title: Localized excitations and their thresholds
abstract: 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.
authors.affiliation: Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 and Department of Physics and Astronomy, Rutgers University 136 Frelinghuysen Road, Piscataway, New Jersey 08854-8019, USA.
authors.initials: PG
authors.lastname: Kevrekidis
authors.initials: KO
authors.lastname: Rasmussen
authors.initials: AR
authors.lastname: Bishop