Group classification of the two-dimensional Green-Naghdi equations with a time dependent bottom topography

TL;DR

This paper performs a group classification of the two-dimensional Green-Naghdi equations with time-dependent bottom topography, using algebraic methods to analyze symmetries related to the bottom profile.

Contribution

It provides a systematic classification of symmetries for these equations considering time-dependent bottom topography, which was not previously addressed.

Findings

Classification of symmetries based on bottom topography functions

Identification of invariant solutions under certain symmetry groups

Extension of symmetry analysis to time-dependent bottom profiles

Abstract

The two-dimensional Green-Naghdi equations with uneven bottom topography are studied in this paper. The function defining the bottom topography can be dependent on time. Group classification of these equations with respect to the function describing the topography of the bottom is performed in the paper. The algebraic approach used for the analysis of the classifying equations.