Compact Discrete Breathers on Flat Band Networks

TL;DR

This paper investigates the existence and stability of compact discrete breathers in flat band networks, revealing how destructive interference enables localized solutions in nonlinear wave equations.

Contribution

It introduces new criteria for the existence and stability of compact discrete breathers based on CLS amplitude distributions and orthogonality conditions.

Findings

Existence of compact discrete breathers relies on destructive interference.

Criteria for stability of breathers are derived from CLS properties.

Breathers can form as families of continued linear eigenstates or on dispersive networks.

Abstract

Linear wave equations on flat band networks host compact localized eigenstates (CLS). Nonlinear wave equations on translationally invariant flat band networks can host compact discrete breathers - time periodic and spatially compact localized solutions. Such solutions can appear as one-parameter families of continued linear compact eigenstates, or as discrete sets on families of non-compact discrete breathers, or even on purely dispersive networks with fine-tuned nonlinear dispersion. In all cases, their existence relies on destructive interference. We use CLS amplitude distribution properties and orthogonality conditions to derive existence criteria and stability properties for compact discrete breathers as continued CLS.