Enhanced computational methods for nonlinear Hamiltonian wave dynamics

It is noted that the nonlinear Hamiltonian dynamical equations describing surface waves are of convolution form in a version derived by Krasitskii. By virtue of the convolution theorem for Fourier transforms, the dynamical equations are thus amenable to numerical calculations using FFT techniques. This, as is well known, renders the calculations much faster than direct numerical integration, of order N logN steps versus N² per convolution integral for N discrete wavenumbers. An illustrative calculation for pure gravity waves in deep water is presented and discussed.