  We investigate numerically interactions between two bright or dark incoherent
localized beams in an strontium barium niobate photorefractive crystal in one
dimension, using the coherent density method. For the case of bright beams, if
the interacting beams are in-phase, they attract each other during propagation
and form bound breathers; if out-of-phase, the beams repel each other and fly
away. The bright incoherent beams do not radiate much and form long-lived
well-defined breathers or quasi-stable solitons. If the phase difference is
$\pi/2$, the interacting beams may both attract or repel each other, depending
on the interval between the two beams, the beam widths, and the degree of
coherence. For the case of dark incoherent beams, in addition to the above the
interactions also depend on the symmetry of the incident beams. As already
known, an even-symmetric incident beam tends to split into a doublet, whereas
an odd-symmetric incident beam tends to split into a triplet. When launched in
pairs, the dark beams display dynamics consistent with such a picture and in
general obey soliton-like conservation laws, so that the collisions are mostly
elastic, leading to little energy and momentum exchange. But they also radiate
and breathe while propagating. In all the cases, the smaller the interval
between the two interacting beams, the stronger the mutual interaction. On the
other hand, the larger the degree of incoherence, the weaker the interaction.
