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

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. Keywords. KeyWords Plus:NONLINEAR SCHRODINGER-EQUATION; QUASI-REVERSIBLE SYSTEMS; NEAR-INTEGRABLE PDE; OPTICAL BISTABILITY; AC-DRIVEN; 3-DIMENSIONAL STRUCTURES; PATTERN SELECTION; PERIODIC ROUTE; RING CAVITY; KERR CAVITY