title: Statics and dynamics of an inhomogeneously nonlinear lattice.
abstract: 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.
authors.affiliation: Department of Mathematics, University of Massachusetts, Amherst, Massachusetts 01003-4515, USA.
authors.forename: Debra L
authors.initials: DL
authors.lastname: Machacek
authors.forename: Elizabeth A
authors.initials: EA
authors.lastname: Foreman
authors.forename: Q E
authors.initials: QE
authors.lastname: Hoq
authors.forename: P G
authors.initials: PG
authors.lastname: Kevrekidis
authors.forename: A
authors.initials: A
authors.lastname: Saxena
authors.forename: D J
authors.initials: DJ
authors.lastname: Frantzeskakis
authors.forename: A R
authors.initials: AR
authors.lastname: Bishop