ИСТИНА

The system of equations of two-dimensional shallow water over a rough bottom is considered. An overdetermined system of equations for finding the allowed symmetries is obtained. Compatibility of the obtained overdetermined system of equations is investigated. A general view of the system solution is obtained. The kernel of the symmetry operators is found. Cases in which kernel extensions of symmetry operators exists are presented. The corresponding classifying equations are given. Based on the results of the group classification, it is concluded that the system of equations of two-dimensional shallow water over a rough bottom cannot be linearized by point change of variables in contrast to the system of equations of one-dimensional shallow water in cases of horizontal and inclined bottom profiles.