  We show that self-organization occurs in the phase dynamics of soliton
modelocking in paramet- ric frequency combs. Reduction of the Lugiato-Lefever
equation (LLE) to a simpler set of phase equations reveals that this
self-organization arises via mechanisms akin to those in the Kuramoto model for
synchronization of coupled oscillators. In addition, our simulations show that
the phase equations evolve to a broadband phase-locked state, analogous to the
soliton formation process in the LLE. Our simplified equations intuitively
explain the origin of the pump phase offset in soliton- modelocked parametric
frequency combs. They also predict that the phase of the intracavity field
undergoes an anti-symmetrization that precedes phase synchronization, and they
clarify the role of chaotic states in soliton formation in parametric combs.
