Localized excitations and their thresholds

We propose a numerical method for identifying localized excitations in disc rete nonlinear Schrodinger type models. This methodology, based on the appl ication of a nonlinear iterative version of the Rayleigh-Ritz variational p rinciple yields breather excitations in a very fast and efficient way in on e or higher spatial dimensions. The typical convergence properties of the m ethod are found to be super-linear, The usefulness of this technique is ill ustrated by studying the properties of the recently developed theoretical c riteria for the excitation power thresholds for nonlinear modes.