Abstract
The problems of the existence, stability, and transversal motion of the discrete dark localized modes in the lattices with saturable nonlinearity are investigated analytically and numerically. The stability analysis shows existence of regions of the parametric space with eigenvalue spectrum branches with non-zeroth real part, which indicates possibility for the propagation of stable on-site and inter-site dark localized modes. The analysis based on the conserved system quantities reveals the existence of regions with a vanishing Peierls-Nabarro barrier which allows transverse motion of the dark breathers. Propagation of the stable on-site and inter-site dark breathers and their free transversal motion are observed numerically.
Highlights
In the past two decades the investigation of discrete nonlinear lattices with continuous evolution variable and discrete spatial variables has exhibited a tremendous growth
Dark solitons were experimentally observed in the defocusing lithium niobate waveguide arrays with saturable nonlinearity [8]
We start our study with the one-dimensional discrete nonlinear Schrodinger (DNLS) lattice model with saturable nonlinearity given by [10, 11]
Summary
In the past two decades the investigation of discrete nonlinear lattices with continuous evolution variable and discrete spatial variables has exhibited a tremendous growth. These phenomena are universal and relevant for many non-optical systems, as localized voltage drops in ladders of the Josephson junctions [3], localized modes in the antiferromagnetic crystals [4], or localization of matter waves in the Bose - Einstein condensates using optically-induced periodic potentials [5]. All results are verified numerically and commented with the respect to the recent results [8, 9]
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