The Soliton Solutions of the Stochastic Shallow Water Wave Equations in the Sense of Beta-Derivative
Wael W. Mohammed, Farah M. Al‐Askar, Clemente Cesarano, Elkhateeb S. Aly
Abstract
The stochastic shallow water wave equation (SSWWE) in the sense of the beta-derivative is considered in this study. The solutions of the SSWWE are obtained using the F-expansion technique with the Riccati equation and He’s semi-inverse method. Since the shallow water equation has many uses in ocean engineering, including river irrigation flows, tidal waves, tsunami prediction, and weather simulations, the solutions discovered can be utilized to represent a wide variety of exciting physical events. We create many 2D and 3D graphs to demonstrate how the beta-derivative and Brownian motion affect the analytical solutions of the SSWWE.
Topics & Concepts
Derivative (finance)Waves and shallow waterSolitonMathematical analysisShallow water equationsSense (electronics)MathematicsApplied mathematicsPhysicsGeologyOceanographyQuantum mechanicsEngineeringNonlinear systemElectrical engineeringFinancial economicsEconomicsNonlinear Waves and SolitonsFractional Differential Equations SolutionsOcean Waves and Remote Sensing