Symmetric waves are traveling waves

2009/03/03 by Mats Ehrnström, Helge Holden, Ehrnström, Mats +3
Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #35Q35 #76B15 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Waves and Solitons #Ocean Waves and Remote Sensing

paper · pdf · doi:10.48550/arxiv.0903.0546

openalex publication_date 2009/03/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/02

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.

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