Bright solitons in a PT-symmetric chain of dimers

TL;DR

This paper investigates the existence, stability, and dynamics of bright discrete solitons in a PT-symmetric chain of dimers modeled by coupled nonlinear Schrödinger equations, revealing stability conditions and dynamic behaviors.

Contribution

It introduces a perturbation theory approach for small coupling to analyze soliton stability in PT-symmetric lattices, contrasting with continuum limit results.

Findings

Both symmetric and antisymmetric onsite modes can be stable for small coupling.

Gain-loss terms generally reduce the stability region of onsite solitons.

Unstable solitons exhibit traveling or blow-up behaviors.

Abstract

We study the existence and stability of fundamental bright discrete solitons in a parity-time (PT)-symmetric coupler composed by a chain of dimers, that is modelled by linearly coupled discrete nonlinear Schrodinger equations with gain and loss terms. We use a perturbation theory for small coupling between the lattices to perform the analysis, which is then confirmed by numerical calculations. Such analysis is based on the concept of the so-called anti-continuum limit approach. We consider the fundamental onsite and intersite bright solitons. Each solution has symmetric and antisymmetric configurations between the arms. The stability of the solutions is then determined by solving the corresponding eigenvalue problem. We obtain that both symmetric and antisymmetric onsite mode can be stable for small coupling, on the contrary of the reported continuum limit where the antisymmetric solutions are always unstable. The instability is either due to the internal modes crossing the origin or the appearance of a quartet of complex eigenvalues. In general, the gain-loss term can be considered parasitic as it reduces the stability region of the onsite solitons. Additionally, we analyse the dynamic behaviour of the onsite and intersite solitons when unstable, where typically it is either in the form of travelling solitons or soliton blow-ups.