Construction of exact traveling wave solutions of the Bogoyavlenskii equation by <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si7.svg"> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:msup> <mml:mrow> <mml:mi>G</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>′</mml:mo> </mml:mrow> </mml:msup> <mml:mo>/</mml:mo> <mml:mi>G</mml:mi> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> <mml:mo>/</mml:mo> <mml:mi>G</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> -expansion and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si8.svg"> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>/</mml:mo> <mml:msup> <mml:mrow> <mml:mi>G</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>′</mml:mo> </mml:mrow> </mml:msup> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> -expansion techniques
Asıf Yokuş, Hülya Durur, Hijaz Ahmad, Phatiphat Thounthong, Ying-Fang Zhang
Abstract
In this article, we construct exact solutions of the Bogoyavlenskii equation using (1/G′)-expansion and (G′/G,1/G)-expansion techniques. Both techniques have been successfully implemented to obtain exact solutions including hyperbolic, complex trigonometric, trigonometric and rational solutions of the Bogoyavlenskii equation. 3D, contour and 2D graphics are presented of the solutions obtained for different special values. Further, the advantages and disadvantages of both the techniques have been discussed in this study. The proposed techniques are reliable and applicable for attaining wave solutions of nonlinear differential equations. Also, these techniques can greatly minimize the size of computing work compared to other available techniques.