Compact discrete breathers on flat-band 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 disper- sive 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 sta- bility properties for compact discrete breathers as continued CLS.