Effects of vorticity on the travelling waves of some shallow water two-component systems
Abstract
In the present study we consider three two-component (integrable and non-integrable) systems which describe the propagation of shallow water waves on a constant shear current. Namely, we consider the two-component Camassa-Holm equations, the Zakharov-Ito system and the Kaup--Boussinesq equations all including constant vorticity effects. We analyze both solitary and periodic-type travelling waves using the simple and geometrically intuitive phase space analysis. We get the pulse-type solitary wave solutions and the front solitary wave solutions. For the Zakharov-Ito system we underline the occurrence of the pulse and anti-pulse solutions. The front wave solutions decay algebraically in the far field. For the Kaup-Boussinesq system, interesting analytical multi-pulsed travelling wave solutions are found.
Keywords
Cite
@article{arxiv.1904.06050,
title = {Effects of vorticity on the travelling waves of some shallow water two-component systems},
author = {Denys Dutykh and Delia Ionescu-Kruse},
journal= {arXiv preprint arXiv:1904.06050},
year = {2020}
}
Comments
27 pages, 14 figures, 45 references. Other author's papers can be downloaded at http://www.denys-dutykh.com/