New Exact Solutions of the Conformable Space-Time Sharma–Tasso–Olver Equation Using Two Reliable Methods

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.

Keywords

• nonlinear conformable space-time Sharma–Tasso–Olver equation
• conformable derivative
• G ′ G )-expansion method%22%2C%22default_operator%22%3A%22AND%22%7D%7D%7D"> novel (<named-content content-type="inline-formula"> <mml:math id="mm500" display="block"> <mml:semantics> <mml:mrow> <mml:mfrac> <mml:msup> <mml:mi>G</mml:mi> <mml:mo>′</mml:mo> </mml:msup> <mml:mi>G</mml:mi> </mml:mfrac> </mml:mrow> </mml:semantics> </mml:math> </named-content>)-expansion method
• generalized Kudryashov method
• singular kink-type solution
• singular multiple-soliton solution