 2015 *

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