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

The origin, stability and bifurcation structure of different types of bright localized structures described by the Lugiato-Lefever equation is studied. This mean field model describes the nonlinear dynamics of light circulating in fiber cavities and microresonators. In the case of anomalous group ve...

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Bibliographic Details
Published inarXiv.org
Main Authors Parra-Rivas, P, Gomila, D, Gelens, L, Knobloch, E
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 15.01.2018
Subjects
Bifurcations
Dispersion
Group velocity
Nonlinear dynamics
Physics - Pattern Formation and Solitons
Structural stability
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Summary:The origin, stability and bifurcation structure of different types of bright localized structures described by the Lugiato-Lefever equation is 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 new bifurcation structure known as foliated snaking emerges.
ISSN:2331-8422
DOI:10.48550/arxiv.1801.04796