Effects of inhomogeneities and drift on the dynamics of temporal solitons in fiber cavities and microresonators

In [Phys. Rev. Lett. 110, 064103 (2013)], using the Swift-Hohenberg equation, we introduced a mechanism that allows to generate oscillatory and excitable soliton dynamics. This mechanism was based on a competition between a pinning force at inhomogeneities and a pulling force due to drift. Here, we study the effect of such inhomogeneities and drift on temporal solitons and Kerr frequency combs in fiber cavities and microresonators, described by the Lugiato-Lefever equation with periodic boundary conditions. We demonstrate that for low values of the frequency detuning the competition between inhomogeneities and drift leads to similar dynamics at the defect location, confirming the generality of the mechanism. The intrinsic periodic nature of ring cavities and microresonators introduces, however, some interesting differences in the final global states. For higher values of the detuning we observe that the dynamics is no longer described by the same mechanism and it is considerably more complex.