American Journal of Applied Mathematics and Statistics
ISSN (Print): 2328-7306 ISSN (Online): 2328-7292 Website: http://www.sciepub.com/journal/ajams Editor-in-chief: Mohamed Seddeek
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American Journal of Applied Mathematics and Statistics. 2013, 1(4), 64-70
DOI: 10.12691/ajams-1-4-3
Open AccessReview Article

The Improved (G/G)-Expansion Method to the (3+1)-Dimensional Kadomstev-Petviashvili Equation

Hasibun Naher1, 2, and Farah Aini Abdullah2

1School of Mathematical Sciences, Universiti Sains Malaysia,Penang, Malaysia

2Department of Mathematics and Natural Sciences, BRAC University, Mohakhali, Dhaka, Bangladesh

Pub. Date: September 17, 2013

Cite this paper:
Hasibun Naher and Farah Aini Abdullah. The Improved (G/G)-Expansion Method to the (3+1)-Dimensional Kadomstev-Petviashvili Equation. American Journal of Applied Mathematics and Statistics. 2013; 1(4):64-70. doi: 10.12691/ajams-1-4-3

Abstract

In this article, the improved (G/G)-expansion method has been implemented to generate travelling wave solutions, where G(ξ) satisfies the second order linear ordinary differential equation. To show the advantages of the method, the (3+1)-dimensional Kadomstev-Petviashvili (KP) equation has been investigated. Higher-dimensional nonlinear partial differential equations have many potential applications in mathematical physics and engineering sciences. Some of our solutions are in good agreement with already published results for a special case and others are new. The solutions in this work may express a variety of new features of waves. Furthermore, these solutions can be valuable in the theoretical and numerical studies of the considered equation. Also, in order to understand the behaviour of solutions, the graphical representations of some obtained solutions have been presented.

Keywords:
the improved (G/G)-expansionmethod the Kadomstev-Petviashvili equation traveling wave solutions nonlinear evolution equations

Creative CommonsThis work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

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