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On the symmetry of spatially periodic two-dimensional water waves

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  • 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 flat bed is symmetric, while the acceleration at the flat bed is anti-symmetric with respect to a common axis of symmetry, necessarily constitutes a traveling wave. The proof makes use complex variables and structural properties of the governing equations for nonlinear water waves.
    Mathematics Subject Classification: Primary: 35Q35; Secondary: 35B50.


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