  We consider a new class of periodic solutions to the Lugiato-Lefever
equations (LLE) that govern the electromagnetic field in a microresonator
cavity. Specifically, we rigorously characterize the stability and dynamics of
the Jacobi elliptic function solutions of LLE and show that the dn solution is
stabilized by the pumping of the microresonator. In analogy with soliton
perturbation theory, we also derive a microcomb perturbation theory that allows
one to consider the effects of physically realizable perturbations on the comb
line stability, including effects of Raman scattering and stimulated emission.
Our results are verified through full numerical simulations of the LLE cavity
dynamics. The perturbation theory gives a simple analytic platform for
potentially engineering new resonator designs.
