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

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.

The exact solutions for the fractional Riemann wave equation in quantum mechanics and optics

“…Due to the significance of RWE, numerous authors have obtained the solution of the Riemann wave equation by employing various methods, including generalized ¢ G G ( )-expansion method [16], new extended direct algebraic method [17], generalized Kudryashov method [18], extended tanh function technique [19], Wronskian method [20], generalized exponential rational function approach [21], and modified q -u exp( ( ))-function method [22]. While, the solutions of FRWE with conformable fractional derivative have acquired by improved ¢ G G ( )-expansion method [23]. Moreover, the stochastic Riemann wave equation was considered by Mohammed et al [24] and they found its solutions by using the extended tanh-coth method and the mapping method.…”