Symmetries and Conservation Laws of the Equations of Two-Dimensional Shallow Water Over Uneven Bottom

Abstract

A system of equations of two-dimensional shallow water over uneven bottom is considered. Overdetermined systems of equations for determining the symmetries and the conservation laws are obtained. The compatibilities of this overdetermined systems of equations are investigated. The general forms of the solutions of the overdetermined systems are found. The kernels of the symmetry operators and conservation laws are found. Cases of kernels extensions of symmetry operators and conservation laws are presented. 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 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.