Group Classification of the System of Equations of Two-Dimensional Shallow Water over Uneven Bottom

Abstract

A system of equations of two-dimensional shallow water over an uneven bottom is considered. An overdetermined system of equations for finding the corresponding symmetries is obtained. The compatibility of this overdetermined system of equations is investigated. A general form of the solution of the overdetermined system is found. The kernel of the symmetry operators is found. The cases of kernel extensions of symmetry operators are presented. The results of group classification indicate that the system of equations of two-dimensional shallow water over an uneven bottom cannot be linearized by point transformation, in contrast to the system of equations of one-dimensional shallow water in the cases of horizontal and inclined bottom profiles.