https://doi.org/10.1140/epjp/s13360-020-00646-8
Regular Article
Role of Gilson–Pickering equation for the different types of soliton solutions: a nonlinear analysis
1
Department of Actuary, Faculty of Science, Firat University, 23100, Elazig, Turkey
2
Department of Computer Engineering, Faculty of Engineering, Ardahan University, 75000, Ardahan, Turkey
3
Faculty of Natural and Agricultural Sciences, Institute of Ground Water Studies, University of the Free State, Bloemfontein, South Africa
4
Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology, Jamshoro, Pakistan
5
Department of Mathematics, Istanbul Commerce University, Uskudar, Istanbul, Turkey
c
kashif.abro@faculty.muet.edu.pk
Received:
2
June
2020
Accepted:
28
July
2020
Published online:
16
August
2020
In this article, the soliton solutions of the Gilson–Pickering equation have been constructed using the sinh-Gordon function method (ShGFM) and (G′/G, 1/G)-expansion method, which are applied to obtain exact solutions of nonlinear partial differential equations. A solution function different from the solution function in the classical (G′/G, 1/G)-expansion method has been considered which are based on complex trigonometric, hyperbolic, and rational solutions. By invoking ShGFM and (G′/G, 1/G)-expansion methods, different traveling wave solutions have been investigated. For the sake of avoiding the complex calculations, the ready package program has been tackled. The comparative analysis of sinh-Gordon function and (G′/G, 1/G)-expansion methods has shown several differences and similarities. A comparative analysis of ShGFM and (G′/G, 1/G)-expansion methods assures that the (G′/G, 1/G)-expansion method has been found to be more intensive, powerful, reliable and effective method for the Gilson–Pickering equation. The graphical illustrations of two-, three-dimensional, and contour graphs have been depicted as well.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020
