Symmetric waves are traveling waves
Analysis of PDEs
2009-03-04 v1
Abstract
We show that horizontally symmetric water waves are traveling waves. The result is valid for the Euler equations, and is based on a general principle that applies to a large class of nonlinear partial differential equations, including some of the most famous model equations for water waves. A detailed analysis is given for weak solutions of the Camassa-Holm equation. In addition, we establish the existence of nonsymmetric linear rotational waves for the Euler equations.
Keywords
Cite
@article{arxiv.0903.0546,
title = {Symmetric waves are traveling waves},
author = {Mats Ehrnström and Helge Holden and Xavier Raynaud},
journal= {arXiv preprint arXiv:0903.0546},
year = {2009}
}