Statics and Dynamics of an Inhomogeneously-Nonlinear Lattice

Details Statics and Dynamics of an Inhomogeneously-Nonlinear Lattice Statics and Dynamics of an Inhomogeneously-Nonlinear Lattice

2006-02-18

arxiv.org/abs/nlin/0602039v1

Nonlinear Sciences

Pattern Formation and Solitons

14 pages, 4 figures

Scientific paper

10.1103/PhysRevE.74.036602

We introduce an inhomogeneously-nonlinear Schr{\"o}dinger 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 than the one expected in their homogeneous counterparts in the vicinity of the interface. 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 anti-continuum 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.

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