Fractional-stochastic shallow water equations and its analytical solutions

Abstract

In this paper, the stochastic shallow water wave equation with M-Truncated derivative is taken into account. New rational, trigonometric and hyperbolic solutions are produced using the He’s semi-inverse method and modified extended tanh-function method. The solutions found can be used to simulate a wide range of fascinating physical phenomena since the shallow water equation has numerous applications including weather simulations, tsunami prediction, tidal waves, and river irrigation flows. Also, we generalize some previous results. To show how M-Truncated Derivative and white noise affect the analytical solutions of the stochastic shallow water wave equation with M-Truncated derivative, we create different two dimension and three dimension graphs.

Keywords

• Exact solutions
• M-truncated derivative
• Multiplicative noise
• Modified extended tanh-function method