Symmetric irrotational water waves are traveling waves

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Abstract

We show that a spatially periodic solution to the irrotational two-dimensional gravity water wave problem, with the property that the horizontal velocity component at the surface, as well as the wave profile is symmetric, necessarily defines a traveling wave. The proof makes use of maximum principles for harmonic functions and structural properties of the governing equations for nonlinear water waves.

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APA

Kogelbauer, F. (2015). Symmetric irrotational water waves are traveling waves. Journal of Differential Equations, 259(10), 5271–5275. https://doi.org/10.1016/j.jde.2015.06.025

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