Abstract
The major purpose of this article is to seek for exact traveling wave solutions of the nonlinear space-time Sharma–Tasso–Olver equation in the sense of conformable derivatives. The novel ( G ′ G ) -expansion method and the generalized Kudryashov method, which are analytical, powerful, and reliable methods, are used to solve the equation via a fractional complex transformation. The exact solutions of the equation, obtained using the novel ( G ′ G ) -expansion method, can be classified in terms of hyperbolic, trigonometric, and rational function solutions. Applying the generalized Kudryashov method to the equation, we obtain explicit exact solutions expressed as fractional solutions of the exponential functions. The exact solutions obtained using the two methods represent some physical behaviors such as a singularly periodic traveling wave solution and a singular multiple-soliton solution. Some selected solutions of the equation are graphically portrayed including 3-D, 2-D, and contour plots. As a result, some innovative exact solutions of the equation are produced via the methods, and they are not the same as the ones obtained using other techniques utilized previously.
Highlights
Many nonlinear physical phenomena, such as those found in solid-state physics, plasma physics, optical fibers, shallow water waves, fluid dynamics, and biology, have been modeled by nonlinear partial differential equations (NPDEs) of integer- or fractional-order
We have constructed explicit exact solutions of the (1+1)-dimensional conformable space-time Sharma–Tasso–Olver equation expressed in Equation (15) using the novel GG -expansion method and the generalized Kudryashov method with the help of the fractional complex transform and the symbolic computation package Maple 17
The novel GG -expansion method gives hyperbolic, trigonometric, and rational function solutions for the equation; the generalized Kudryashov method provides fractional solutions of the exponential functions, which are possibly converted into hyperbolic function solutions
Summary
Many nonlinear physical phenomena, such as those found in solid-state physics, plasma physics, optical fibers, shallow water waves, fluid dynamics, and biology, have been modeled by nonlinear partial differential equations (NPDEs) of integer- or fractional-order. Hafez et al [21] employed the novel ( GG )-expansion method to obtain exact traveling wave solutions of the Klein–Gordon equation. Employed the novel ( GG )-expansion method to construct some new traveling wave solutions of the (1 + 1)-dimensional cubic nonlinear Schrödinger’s equation. Through applying the generalized Kudryashov and the novel GG -expansion methods to the nonlinear complex fractional generalized-Zakharov system, Lu et al [36] obtained its new forms of analytical and solitary traveling wave solutions. The objective of this paper is to apply the novel ( GG )-expansion method and the generalized Kudryashov method to analytically solve the conformable space-time Sharma–Tasso–Olver (STO) equation in the sense of conformable derivatives to obtain a considerable number of exact solutions.
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