Breathers in the weakly coupled topological discrete sine-Gordon system

TL;DR

This paper proves the existence of breathers in the topological discrete sine-Gordon system under weak coupling, highlighting their unique properties and providing a systematic numerical analysis of their profiles and existence domain.

Contribution

It demonstrates the existence of breathers in a non-decoupling topological system and offers the first systematic numerical characterization of these solutions.

Findings

Breathers exist in the weakly coupled topological discrete sine-Gordon system.

Breather profiles and existence domains are mapped in frequency-coupling space.

Breathers differ qualitatively from those in conventional discrete systems.

Abstract

Existence of breather (spatially localized, time periodic, oscillatory) solutions of the topological discrete sine-Gordon (TDSG) system, in the regime of weak coupling, is proved. The novelty of this result is that, unlike the systems previously considered in studies of discrete breathers, the TDSG system does not decouple into independent oscillator units in the weak coupling limit. The results of a systematic numerical study of these breathers are presented, including breather initial profiles and a portrait of their domain of existence in the frequency-coupling parameter space. It is found that the breathers are uniformly qualitatively different from those found in conventional spatially discrete systems.