Discrete solitons in PT-symmetric lattices

TL;DR

This paper proves the existence and stability of discrete solitons in infinite PT-symmetric lattices using analytical methods, focusing on chains of coupled dimers and quadrimers, and analyzing bifurcations from the anticontinuum limit.

Contribution

It introduces a novel analytical approach to establish the existence and stability of discrete solitons in PT-symmetric lattices from the anticontinuum limit.

Findings

Discrete solitons exist in PT-symmetric lattices.

Stable solitons are found in large parameter regions.

The approach applies to chains of dimers and quadrimers.

Abstract

We prove existence of discrete solitons in infinite parity-time (PT-) symmetric lattices by means of analytical continuation from the anticontinuum limit. The energy balance between dissipation and gain implies that in the anticontinuum limit the solitons are constructed from elementary PT-symmetric blocks such as dimers, quadrimers, or more general oligomers. We consider in detail a chain of coupled dimers, analyze bifurcations of discrete solitons from the anticontinuum limit and show that the solitons are stable in a sufficiently large region of the lattice parameters. The generalization of the approach is illustrated on two examples of networks of quadrimers, for which stable discrete solitons are also found.