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

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.

arXiv comment13 pages, 3 tables

References in corpus (6)

• Water waves generated by a moving bottom
• Hamiltonian formulation of the extended Green-Naghdi equations
• Dispersive shallow water wave modelling. Part I: Model derivation on a globally flat space
• Enhanced group classification of nonlinear diffusion-reaction equations with gradient-dependent diffusion
• Hamiltonian structure for two-dimensional extended Green-Naghdi equations
• Symmetries, conservation laws, invariant solutions and difference schemes of the one-dimensional Green-Naghdi equations