Novel Soliton Solutions of the Fractional Riemann Wave Equation via a Mathematical Method

Shumaila Naz, Attia Rani, Muhammad Shakeel, Nehad Ali Shah and Jae Dong Chung ()
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Shumaila Naz: Department of Mathematics, University of Wah, Wah Cantt., Rawalpindi 47040, Pakistan
Attia Rani: Department of Mathematics, University of Wah, Wah Cantt., Rawalpindi 47040, Pakistan
Muhammad Shakeel: Department of Mathematics, University of Wah, Wah Cantt., Rawalpindi 47040, Pakistan
Nehad Ali Shah: Department of Mechanical Engineering, Sejong University, Seoul 05006, Republic of Korea
Jae Dong Chung: Department of Mechanical Engineering, Sejong University, Seoul 05006, Republic of Korea

Mathematics, 2022, vol. 10, issue 22, 1-21

Abstract: The Riemann wave equation is an intriguing nonlinear equation in the areas of tsunamis and tidal waves in oceans, electromagnetic waves in transmission lines, magnetic and ionic sound radiations in plasmas, static and uniform media, etc. In this innovative research, the analytical solutions of the fractional Riemann wave equation with a conformable derivative were retrieved as a special case, and broad-spectrum solutions with unknown parameters were established with the improved (G’/G)-expansion method. For the various values of these unknown parameters, the renowned periodic, singular, and anti-singular kink-shaped solitons were retrieved. Using the Maple software, we investigated the solutions by drawing the 3D, 2D, and contour plots created to analyze the dynamic behavior of the waves. The discovered solutions might be crucial in the disciplines of science and ocean engineering.

Keywords: conformable fractional derivative; nonlinear partial differential equations; solitary wave solutions; fractional Riemann wave equation; improved (G’/G)-expansion method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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