Statics and dynamics of an inhomogeneously nonlinear lattice

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Debra L. Machacek,¹ Elizabeth A. Foreman,¹ Q. E. Hoq,² P. G. Kevrekidis,¹ A. Saxena,³ D. J. Frantzeskakis,⁴ and A. R. Bishop³
¹Department of Mathematics, University of Massachusetts, Amherst, Massachusetts, 01003-4515, USA
²Department of Mathematics, Western New England College, Springfield, Massachusetts 011119, USA
³Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
⁴Department of Physics, University of Athens, Panepistimiopolis, Zografos, Athens 15784, Greece

Received 17 February 2006; revised 29 June 2006; published 5 September 2006

Weintroduce an inhomogeneously nonlinear Schrödinger lattice, featuring a defocusing segment,a focusing segment and a transitional interface between the two.We illustrate that such inhomogeneous settings present vastly different dynamicalbehavior in the vicinity of the interface than the oneexpected in their homogeneous counterparts. We analyze the relevant stationarystates, as well as their stability, by means of perturbationtheory and linear stability analysis. We find good agreement withthe numerical findings in the vicinity of the anticontinuum limit.For larger values of the coupling, we follow the relevantbranches numerically and show that they terminate at values ofthe coupling strength which are larger for more extended solutions.The dynamical development of relevant instabilities is also monitored inthe case of unstable solutions.

URL:	http://link.aps.org/doi/10.1103/PhysRevE.74.036602
DOI:	10.1103/PhysRevE.74.036602
PACS:	05.45.Yv; 03.75.Lm; 63.20.Pw 05.45.Yv Solitons 03.75.Lm Josephson effect, tunneling, Bose-Einstein condensates in periodic potentials, solitons, vortices, and topological excitations 63.20.Pw Localized modes in crystal lattices YEAR: 2006
KEYWORDS:	lattice theory, nonlinear dynamical systems, lattice dynamics, perturbation theory

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