Water Waves and Integrability

TL;DR

This paper reviews how integrable equations derived from Euler's equations model shallow water wave motion, highlighting recent advances in the application of integrable systems in fluid dynamics.

Contribution

It provides a review of recent results connecting shallow water wave modeling to integrable equations derived from Euler's equations.

Findings

Integrable equations can effectively model shallow water wave dynamics.

Asymptotic expansions of Euler's equations reveal integrable structures.

Recent research demonstrates the practical application of integrable models in fluid mechanics.

Abstract

The Euler's equations describe the motion of inviscid fluid. In the case of shallow water, when a perturbative asymtotic expansion of the Euler's equations is taken (to a certain order of smallness of the scale parameters), relations to certain integrable equations emerge. Some recent results concerning the use of integrable equation in modeling the motion of shallow water waves are reviewed in this contribution.