Eur. Phys. J. D (2017) 71: 172
https://doi.org/10.1140/epjd/e2017-80072-3

Regular Article

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

¹ Departamento de Física, FCFM, Universidad de Chile, Casilla 487-3 Santiago, Chile
² Université de Lille, CNRS, UMR 8523 - PhLAM - Physique des Lasers Atomes et Molécules, 59000 Lille, France
³ Intituto de Física, Pontificia Universidad Católica de Valparaíso, Casilla 4059, Valparaíso, Chile
⁴ Faculté des Sciences, Université Libre de Bruxelles (U.L.B.), CP 231, Campus Plaine, 1050 Bruxelles, Belgium

^a e-mail: marcel@dfi.uchile.cl

Received: 31 January 2017
Received in final form: 11 April 2017
Published online: 22 June 2017

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.