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Abstract: This is a study of two-dimensional steady periodic travelling waves on thesurface of an infinitely deep irrotational ocean, when the top streamline is incontact with a membrane which has a nonlinear response to stretching andbending, and the pressure in the air above is constant. It is not supposed thatthe waves have small amplitude. The problem of existence of such waves isaddressed using methods from the calculus of variations. The analysis involvesthe Hilbert transform and a Riemann-Hilbert formulation.



Author: Pietro Baldi, John F. Toland

Source: https://arxiv.org/



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