On the New Wave Behaviors of the Gilson-Pickering Equation
Karmina K. Ali, Hemen Dutta, Reşat Yılmazer, Samad Noeiaghdam
Abstract
In this article, we study the fully non-linear third-order partial differential equation, namely the Gilson–Pickering equation. The $\left(1/{{G}^{'}}\right)$-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, topological, and non-topological solutions. Besides, the 2D, 3D and contour surfaces are plotted for all obtained solutions by choosing appropriate parameter values.