Nonlinear Sciences – Chaotic Dynamics
Scientific paper
2004-07-26
Journal of Physics A 38 (2005) 5381
Nonlinear Sciences
Chaotic Dynamics
Scientific paper
10.1088/0305-4470/38/24/001
In this paper, we present a model describing the time evolution of two dimensional surface waves in gravity and infinite depth. The model of six interacting modes derives from the normal form of the system describing the dynamics of surface waves and is governed by a Hamiltonian system of equations of cubic order in the amplitudes of the waves. We derive a Hamiltonian system with two degrees of freedom from this Hamiltonian using conserved quantities. The interactions are those of two coupled Benjamin-Feir resonances. The temporal evolution of the amplitude of the different modes is described according to the parameters of the system. In particular, we study the energy exchange produced by the modulations of the amplitudes of the modes. The evolution of the modes reveals a chaotic dynamics.
Benzekri Tounsia
Chandre Cristel
Lima Ricardo
Vittot Michel
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