Steady periodic water waves under nonlinear elastic membranes

P Baldi, John F Toland

Research output: Contribution to journalArticlepeer-review

15 Citations (SciVal)


This is a study of two-dimensional steady periodic travelling waves on the surface of an infinitely deep irrotational ocean, when the top streamline is in contact with a membrane which has a nonlinear response to stretching and bending, and the pressure in the air above is constant. It is not supposed that the waves have small amplitude. The problem of existence of such waves is addressed using methods from the calculus of variations. The analysis involves the Hilbert transform and a Riemann-Hilbert formulation.
Original languageEnglish
Pages (from-to)67-112
Number of pages46
JournalJournal Fur Die Reine Und Angewandte Mathematik
Publication statusPublished - Mar 2011


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