Variational derivation of the Camassa-Holm shallow water equation

TL;DR

This paper derives the Camassa-Holm shallow water equation using a variational approach within the Lagrangian formalism, providing a physical basis for this approximate water wave model.

Contribution

It introduces a variational derivation of the Camassa-Holm equation for shallow water waves from physical assumptions.

Findings

Derivation of the Camassa-Holm equation from physical hypotheses

Application of variational methods in Lagrangian formalism to water waves

Provides a physical interpretation of the Camassa-Holm model

Abstract

We describe the physical hypothesis in which an approximate model of water waves is obtained. For an irrotational unidirectional shallow water flow, we derive the Camassa-Holm equation by a variational approach in the Lagrangian formalism.