  A homogeneously broadened unidirectonal ring laser can emit in several
longitudinal modes for large enough pump and cavity length because of Rabi
splitting induced gain. This is the so called Risken-Nummedal-Graham-Haken
(RNGH) instability. We investigate numerically the properties of the multi-mode
solution. We show that this solution can coexist with the single-mode one, and
its stability domain can extend to pump values smaller than the critical pump
of the RNGH instability. Morevoer, we show that the multi-mode solution for
large pump values is affected by two different instabilities: a pitchfork
bifurcation, which preserves phase-locking, and a Hopf bifurcation, which
destroys it.
