Localized excitations and their thresholds

We propose a numerical method for identifying localized excitations in discrete nonlinear Schrodinger type models. This methodology, based on the application of a nonlinear iterative version of the Rayleigh-Ritz variational principle yields breather excitations in a very fast and efficient way in one or higher spatial dimensions. The typical convergence properties of the method are found to be super-linear, The usefulness of this technique is illustrated by studying the properties of the recently developed theoretical criteria for the excitation power thresholds for nonlinear modes.