# Bright Breathers in Nonlinear Left-Handed Metamaterial Lattices

## TL;DR

This paper investigates the formation, stability, and dynamics of bright breathers in nonlinear left-handed metamaterial lattices, combining analytical and numerical methods to understand their bifurcation, stability, and mobility properties.

## Contribution

It introduces a multiscale approximation for bright breathers in nonlinear left-handed metamaterials and analyzes their stability and mobility through numerical and Floquet analysis.

## Key findings

- Bright breathers bifurcate from the linear dispersion edge at wavenumber π.
- Stable inter-site and unstable site-centered breather solutions are identified.
- The stability analysis reveals potential for breather pinning or mobility.

## Abstract

In the present work, we examine a prototypical model for the formation of bright breathers in nonlinear left-handed metamaterial lattices. Utilizing the paradigm of nonlinear transmission lines, we build a relevant lattice and develop a quasi-continuum multiscale approximation that enables us to appreciate both the underlying linear dispersion relation and the potential for bifurcation of nonlinear states. We focus here, more specifically, on bright discrete breathers which bifurcate from the lower edge of the linear dispersion relation at wavenumber $k=\pi$. Guided by the multiscale analysis, we calculate numerically both the stable inter-site centered and the unstable site-centered members of the relevant family. We quantify the associated stability via Floquet analysis and the Peierls-Nabarro barrier of the energy difference between these branches. Finally, we explore the dynamical implications of these findings towards the potential mobility or lack thereof (pinning) of such breather solutions.