✦ LIBER ✦

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

✍ Scribed by Tounsia Benzekri; Ricardo Lima; Michel Vittot

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 160 KB
Volume: 19
Category: Article
ISSN: 0997-7546
DOI: 10.1016/s0997-7546(00)00121-7

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✦ Synopsis

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 a n and a * n (n ∈ Z), 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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