Explicit Dirichlet-neumann Operator For Water Waves

DOI10.1017/JFM.2022.830zbMATH Open1515.76024arXiv2209.06490MaRDI QIDQ6410714

Publication date: 14 September 2022

Abstract: An explicit expression for the Dirichlet-Neumann operator for surface water waves is presented. For non-overturning waves, but without assuming small amplitudes, the formula is first derived in two dimensions, subsequently extrapolated in higher dimensions and with a moving bottom. Although described here for water waves, this elementary approach could be adapted to many other problems having similar mathematical formulations.

Mathematics Subject Classification ID

Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Complex variables methods applied to problems in fluid mechanics (76M40)

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