Titel: „Towards conservative solitons and reversibility in time delayed systems”

Abstract: Delayed interactions are a ubiquitous feature of many real-world systems and the time lags become important in situations where distant, point-wise, nonlinear nodes exchange information propagating at a finite speed or possess finite reaction times. Nonlinear time-delay systems (TDSs) not only pose a fundamental challenge for theoretical studies but are of crucial importance for applications ranging from traffic flow dynamics and economy to active matter systems and laser physics, to name just a few. Furthermore, external time-delayed feedback control loops have proven to be an efficient tool for an effective non-invasive stabilization of unstable dynamical states. However, in physics, TDSs mostly have been limited to the study of dissipative dynamics. Recently an example of a photonic system modeled by a nonlinear, time-reversible, conservative time-delayed system has been shown.
In this talk we start with a basic review of TDSs and then review our recent theoretical results regarding the existence of reversible conservative TDSs considering a dispersive microcavity containing a Kerr medium coupled to a distant external mirror. In the long delay limit, the normal form identifies with the nonlinear Schrödinger equation, thereby allowing for bright and dark solitons although the lack of integrability can be observed at high energies. We unveil some of the symmetries and conserved quantities and recover the Lugiato-Lefever equation in the weakly dissipative regime.

Der Vortrag findet statt am
Mittwoch, den 17.05.2023 um 17:15 Uhr im Raum W01 0-006

Interessierte sind herzlich eingeladen.