Hamiltonian models for the propagation of long gravity waves, higher-order KdV-type equations and integrability
arXiv:2409.03091 · doi:10.1007/978-3-031-63512-0_5
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.
arXiv comment16 pages, 1 figure, book chapter
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