Two new standing solitary waves in shallow water
Abstract
In this paper, the closed-form analytic solutions of two new Faraday's standing solitary waves due to the parametric resonance of liquid in a vessel vibrating vertically with a constant frequency are given for the first time. Using a model based on the symmetry of wave elevation and the linearized Boussinesq equation, we gain the closed-form wave elevations of the two kinds of non-monotonically decaying standing solitary waves with smooth crest and the even or odd symmetry. All of them have never been reported, to the best of our knowledge. Besides, they can well explain some experimental phenomena. All of these are helpful to deepen and enrich our understandings about standing solitary waves and Faraday's wave.
Keywords
Cite
@article{arxiv.1302.2714,
title = {Two new standing solitary waves in shallow water},
author = {Shijun Liao},
journal= {arXiv preprint arXiv:1302.2714},
year = {2013}
}
Comments
12 pages, 4 figures, accepted by Wave Motion