On the modelling of short and intermediate water waves

Abstract

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.

arXiv comment8 pages, 1 figure

References in corpus (5)

• Effect of non-zero constant vorticity on the nonlinear resonances of capillary water waves
• On the intermediate long wave propagation for internal waves in the presence of currents
• Nonlinear resonances of water waves
• On the time-evolution of resonant triads in rotational capillary-gravity water waves
• Benjamin-Ono model of an internal wave under a flat surface

Cited by in corpus (2)

• The Lagrangian formulation for wave motion with a shear current and surface tension
• Hamiltonian models for the propagation of long gravity waves, higher-order KdV-type equations and integrability