A generalized parametrically driven damped nonlinear Schrödinger equation is used to describe, close to the resonance, the dynamics of weakly dissipative systems, like a harmonically coupled pendula chain or an easy-plane magnetic wire. The combined effects of parametric forcing, spatial coupling, and dissipation allows for the existence of stable non-trivial uniform states as well as homogeneous pattern states. The latter can be regular or chaotic. A new family of localized states that connect asymptotically a non-trivial uniform state with a spatio-temporal chaotic pattern is numerically found. We discuss the parameter range, where these localized structures exist. This article is dedicated to Prof. Helmut R. Brand on the occasion of his 60th birthday.
Bibliographical noteFunding Information:
D.U. and D.L. would like to thank M.G. Clerc (Univ. of Chile) for valuable discussions on the generalization of the PDDNLS equation. D. L. acknowledges partial financial support from FONDECYT 1120764, Millennium Scientific Initiative, P10−061−F, Basal Program Center for Development of Nanoscience and Nanotechnology (CEDENNA), UTA-project 8750−12. D. U. acknowledges the PhD program fellowship through the Performance Agreement Project’s UTA/Mineduc.