Explicit Dirichlet-neumann Operator For Water Waves

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.

References in corpus (2)

• Gravity capillary standing water waves
• A three dimensional Dirichlet-to-Neumann operator for waves over topography

Cited by in corpus (1)

• Three-layer water flows: Dirichlet-Neumann operators and approximations