  We have performed a systematic study quantifying the variation of solitary
wave behavior from that of an ordered cloud resembling a "crystalline"
configuration to that of a disordered state that can be characterized as a
soliton "gas". As our illustrative examples, we use both one-component, as well
as two-component, one dimensional atomic gases very close to zero temperature,
where in the presence of repulsive inter-atomic interactions and of a parabolic
trap, a cloud, respectively of dark (dark-bright) solitons can form in the one-
(two-) component system. We corroborate our findings through three distinct
types of approaches, namely a Gross-Pitaevskii type of partial differential
equation, particle-based ordinary differential equations describing the soliton
dynamical system and Monte-Carlo simulations for the particle system. We define
an "empirical" order parameter to characterize the order of the soliton
lattices and study how this changes as a function of the strength of the
"thermally" (i.e., kinetically) induced perturbations. As may be anticipated by
the one-dimensional nature of our system, the transition from order to disorder
is gradual without, apparently, a genuine phase transition ensuing in the
intermediate regime.
