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

TL;DR

This paper classifies Lie symmetries of two-dimensional shallow water equations with variable bottom topography, identifying symmetries and equivalences to facilitate analytical solutions and understanding of the equations.

Contribution

It provides a comprehensive group classification of the equations using optimized methods and algebraic techniques, revealing new symmetry relations.

Findings

Identified the equivalence group of the class.

Constructed additional point equivalences between symmetry cases.

Classified Lie symmetry extensions for the equations.

Abstract

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.