H. Xu, P.G. Kevrekidis, and D.E. Pelinovsky

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

Physica D 326 (2016), 1-20

Vortices symmetric with respect to simultaneous parity and time reversing transformations are considered on the square lattice in the framework of the discrete nonlinear Schrodinger 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.

discrete nonlinear Schrodinger equation, vortices, existence and stability, parity-time reversal symmetry, anti-continuum limit.