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Stability of Discrete Breathers in Magnetic Metamaterials

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Localized Excitations in Nonlinear Complex Systems

Part of the book series: Nonlinear Systems and Complexity ((NSCH,volume 7))

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Abstract

We consider the discrete Klein–Gordon equation for magnetic metamaterials derived by Lazarides, Eleftheriou, and Tsironis Phys Rev Lett 97:157406, 2006). We obtain a general criterion for spectral stability of multi-site breathers for a small coupling constant. We show how this criterion differs from the one derived in the standard discrete Klein–Gordon equation (Koukouloyannis and Kevrekidis, Nonlinearity 22:2269–2285, 2009; Pelinovsky and Sakovich, Nonlinearity 25:3423–3451, 2012).

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Acknowledgements

The research D.P. is supported by the NSERC Discovery grant. The research of V.R. has been co-financed by the European Union (European Social Fund – ESF) and Greek national funds through the Operational Program “Education and Lifelong Learning” of the National Strategic Reference Framework (NSRF) – Research Funding Program: THALES – Investing in knowledge society through the European Social Fund.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, McMaster University, Hamilton, ON, L8S 4K1, Canada

    Dmitry Pelinovsky

  2. Faculty of Engineering, School of Mathematics, Physics and Computer Sciences, Aristotle University, GR54124, Thessaloniki, Greece

    Vassilis Rothos

Authors
  1. Dmitry Pelinovsky
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  2. Vassilis Rothos
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Correspondence to Dmitry Pelinovsky .

Editor information

Editors and Affiliations

  1. Dept. of Mathematics and Statistics, San Diego State University, San Diego, California, USA

    Ricardo Carretero-González

  2. Dept. de Física Aplicada I, Escuela Politécnica Superior, University of Sevilla, Sevilla, Spain

    Jesús Cuevas-Maraver

  3. Dept. of Physics, University of Athens, Athens, Greece

    Dimitri Frantzeskakis

  4. Dept. of Mathematics, University of the Aegean, Samos, Greece

    Nikos Karachalios

  5. Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts, USA

    Panayotis Kevrekidis

  6. Dept. de Física Aplicada I, E.T.S.I. Informática, University of Sevilla, Sevilla, Spain

    Faustino Palmero-Acebedo

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Pelinovsky, D., Rothos, V. (2014). Stability of Discrete Breathers in Magnetic Metamaterials. In: Carretero-González, R., Cuevas-Maraver, J., Frantzeskakis, D., Karachalios, N., Kevrekidis, P., Palmero-Acebedo, F. (eds) Localized Excitations in Nonlinear Complex Systems. Nonlinear Systems and Complexity, vol 7. Springer, Cham. https://doi.org/10.1007/978-3-319-02057-0_18

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  • DOI: https://doi.org/10.1007/978-3-319-02057-0_18

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-02056-3

  • Online ISBN: 978-3-319-02057-0

  • eBook Packages: EngineeringEngineering (R0)

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