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Doubly periodic travelling gravity-capillary and hydroelastic surface waves

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HYD2 - Dispersive hydrodynamics: mathematics, simulation and experiments, with applications in nonlinear waves

A doubly periodic travelling surface wave is periodic in two independent horizontal directions. Small-amplitude doubly periodic gravity-capillary water waves with arbitrary periodic domains have been constructed by two different methods, namely using spatial dynamics and a Lyapunov centre theorem (notably by Groves and Haragus) and using Dirichlet-Neumann formalism and Lyapunov-Schmidt reduction (notably by Craig and Nicholls). In this talk I review these methods and show how both can be refined. I will discuss how the refined methods can be used in existence theories for small-amplitude doubly periodic hydroelastic waves.  

This talk is part of the Isaac Newton Institute Seminar Series series.

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