We analyze the velocity distribution function of force-free granular gases in the regime of homogeneous cooling when deviations from the Maxwellian distribution may be accounted only by the leading term in the Sonine polynomial expansion, quantified by the second coefficient $a_2.$ We go beyond the linear approximation for $a_2$ and find three different values (three roots) for this coefficient which correspond to a scaling solution of the Boltzmann equation. The stability analysis performed showed, however, that among these three roots only one corresponds to a stable scaling solution. This is very close to $a_2,$ obtained in previous studies in a linear with respect to $a_2$ approximation.

• Received 28 June 1999

DOI:https://doi.org/10.1103/PhysRevE.61.2809