Random behaviour of nonlinear waves in a closed basin

This paper concerns the Hamiltonian formulation of non-linear waves in a closed basin. Using the spectral representation of the functional Hamiltonian, we transform our problem in continuous mechanics into a problem in classical mechanics. Truncating the new Hamiltonian at the first order in the slope of the surface elevation and considering only two degrees of freedom, we study the statistical behaviour of this system. We find that under a critical energy the motion in phase space appears to be ordered, whereas above the critical value we have a random behaviour. © 1979 Società Italiana di Fisica.