Symmetric waves are traveling waves

Details Symmetric waves are traveling waves Symmetric waves are traveling waves

2009-03-03

arxiv.org/abs/0903.0546v1

Mathematics

Analysis of PDEs

Scientific paper

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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