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The origin, stability and bifurcation structure of different types of brightlocalized structures described by the Lugiato-Lefever equation is studied. Thismean field model describes the nonlinear dynamics of light circulating in fibercavities and microresonators. In the case of anomalous group velocitydispersion and low values of the intracavity phase detuning these bright statesare organized in a homoclinic snaking bifurcation structure. We describe howthis bifurcation structure is destroyed when the detuning is increased across acritical value, and determine how a new bifurcation structure known as foliatedsnaking emerges.

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