  Soliton gas or soliton turbulence is a subject of intense studies due to its
great importance to optics, hydrodynamics, electricity, chemistry, biology and
plasma physics. Usually, this term is used for integrable models where solitons
interact elastically. However, soliton turbulence can also be a part of
non-integrable dynamics, where long-lasting solutions in the form of almost
solitons may exist. In the present paper, the complex dynamics of ensembles of
solitary waves is studied within the Schamel equation using direct numerical
simulations. Some important statistical characteristics (distribution
functions, moments) are calculated numerically for unipolar and bipolar soliton
gases. Comparison of results with integrable Korteweg-de Vries (KdV) and
modified KdV (mKdV) models are given qualitatively. Our results agree well with
the predictions of the KdV equation in the case of unipolar solitons. However,
in the bipolar case, we observed a notable departure from the mKdV model,
particularly in the behavior of kurtosis. The observed increase in kurtosis
signifies the amplification of distribution function tails, which, in turn,
corresponds to the presence of high-amplitude waves.
