dc.creator | Hennig D., Karachalios N.I. | en |
dc.date.accessioned | 2023-01-31T08:28:06Z | |
dc.date.available | 2023-01-31T08:28:06Z | |
dc.date.issued | 2022 | |
dc.identifier | 10.1016/j.na.2021.112647 | |
dc.identifier.issn | 0362546X | |
dc.identifier.uri | http://hdl.handle.net/11615/73951 | |
dc.description.abstract | Discrete Ginzburg–Landau (DGL) equations with non-local nonlinearities have been established as significant inherently discrete models in numerous physical contexts, similar to their counterparts with local nonlinear terms. We study two prototypical examples of non-local and local DGLs on the one-dimensional infinite lattice. For the non-local DGL, we identify distinct scenarios for the asymptotic behavior of the globally existing in time solutions depending on certain parametric regimes. One of these scenarios is associated with a restricted compact attractor according to J. K. Hale's definition. We also prove the closeness of the solutions of the two models in the sense of a “continuous dependence on their initial data” in the l2 metric under general conditions on the intrinsic linear gain or loss incorporated in the model. As a consequence of the closeness results, in the dissipative regime we establish the congruence of the attractors possessed by the semiflows of the non-local and of the local model respectively, for initial conditions in a suitable domain of attraction defined by the non-local system. © 2021 Elsevier Ltd | en |
dc.language.iso | en | en |
dc.source | Nonlinear Analysis, Theory, Methods and Applications | en |
dc.source.uri | https://www.scopus.com/inward/record.uri?eid=2-s2.0-85118336829&doi=10.1016%2fj.na.2021.112647&partnerID=40&md5=7ce467f1ded69254da0dbef0eca7ea82 | |
dc.subject | Control nonlinearities | en |
dc.subject | Solitons | en |
dc.subject | Attractor congruence | en |
dc.subject | Discrete ginzburg–landau equation | en |
dc.subject | Discrete models | en |
dc.subject | Discrete non-local nonlinearity | en |
dc.subject | Dissipative solitons | en |
dc.subject | Ginzburg-Landau equations | en |
dc.subject | Global attractor | en |
dc.subject | Nonlinear terms | en |
dc.subject | Nonlocal | en |
dc.subject | Restricted attractor | en |
dc.subject | Dynamical systems | en |
dc.subject | Elsevier Ltd | en |
dc.title | Dynamics of nonlocal and local discrete Ginzburg–Landau equations: Global attractors and their congruence | en |
dc.type | journalArticle | en |