  In this paper, we analyze the dynamics and formation mechanisms of bound
states (BSs) of light bullets in the output of a laser coupled to a distant
saturable absorber. First we approximate the full three-dimensional set of Haus
master equations by a reduced equation governing the dynamics of the transverse
profile. This effective theory allows us to perform a detailed multiparameter
bifurcation study and to identify the different mechanisms of instability of
BSs. In addition, our analysis reveals a non-intuitive dependence of the
stability region as a function of the linewidth enhancement factors and the
field diffusion. Our results are confirmed by direct numerical simulations of
the full system.
