Hamiltonian models for the propagation of long gravity waves, higher-order KdV-type equations and integrability

Abstract

A single incompressible, inviscid, irrotational fluid medium bounded above by a free surface is considered. The Hamiltonian of the system is expressed in terms of the so-called Dirichlet-Neumann operators. The equations for the surface waves are presented in Hamiltonian form. Specific scaling of the variables is selected which leads to a KdV approximation with higher order nonlinearities and dispersion (higher-order KdV-type equation, or HKdV). The HKdV is related to the known integrable PDEs with an explicit nonlinear and nonlocal transformation.

16 pages, 1 figure, book chapter

References in corpus (5)

• Water Waves and Integrability
• Hamiltonian description of internal ocean waves with Coriolis force
• Nonlinear two-dimensional water waves with arbitrary vorticity
• On the modelling of short and intermediate water waves
• The Lagrangian formulation for wave motion with a shear current and surface tension

Cited by in corpus (1)

• Higher-order integrable models for oceanic internal wave-current interactions