Title: A novel (G′/G)-expansion method for solving the (3 + 1)-dimensional modified KdV-Zakharov-Kuznetsov equation in mathematical physics

Authors: Md. Nur Alam; 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: A novel (G′/G)-expansion method is presented in this article to construct more general type and new travelling wave solutions of non-linear evolution equations. The method is illustrated in its application via the (3 + 1)-dimensional modified KdV-Zakharov-Kuznetsov equation which is used to model different non-linear phenomena. Through the assistance of Maple, we obtain several new and more general travelling wave solutions in terms of the hyperbolic functions, the trigonometric functions, the rational functions and their combination with parameters. The solutions obtained in this article can successfully recover previously known solutions by setting particular values of the parameters that have been found by other sophisticated methods.

Keywords: modified KdV-Zakharov-Kuznetsov equation; (G′/G)-expansion method; homogeneous balance; travelling wave solutions; solitary wave solutions; nonlinear equations; evolution equations; mathematical physics.

DOI: 10.1504/IJCSM.2015.071812

International Journal of Computing Science and Mathematics, 2015 Vol.6 No.4, pp.404 - 415

Received: 19 Oct 2013
Accepted: 30 Jan 2014

Published online: 19 Sep 2015 *

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