The symmetry analysis and analytical studies of the rotational GreenNaghdi (R-GN) equation

Document Type : Research Paper


Tekirdağ Namık Kemal University, Faculty of Arts and Science, Department of Mathematics, 59030 Merkez-Tekirdağ, Turkey.


The simplified phenomenological model of long-crested shallow-water wave propagations is 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.