  The collective behaviour of soliton ensembles (i.e. the solitonic gas) is
studied using the methods of the direct numerical simulation. Traditionally
this problem was addressed in the context of integrable models such as the
celebrated KdV equation. We extend this analysis to non-integrable KdV-BBM type
models. Some high resolution numerical results are presented in both integrable
and nonintegrable cases. Moreover, the free surface elevation probability
distribution is shown to be quasi-stationary. Finally, we employ the asymptotic
methods along with the Monte-Carlo simulations in order to study quantitatively
the dependence of some important statistical characteristics (such as the
kurtosis and skewness) on the Stokes-Ursell number (which measures the relative
importance of nonlinear effects compared to the dispersion) and also on the
magnitude of the BBM term.
