Shallow-water equations with complete Coriolis force: Group Properties and Similarity Solutions

TL;DR

This paper uses Lie symmetry analysis to classify the shallow-water equations with the full Coriolis force, deriving new similarity solutions and advancing understanding of their symmetry properties.

Contribution

It provides a comprehensive classification of symmetries and derives new similarity solutions for the shallow-water equations with complete Coriolis force.

Findings

Classification of Lie point symmetries for the equations

Determination of one-dimensional optimal systems

Derivation of new similarity solutions

Abstract

The group properties of the shallow-water equations with the complete Coriolis force is the subject of this study. In particular we apply the Lie theory to classify the system of three nonlinear partial differential equations according to the admitted Lie point symmetries. For each case of the classification problem the one-dimensional optimal system is determined. The results are applied for the derivation of new similarity solutions.