  Stable light bullets and clusters of them are presented in the monostable
regime using the mean-field Lugiato-Lefever equation [Gopalakrishnan,
Panajotov, Taki, and Tlidi, Phys. Rev. Lett. 126, 153902 (2021)]. It is shown
that three-dimensional (3D) dissipative structures occur in a strongly
nonlinear regime where modulational instability is subcritical. We provide a
detailed analysis on the formation of optical 3D crystals in both the super-
and sub-critical modulational instability regimes, and we highlight their link
to the formation of light bullets in diffractive and dispersive Kerr
resonators. We construct bifurcation diagrams associated with the formation of
optical crystals in both monostable and bistable regimes. An analytical study
has predicted the predominance of body-centered-cubic (bcc) crystals in the
intracavity field over a large variety of other 3D solutions with less
symmetry. These results have been obtained using a weakly nonlinear analysis
but have never been checked numerically. We show numerically that indeed the
most robust structures over other self-organized crystals are the bcc crystals.
Finally, we show that light-bullets and clusters of them can occur also in a
bistable regime.
