Lie symmetries of two-dimensional shallow water equations with variable bottom topography

We carry out the group classification of the class of two-dimensional shallow water equations with variable bottom topography using an optimized version of the method of furcate splitting. The equivalence group of this class is found by the algebraic method. Using algebraic techniques, we construct additional point equivalences between some of the listed cases of Lie-symmetry extensions, which are inequivalent up to transformations from the equivalence group.