Author ORCID Identifier
https://orcid.org/0000-0003-1008-8272
Document Type
Book Chapter
Disciplines
Applied mathematics, Fluids and plasma physics
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.
DOI
10.1007/978-3-031-63512-0_5
Recommended Citation
Ivanov, Rossen, "Hamiltonian models for the propagation of long gravity waves, higher-order KdV-type equations and integrability" (2024). Book chapter/book. 7.
https://arrow.tudublin.ie/scschmatbk/7
Funder
SFI
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 4.0 International License.
Included in
Fluid Dynamics Commons, Non-linear Dynamics Commons, Partial Differential Equations Commons
Publication Details
R.I. Ivanov, Hamiltonian models for the propagation of long gravity waves, higher-order KdV-type equations and integrability. In: Henry, D. (eds) Nonlinear Dispersive Waves. Advances in Mathematical Fluid Mechanics. Birkhäuser, Cham, 2024;
doi:10.1007/978-3-031-63512-0_5