Hamiltonian models for the propagation of long gravity waves, higher-order KdV-type equations and integrability
Exactly Solvable and Integrable Systems
2024-09-06 v1
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.
Cite
@article{arxiv.2409.03091,
title = {Hamiltonian models for the propagation of long gravity waves, higher-order KdV-type equations and integrability},
author = {Rossen I. Ivanov},
journal= {arXiv preprint arXiv:2409.03091},
year = {2024}
}
Comments
16 pages, 1 figure, book chapter