TITLE
	A Hamiltonian system for interacting Benjamin-Feir resonances
	
AUTHOR
	Tounsia BENZEKRI & Cristel CHANDRE & Ricardo LIMA & Michel VITTOT

ABSTRACT 
	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.