AUTHOR=Liu Yue , Zhang Yanni , Pang Jing TITLE=Approximate solutions to shallow water wave equations by the homotopy perturbation method coupled with Mohand transform JOURNAL=Frontiers in Physics VOLUME=10 YEAR=2023 URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2022.1118898 DOI=10.3389/fphy.2022.1118898 ISSN=2296-424X ABSTRACT=

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.