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

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