  We present a detailed description of the formation of bright solitary waves
in optical lattices. To this end, we have considered a ring lattice geometry
with large radius. In this case, the ring shape does not have a relevant effect
in the local dynamics of the condensate, while offering a realistic set up to
implement experiments with conditions usually not available with linear
lattices (in particular, to study collisions). Our numerical results suggest
that the condensate radiation is the relevant dissipative process in the
relaxation towards a self-trapped solution. We show that the source of
dissipation can be attributed to the presence of higher order dispersion terms
in the effective mass approach. In addition, we demonstrate that the stability
of the solitary solutions is linked with particular values of the width of the
wavepacket in the reciprocal space. Our study suggests that these critical
widths for stability depend on the geometry of the energy band, but are
independent of the condensate parameters (momentum, atom number, etc.).
Finally, the non-solitonic nature of the solitary waves is evidenced showing
their instability under collisions.
