Pınar, Zehra2023-05-062023-05-0620212345-3982https://doi.org/10.22034/cmde.2020.41145.1785https://hdl.handle.net/20.500.11776/11967The simplified phenomenological model of long-crested shallow-water wave propagations are considered without/with the Coriolis effect. Symmetry analysis is taken into consideration to obtain exact solutions. Both classical wave transformation and transformations are obtained with symmetries and solvable equations are kept thanks to these transformations. Additionally, the exact solutions are obtained via various methods which are ansatz based methods. The obtained results have a major role in the literature so that the considered equation is seen in a large scale of applications in the area of geophysical. © 2021 Authors. All rights reserved.en10.22034/cmde.2020.41145.1785info:eu-repo/semantics/closedAccessExact solutionsGroup transformationsRotational Green-Naghdi equationsArticle94122312322-s2.0-85144181197N/A