Instability of breathers in the topological discrete sine-Gordon system

TL;DR

This paper shows that breathers in a topological discrete sine-Gordon system are spectrally unstable, unlike in conventional systems where they remain stable at weak coupling, highlighting a fundamental difference due to topology.

Contribution

It reveals the spectral instability of breathers in topological discrete sine-Gordon systems, contrasting with their stability in traditional discrete systems.

Findings

Breathers are spectrally unstable in the topological system.

Conventional discrete breathers are stable at weak coupling.

Topological properties influence breather stability.

Abstract

It is demonstrated that the breather solutions recently discovered in the weakly coupled topological discrete sine-Gordon system are spectrally unstable. This is in contrast with more conventional spatially discrete systems, whose breathers are always spectrally stable at sufficiently weak coupling.