Approximate solutions to shallow water wave equations by the homotopy perturbation method coupled with Mohand transform

In this paper, the Mohand transform-based homotopy perturbation method is proposed to solve two-dimensional linear and non-linear shallow water wave equations. This approach has been proved suitable for a broad variety of non-linear differential equations in science and engineering. The variation trend of the water surface elevation at different time levels and depths are given by some graphs. Moreover, the obtained solutions are compared with the existing results, which show higher efficiency and fewer computations than other approaches studied in the literature.

Automated summary

In this paper, the Mohand transform-based homotopy perturbation method is proposed for solving two-dimensional linear and non-linear shallow water wave equations. This approach has been proven to be suitable for a wide range of non-linear differential equations in both science and engineering. Graphs are provided to show the variation trend of the water surface elevation at different time levels and depths. Additionally, the obtained solutions are compared with existing results, demonstrating higher efficiency and fewer computations than other approaches studied in the literature.