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We have performed a systematic study quantifying the variation of solitarywave behavior from that of an ordered cloud resembling a "crystalline"configuration to that of a disordered state that can be characterized as asoliton "gas". As our illustrative examples, we use both one-component, as wellas two-component, one dimensional atomic gases very close to zero temperature,where in the presence of repulsive inter-atomic interactions and of a parabolictrap, a cloud, respectively of dark (dark-bright) solitons can form in the one-(two-) component system. We corroborate our findings through three distincttypes of approaches, namely a Gross-Pitaevskii type of partial differentialequation, particle-based ordinary differential equations describing the solitondynamical system and Monte-Carlo simulations for the particle system. We definean "empirical" order parameter to characterize the order of the solitonlattices and study how this changes as a function of the strength of the"thermally" (i.e., kinetically) induced perturbations. As may be anticipated bythe one-dimensional nature of our system, the transition from order to disorderis gradual without, apparently, a genuine phase transition ensuing in theintermediate regime.

Transitions From Order to Disorder in Multi-Dark and Multi-Dark-Bright Soliton Atomic Clouds