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

TL;DR

This paper investigates two-dimensional discrete solitons and vortices in a nonlinear Schrödinger system with spatially increasing defocusing nonlinearity, analyzing their construction, stability, and dynamic behavior from the anti-continuum limit.

Contribution

It extends the 2D model of nonlinear Schrödinger equations with spatially modulated nonlinearity, constructing various solutions including solitons and vortices, and analyzing their stability.

Findings

Multiple stable and unstable solution families identified.

Vortex cross solutions exhibit specific stability properties.

Dynamic instability scenarios demonstrated through simulations.

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.