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Non-permanent form solutions in the Hamiltonian formulation of surface water waves

Tounsia Benzekri·Ricardo Lima·Michel Vittot
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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.

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Tounsia Benzekri, Ricardo Lima, Michel Vittot. 2006-09-21. Non-permanent form solutions in the Hamiltonian formulation of surface water waves. https://arxiv.org/abs/nlin/0609053

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