  The generation of optical frequency combs in microresonators is considered
without resorting to the mean-field approximation. New dynamical regimes are
found to appear for high intracavity power that cannot be modeled using the
Lugiato-Lefever equation. Using the Ikeda map we show the existence of
multi-valued stationary states and analyse their stability. Period doubled
patterns are considered and a novel type of super cavity soliton associated
with the multi-stable states is predicted.
