Discrete PT-symmetric solitons on branched lattices: Vertex states, stability, and vortices

Abstract

Branching fundamentally modifies nonlinear localization by introducing vertex degrees of freedom absent in one-dimensional lattices. We investigate localized states in a PT-symmetric four-edge star graph described by the discrete nonlinear Schrödinger equation. We identify a discrete vortex state with a fixed topological charge, supported by the branching geometry. Constructed by continuation from the anticontinuum limit, the vortex evolves into a current-carrying state in the presence of balanced gain and loss and exhibits stability windows absent for the conventional branches. A possible electric-circuit realization of the proposed model is discussed.