Role of Gilson-Pickering equation for the different types of soliton solutions: a nonlinear analysis

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.