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Abstract: We show that horizontally symmetric water waves are traveling waves. Theresult is valid for the Euler equations, and is based on a general principlethat applies to a large class of nonlinear partial differential equations,including some of the most famous model equations for water waves. A detailedanalysis is given for weak solutions of the Camassa-Holm equation. In addition,we establish the existence of nonsymmetric linear rotational waves for theEuler equations.



Author: Mats Ehrnström, Helge Holden, Xavier Raynaud

Source: https://arxiv.org/



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