A comparative study of bi-directional Whitham systems
Abstract
In 1967, Whitham proposed a simplified surface water-wave model which combined the full linear dispersion relation of the full Euler equations with a weakly linear approximation. The equation he postulated which is now called the Whitham equation has recently been extended to a system of equations allowing for bi-directional propagation of surface waves. A number of different two-way systems have been put forward, and even though they are similar from a modeling point of view, these systems have very different mathematical properties. In the current work, we review some of the existing fully dispersive systems. We use state-of-the-art numerical tools to try to understand existence and stability of solutions to the initial-value problem associated to these systems. We also put forward a new system which is Hamiltonian and semi-linear. The new system is shown to perform well both with regard to approximating the full Euler system, and with regard to well posedness properties.
Cite
@article{arxiv.1902.07317,
title = {A comparative study of bi-directional Whitham systems},
author = {Evgueni Dinvay and Denys Dutykh and Henrik Kalisch},
journal= {arXiv preprint arXiv:1902.07317},
year = {2020}
}
Comments
22 pages, 11 figures, 2 tables, 31 references. Other author's papers can be downloaded at http://www.denys-dutykh.com/