On the modelling of short and intermediate water waves

The propagation of water waves of finite depth and flat bottom is studied in the case when the depth is not small in comparison to the wavelength. This propagation regime is complementary to the long-wave regime described by the famous KdV equation. The Hamiltonian approach is employed in the derivation of a model equation in evolutionary form, which is both nonlinear and nonlocal, and most likely not integrable. Possible implications for the numerical solutions are discussed.(c) 2023 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Automated summary

This study investigates the propagation of water waves of finite depth and flat bottom when the depth is not small compared to the wavelength. It complements the well-known KdV equation that describes the long-wave regime. The derivation of a nonlinear and nonlocal model equation in evolutionary form using the Hamiltonian approach is discussed, and its potential implications for numerical solutions are considered.