Explicit Dirichlet-Neumann operator for water waves

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, and subsequently extrapolated to 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.

Automated summary

This study presents an explicit expression for the Dirichlet-Neumann operator for surface water waves and demonstrates its applicability. The findings of this study are not limited to water waves and can be adapted to many other problems with similar mathematical formulations.