A connection between the shallow-water equations and the Euler-Poincar\'e equations
Mathematical Physics
2014-04-22 v1 math.MP
Abstract
The Euler-Poincar\'e differential (EPDiff) equations and the shallow water (SW) equations share similar wave characteristics. Using the Hamiltonian structure of the SW equations with flat bottom topography, we establish a connection between the EPDiff equations and the SW equations in one and multi-dimensions. Additionally, we show that the EPDiff equations can be recast in a curl formulation.
Keywords
Cite
@article{arxiv.1404.4900,
title = {A connection between the shallow-water equations and the Euler-Poincar\'e equations},
author = {Roberto Camassa and Long Lee},
journal= {arXiv preprint arXiv:1404.4900},
year = {2014}
}