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.
Highlights
Nonlinear partial differential equations (NLPDEs) are used to represent a variety of nonlinear physical phenomena in different areas of applied sciences like fluid dynamics, plasma physics, optical fibers, and biology
Among the most profitable strategies for examining such nonlinear physical phenomena is to seek for the exact solutions of NLPDEs [1,2,3,4,5]
A variety of effective methods have been implemented to investigate the exact solutions of nonlinear partial differential equations, such as Hirota’s bilinear method [6], the Adomian decomposition method [7], the exp(− (ξ ))-expansion method [8], the sine-Gordon expansion method [9], the Bernoulli sub-equation method [10, 11], the shooting method with the fourth-order Runge-Kutta scheme [12, 13], the generalized exponential rational function method [14,15,16,17,18], the modified exponential function method [19], the modified auxiliary expansion method [20], the homotopy perturbation Sumudu transform method [21], the homotopy perturbation transform method [22, 23], and the fractional homotopy analysis transform method [24]
Summary
Nonlinear partial differential equations (NLPDEs) are used to represent a variety of nonlinear physical phenomena in different areas of applied sciences like fluid dynamics, plasma physics, optical fibers, and biology. A variety of effective methods have been implemented to investigate the exact solutions of nonlinear partial differential equations, such as Hirota’s bilinear method [6], the Adomian decomposition method [7], the exp(− (ξ ))-expansion method [8], the sine-Gordon expansion method [9], the Bernoulli sub-equation method [10, 11], the shooting method with the fourth-order Runge-Kutta scheme [12, 13], the generalized exponential rational function method [14,15,16,17,18], the modified exponential function method [19], the modified auxiliary expansion method [20], the homotopy perturbation Sumudu transform method [21], the homotopy perturbation transform method [22, 23], and the fractional homotopy analysis transform method [24]. The core of this paper is to investigate the Gilson-Pickering equation using the (1/G′)-expansion method and the generalized exponential rational function method (GERF)
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
