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Localized structures and spatiotemporal chaos: comparison between the driven damped sine-Gordon and the Lugiato-Lefever model

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Abstract

Driven damped coupled oscillators exhibit complex spatiotemporal dynamics. An archetype model is the driven damped sine-Gordon equation, which can describe several physical systems such as coupled pendula, extended Josephson junction, optical systems and driven magnetic wires. Close to resonance an enveloped model in the form Lugiato-Lefever equation can be derived from the driven damped sine-Gordon equation. We compare the dynamics obtained from both models. Unexpectedly, qualitatively similar dynamical behaviors are obtained for both models including homogeneous steady states, localized structures, and pattern waves. For large forcing, both systems share similar spatiotemporal chaos.

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Authors and Affiliations

  1. Departamento de Física, FCFM, Universidad de Chile, Casilla 487-3, Santiago, Chile

    Michel A. Ferré & Marcel G. Clerc

  2. Université de Lille, CNRS, UMR 8523 - PhLAM - Physique des Lasers Atomes et Molécules, 59000, Lille, France

    Saliya Coulibally

  3. Intituto de Física, Pontificia Universidad Católica de Valparaíso, Casilla 4059, Valparaíso, Chile

    René G. Rojas

  4. Faculté des Sciences, Université Libre de Bruxelles (U.L.B.), CP 231, Campus Plaine, 1050, Bruxelles, Belgium

    Mustapha Tlidi

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  1. Michel A. Ferré
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  2. Marcel G. Clerc
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  3. Saliya Coulibally
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  4. René G. Rojas
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  5. Mustapha Tlidi
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Correspondence to Marcel G. Clerc.

Additional information

Contribution to the Topical Issue: “Theory and Applications of the Lugiato-Lefever Equation”, edited by Yanne K. Chembo, Damia Gomila, Mustapha Tlidi, Curtis R. Menyuk.

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Ferré, M.A., Clerc, M.G., Coulibally, S. et al. Localized structures and spatiotemporal chaos: comparison between the driven damped sine-Gordon and the Lugiato-Lefever model. Eur. Phys. J. D 71, 172 (2017). https://doi.org/10.1140/epjd/e2017-80072-3

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  • DOI: https://doi.org/10.1140/epjd/e2017-80072-3

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