Fractal soliton solutions for the fractal-fractional shallow water wave equation arising in ocean engineering

Abstract

The generalized shallow water wave equation is an important mathematical model that is used to elaborate ocean engineering, weather simulations, tsunami prediction and tidal currents. In this work, the generalized (3 + 1)-dimensional fractal-fractional shallow water wave equation (FFSWWE) is investigated where fractal-fractional derivative is taken in the conformable derivative sense. Some new fractal soliton solutions of FFSWWE are successfully derived by the fractal-fractional variational wave method (FFVWM), which is a new mathematical technology. This new method has the advantages of being simple, efficient, and direct. The 3D graphics that describe these new fractal soliton solutions that were obtained are tremendously important for improving our understanding of physical oceanography.