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. The consistency of this overdetermined system of equations is investigated. A general form of the solution of this system is obtained. The kernel of the symmetry operators is found. Cases are presented where kernel extensions of symmetry operators exist. The corresponding classifying equations are given. The results of the group classification have indicated 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 the cases of horizontal and inclined bottom profiles.