Ground-state properties of small-size nonlinear dynamical lattices

Year: 2007

Authors: Buonsante P., Kevrekidis P.G., Penna V, Vezzani A.

Autors Affiliation: Dipartimento di Fisica, Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy; Department of Mathematics and Statistics, University of Massachusetts, Amherst Massachusetts 01003-4515, USA; Dipartimento di Fisica and CNR-INFM, Università degli Studi di Parma, Parco Area delle Scienze 7/a, I-43100 Parma, Italy

Abstract: We investigate the ground state of a system of interacting particles in small nonlinear lattices with M >= 3 sites, using as a prototypical example the discrete nonlinear Schrodinger equation that has been recently used extensively in the contexts of nonlinear optics of waveguide arrays and Bose-Einstein condensates in optical lattices. We find that, in the presence of attractive interactions, the dynamical scenario relevant to the ground-state and the lowest-energy modes of such few-site nonlinear lattices reveals a variety of nontrivial features that are absent in the large/infinite lattice limits: the single-pulse solution and the uniform solution are found to coexist in a finite range of the lattice intersite coupling where, depending on the latter, one of them represents the ground state; in addition, the single-pulse mode does not even exist beyond a critical parametric threshold. Finally, the onset of the ground-state (modulational) instability appears to be intimately connected with a nonstandard (\”double transcritical\”) type of bifurcation that, to the best of our knowledge, has not been reported previously in other physical systems.

Journal/Review: PHYSICAL REVIEW E

Volume: 75      Pages from: 016212-1  to: 016212-8

KeyWords: discrete nonlinear schroedinger equation; attractive interactions;
DOI: 10.1103/PhysRevE.75.016212

ImpactFactor: 2.483
Citations: 10
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