Non-permanent form solutions in the Hamiltonian formulation of surface water waves
Chaotic Dynamics
2007-05-23 v1 Exactly Solvable and Integrable Systems
Abstract
Using the KAM method, we exhibit some solutions of a finite-dimensional approximation of the Zakharov Hamiltonian formulation of gravity water waves, which are spatially periodic, quasi-periodic in time, and not permanent form travelling waves. For this Hamiltonian, which is the total energy of the waves, the canonical variables are some complex quantities an and a*n, which are linear combinations of the Fourier components of the free surface elevation and the velocity potential evaluated at the surface. We expose the method for the case of a system with a finite number of degrees of freedom, the Zufiria model, with only 3 modes interacting.
Keywords
Cite
@article{arxiv.nlin/0609053,
title = {Non-permanent form solutions in the Hamiltonian formulation of surface water waves},
author = {Tounsia Benzekri and Ricardo Lima and Michel Vittot},
journal= {arXiv preprint arXiv:nlin/0609053},
year = {2007}
}