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Travelling Waves in Nonlinear Magnetic Metamaterials

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Localized Excitations in Nonlinear Complex Systems

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

Abstract

In this article, a model of one-dimensional metamaterial formed by a discrete array of nonlinear resonators is considered. The existence and uniqueness results of periodic and asymptotic travelling waves of the system are presented. The existence and the stability of asymptotic waves are also computed and discussed numerically.

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Acknowledgements

We thank the reviewers for valuable comments and suggestions which improved our paper. J.D. is supported by the Grant GAČR P201/11/0768. M.F. is partially supported by grants VEGA-MS 1/0507/11, VEGA-SAV 2/0029/13 and APVV-0134-10. M.P. is supported by the project No. CZ.1.07/2.3.00/30.0005 funded by European Regional Development Fund. V.R. and H.S. acknowledge a partial support from the London Mathematical Society through a visitor grant. This research (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. V.R. also acknowledges support from AUTH-Research Council Grant.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Electrical Engineering and Communication, Brno University of Technology, Technická 3058/10, 616 00, Brno, Czech Republic

    J. Diblík

  2. Department of Mathematical Analysis and Numerical Mathematics, Comenius University, Mlynská dolina, 842 48, Bratislava, Slovakia

    M. Fečkan

  3. Mathematical Institute of Slovak Academy of Sciences, Štefánikova 49, 814 73, Bratislava, Slovakia

    M. Fečkan

  4. Centre for Research and Utilization of Renewable Energy, Faculty of Electrical Engineering and Communication, Brno University of Technology, Technická 3058/10, 616 00, Brno, Czech Republic

    M. Pospíšil

  5. Department of Mathematics, Physics and Computational Sciences, Mathematics Division, Faculty of Engineering, Aristotle University of Thessaloniki, Thessaloniki, GR54124, Greece

    V. M. Rothos

  6. School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK

    H. Susanto

Authors
  1. J. Diblík
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  2. M. Fečkan
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  3. M. Pospíšil
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  4. V. M. Rothos
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  5. H. Susanto
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Corresponding author

Correspondence to M. Fečkan .

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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Diblík, J., Fečkan, M., Pospíšil, M., Rothos, V.M., Susanto, H. (2014). Travelling Waves in Nonlinear 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_17

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  • DOI: https://doi.org/10.1007/978-3-319-02057-0_17

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  • Print ISBN: 978-3-319-02056-3

  • Online ISBN: 978-3-319-02057-0

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