Enhanced Computational Methods for Nonlinear Hamiltonian Wave Dynamics. Part II: New Results

Abstract

It has been noted that the nonlinear Hamiltonian dynamical equations describing surface waves are of convolution form in a version derived by Krasitskii, and thus they are amenable to numerical calculations using fast Fourier transform techniques. In this paper new results regarding the nature of the solutions are presented and numerical instabilities that may develop are discussed. Additionally various ways of displaying features of the nonlinear wave evolution are explored within the context of specific examples.