Statics and Dynamics of an Inhomogeneously-Nonlinear Lattice

Abstract

We introduce an inhomogeneously-nonlinear Schr{ö}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.

arXiv comment14 pages, 4 figures

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Cited by in corpus (10)

• Solitons in nonlinear lattices
• Spontaneous symmetry breaking in a nonlinear double-well structure
• Bright solitons from defocusing nonlinearities
• Solitons supported by localized nonlinearities in periodic media
• Localized gap soliton trains of Bose-Einstein condensates in an optical lattice
• Arrayed and checkerboard optical waveguides controlled by the electromagnetically-induced transparency
• Solitons supported by spatially inhomogeneous nonlinear losses
• Surface Solitons in Three Dimensions
• Transfer and scattering of wave packets by a nonlinear trap
• Self-trapped spatially localized states in combined linear-nonlinear periodic potentials