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Entropy 2015, 17(6), 4255-4270; doi:10.3390/e17064255

New Hyperbolic Function Solutions for Some Nonlinear Partial Differential Equation Arising in Mathematical Physics

1
Department of Computer Engineering, Tunceli University, Tunceli, 62100, Turkey
2
Department of Mathematics, University of Firat, Elazig, 23119, Turkey
*
Author to whom correspondence should be addressed.
Academic Editor: J. A. Tenreiro Machado
Received: 20 May 2015 / Revised: 15 June 2015 / Accepted: 17 June 2015 / Published: 19 June 2015
(This article belongs to the Section Complexity)
View Full-Text   |   Download PDF [2473 KB, uploaded 19 June 2015]   |  

Abstract

In this study, we investigate some new analytical solutions to the (1 + 1)-dimensional nonlinear Dispersive Modified Benjamin–Bona–Mahony equation and the (2 + 1)-dimensional cubic Klein–Gordon equation by using the generalized Kudryashov method. After we submitted the general properties of the generalized Kudryashov method in Section 2, we applied this method to these problems to obtain some new analytical solutions, such as rational function solutions, exponential function solutions and hyperbolic function solutions in Section 3. Afterwards, we draw two- and three-dimensional surfaces of analytical solutions by using Wolfram Mathematica 9. View Full-Text
Keywords: the generalized Kudryashov method; (1 + 1)-dimensional nonlinear Dispersive Modified Benjamin–Bona–Mahony equation; (2 + 1)-dimensional cubic Klein–Gordon equation; soliton solutions; rational function solutions; hyperbolic function solutions; trigonometric function solutions; exponential function solution the generalized Kudryashov method; (1 + 1)-dimensional nonlinear Dispersive Modified Benjamin–Bona–Mahony equation; (2 + 1)-dimensional cubic Klein–Gordon equation; soliton solutions; rational function solutions; hyperbolic function solutions; trigonometric function solutions; exponential function solution
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Baskonus, H.M.; Bulut, H. New Hyperbolic Function Solutions for Some Nonlinear Partial Differential Equation Arising in Mathematical Physics. Entropy 2015, 17, 4255-4270.

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