Solitons and Vortices in Two-dimensional Discrete Nonlinear Schrodinger Systems with Spatially Modulated Nonlinearity

Abstract

We consider a two-dimensional (2D) generalization of a recently proposed model [Phys. Rev. E 88, 032905 (2013)], which gives rise to bright discrete solitons supported by the defocusing nonlinearity whose local strength grows from the center to the periphery. We explore the 2D model starting from the anti-continuum (AC) limit of vanishing coupling. In this limit, we can construct a wide variety of solutions including not only single-site excitations, but also dipole and quadrupole ones. Additionally, two separate families of solutions are explored: the usual "extended" unstaggered bright solitons, in which all sites are excited in the AC limit, with the same sign across the lattice (they represent the most robust states supported by the lattice, their 1D counterparts being what was considered as 1D bright solitons in the above-mentioned work), and the vortex cross, which is specific to the 2D setting. For all the existing states, we explore their stability (analytically, whenever possible). Typical scenarios of instability development are exhibited through direct simulations.

13 pages, 13 figures

References in corpus (8)

• Twisted toroidal vortex-solitons in inhomogeneous media with repulsive nonlinearity
• The Discrete Nonlinear Schrödinger equation - 20 Years on
• Formation and light guiding properties of dark solitons in one-dimensional waveguide arrays
• Three-dimensional hybrid vortex solitons
• High-Order-Mode Soliton Structures in Two-Dimensional Lattices with Defocusing Nonlinearity
• Peierls-Nabarro Barrier and Protein Loop Propagation
• Saturable discrete vector solitons in one-dimensional photonic lattices
• Quantum bright solitons in the Bose-Hubbard model with site-dependent repulsive interactions