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

• Published in: The European physical journal. D, Atomic, molecular, and optical physics Vol. 71; no. 6; pp. 1 - 8
• Main Authors: Ferré, Michel A., Clerc, Marcel G., Coulibally, Saliya, Rojas, René G., Tlidi, Mustapha
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2017; Springer Nature B.V; EDP Sciences
• Subjects: Applications of Nonlinear Dynamics and Chaos Theory; Atomic; Chaos theory; Chaotic Dynamics; Dynamical systems; Dynamics; Magnetic resonance; Molecular; Nonlinear Sciences; Optical and Plasma Physics; Oscillators; Pattern Formation and Solitons; Physical Chemistry; Physics; Physics and Astronomy; Plasma; Quantum Information Technology; Quantum Physics; Regular Article; Spectroscopy/Spectrometry; Spintronics; Topical Issue: Theory and applications of the Lugiato-Lefever Equation
• ISSN: 1434-6060; 1434-6079
• DOI: 10.1140/epjd/e2017-80072-3

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. Graphical abstract