Soliton hopping in a photonic dimer arises via a subcritical Hopf bifurcation from a stable soliton branch, while in a trimer it arises supercritically from an already unstable branch, leading to different pump power thresholds and observable regimes.
Dark solitons in the Lugiato-Lefever equation with normal dispersion
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abstract
The regions of existence and stability of dark solitons in the Lugiato-Lefever model with normal chromatic dispersion are described. These localized states are shown to be organized in a bifurcation structure known as collapsed snaking implying the presence of a region in parameter space with a finite multiplicity of dark solitons. For some parameter values dynamical instabilities are responsible for the appearance of oscillations and temporal chaos. The importance of the results for understanding frequency comb generation in microresonators is emphasized.
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Nonlinear periodic orbit solutions and their bifurcation structure at the origin of soliton hopping in coupled microresonators
Soliton hopping in a photonic dimer arises via a subcritical Hopf bifurcation from a stable soliton branch, while in a trimer it arises supercritically from an already unstable branch, leading to different pump power thresholds and observable regimes.