AUTHOR=Ali Karmina K. , Dutta Hemen , Yilmazer Resat , Noeiaghdam Samad 

TITLE=On the New Wave Behaviors of the Gilson-Pickering Equation

JOURNAL=Frontiers in Physics

VOLUME=8

YEAR=2020

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2020.00054

DOI=10.3389/fphy.2020.00054

ISSN=2296-424X

ABSTRACT=<p>In this article, we study the fully non-linear third-order partial differential equation, namely the Gilson-Pickering equation. The (1/<italic>G</italic>′)-expansion method, and the generalized exponential rational function method are used to construct various exact solitary wave solutions for a given equation. These methods are based on a homogeneous balance technique that provides an order for the estimation of a polynomial-type solution. In order to convert the governing equation into a nonlinear ordinary differential equation, a traveling wave transformation has been implemented. As a result, we have constructed a variety of solitary wave solutions, such as singular solutions, compound singular solutions, complex solutions, and topological and non-topological solutions. Besides, the 2D, 3D, and contour surfaces are plotted for all obtained solutions by choosing appropriate parameter values.</p>