Existence and stability of PT-symmetric vortices in nonlinear two-dimensional square lattices

TL;DR

This paper investigates the existence and stability of PT-symmetric vortices in nonlinear 2D square lattices using analytical and numerical methods, focusing on weak coupling regimes to extend local predictions to larger arrays.

Contribution

It provides new analytical and numerical analysis of PT-symmetric vortex configurations in 2D lattices, highlighting their stability properties in the weak coupling limit.

Findings

Analytical predictions match numerical results

Vortex stability depends on coupling strength

PT-symmetric vortices exist in discrete nonlinear Schrödinger lattices

Abstract

Vortices symmetric with respect to simultaneous parity and time reversing transformations are considered on the square lattice in the framework of the discrete nonlinear Schr\"{o}dinger equation. The existence and stability of vortex configurations is analyzed in the limit of weak coupling between the lattice sites, when predictions on the elementary cell of a square lattice (i.e., a single square) can be extended to a large (yet finite) array of lattice cells. Our analytical predictions are found to be in good agreement with numerical computations.