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Math. Comput. Appl. 2016, 21(2), 6; doi:10.3390/mca21020006

New Complex Hyperbolic Function Solutions for the (2+1)-Dimensional Dispersive Long Water–Wave System

1
Department of Mathematics, Firat University, Elazig 23119, Turkey
2
Department of Computer Engineering, Tunceli University, Tunceli 62100, Turkey
These authors contributed equally to this work.
*
Author to whom correspondence should be addressed.
Academic Editor: Mehmet Pakdemirli
Received: 18 February 2016 / Revised: 18 March 2016 / Accepted: 18 March 2016 / Published: 24 March 2016

Abstract

In this paper, new algorithms called the “Modified exp(−Ω)-expansion function method” and “Improved Bernoulli sub-equation function method” have been proposed. The first algorithm is based on the exp(−Ω(ξ))-expansion method; the latter is based on the Bernoulli sub-Ordinary Differential Equation method. The methods proposed have been expressed comprehensively in this manuscript. The analytical solutions and application results are presented by drawing the two- and three-dimensional surfaces of solutions such as hyperbolic, complex, trigonometric and exponential solutions for the (2+1)-dimensional dispersive long water–wave system. Finally, a conclusion has been presented by mentioning the important discoveries in this manuscript. View Full-Text
Keywords: modified exp(−Ω(ξ))-expansion function method; improved Bernoulli sub-equation function method; the (2+1)-dimensional dispersive long water–wave system; hyperbolic function solution; trigonometric function solution; complex function solution; exponential function solution modified exp(−Ω(ξ))-expansion function method; improved Bernoulli sub-equation function method; the (2+1)-dimensional dispersive long water–wave system; hyperbolic function solution; trigonometric function solution; complex function solution; exponential function solution
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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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MDPI and ACS Style

Bulut, H.; Baskonus, H.M. New Complex Hyperbolic Function Solutions for the (2+1)-Dimensional Dispersive Long Water–Wave System. Math. Comput. Appl. 2016, 21, 6.

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