Statics and dynamics of an inhomogeneously nonlinear lattice

We introduce 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 dynamical behavior in the vicinity of the interface than the one exp...

Full description

Saved in:
Bibliographic Details
Published in:Physical review. E, Statistical, nonlinear, and soft matter physics Statistical, nonlinear, and soft matter physics, 2006-09, Vol.74 (3 Pt 2), p.036602-036602, Article 036602
Main Authors: Machacek, Debra L, Foreman, Elizabeth A, Hoq, Q E, Kevrekidis, P G, Saxena, A, Frantzeskakis, D J, Bishop, A R
Format: Article
Language:English
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We introduce 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 dynamical behavior in the vicinity of the interface than the one expected in their homogeneous counterparts. We analyze the relevant stationary states, as well as their stability, by means of perturbation theory and linear stability analysis. We find good agreement with the numerical findings in the vicinity of the anticontinuum limit. For larger values of the coupling, we follow the relevant branches numerically and show that they terminate at values of the coupling strength which are larger for more extended solutions. The dynamical development of relevant instabilities is also monitored in the case of unstable solutions.
ISSN:1539-3755
1550-2376
DOI:10.1103/PhysRevE.74.036602