Bifurcation structure of localized states in the Lugiato-Lefever equation with anomalous dispersion

Physical Review. E
P Parra-RivasEdgar Knobloch

Abstract

The origin, stability, and bifurcation structure of different types of bright localized structures described by the Lugiato-Lefever equation are studied. This mean field model describes the nonlinear dynamics of light circulating in fiber cavities and microresonators. In the case of anomalous group velocity dispersion and low values of the intracavity phase detuning these bright states are organized in a homoclinic snaking bifurcation structure. We describe how this bifurcation structure is destroyed when the detuning is increased across a critical value, and determine how a bifurcation structure known as foliated snaking emerges.

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Citations

Dec 15, 2018·Optics Letters·Tobias HanssonStefan Wabnitz
Jun 25, 2020·Physical Review. E·P Parra-Rivas, C Fernandez-Oto
Feb 27, 2021·Physical Review Letters·Salim B IvarsCarles Milián
Nov 9, 2021·Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences·Fahad Al Saadi, Alan Champneys

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