# Hybrid Breathers in Nonlinear $\mathcal{PT}$-Symmetric Metamaterials

## TL;DR

This paper investigates hybrid breather solutions in a nonlinear $ ext{PT}$-symmetric magnetic metamaterial, revealing stable oscillations that combine localized breathers and plane waves, supported by analytical and numerical methods.

## Contribution

It introduces the concept of hybrid breathers in $ ext{PT}$-symmetric metamaterials and provides an analytical framework for understanding these complex oscillations.

## Key findings

- Existence of stable hybrid breather solutions.
- Hybrid breathers are superpositions of breathers and plane waves.
- Numerical and analytical methods confirm the stability of these solutions.

## Abstract

On a two-dimensional planar parity-time-($\mathcal{PT}$-)symmetric nonlinear magnetic metamaterial, consisting of split-ring dimers with balanced gain and loss, discrete breather solutions can be found. We extend these studies and by numerical calculations reveal the existence of further stable, long-lived oscillations, with certain frequencies, in the breather spectrum. We describe these oscillations in terms of an analytical breather theory, and show that they can be interpreted as superpositions of a breather oscillation and a plane wave. We coin the term `hybrid breather' solutions for these solutions.