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

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 f...

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Bibliographic Details
Published in:Mathematics (Basel) 2022-11, Vol.10 (22), p.4171
Main Authors: Naz, Shumaila, Rani, Attia, Shakeel, Muhammad, Shah, Nehad Ali, Chung, Jae Dong
Format: Article
Language:English
Subjects:
Analysis
conformable fractional derivative
fractional Riemann wave equation
improved (G’/G)-expansion method
nonlinear partial differential equations
Riemann integral
solitary wave solutions
Solitons
Wave equation
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Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math10224171