  We investigate the formation, gravitational clustering and interactions of
solitons in a self-interacting, non-relativistic scalar field in an expanding
universe. Rapid formation of large number of solitons is driven by attractive
self-interactions of the field, whereas the slower clustering of solitons is
driven by gravitational forces. Driven closer together by gravity, we see a
rich plethora of dynamics in the soliton "gas" including mergers, scatterings
and formation of soliton binaries. The numerical simulations are complemented
by analytic calculations and estimates of (i) the relevant instability length
and time scales, (ii) individual soliton profiles and their stability, (iii)
number density of produced solitons, and (iv) the two point correlation
function of soliton positions as evidence for gravitational clustering.
