Compact discrete breathers on flat-band networks

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 famil...

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Bibliographic Details
Published in:Low temperature physics (Woodbury, N.Y.) N.Y.), 2018-07, Vol.44 (7), p.678-687
Main Authors: Danieli, C., Maluckov, A., Flach, S.
Format: Article
Language:English
Subjects:
Breathers
Eigenvectors
Mathematical analysis
Networks
Nonlinear equations
Orthogonality
Stability criteria
Wave dispersion
Wave equations
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Summary: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.
ISSN:1063-777X
1090-6517
DOI:10.1063/1.5041434