  N.N. Bogolyubov discovered that the Boltzmann-Enskog kinetic equation has
microscopic solutions. They have the form of sums of delta-functions and
correspond to trajectories of individual hard spheres. But the rigorous sense
of the product of the delta-functions in the collision integral was not
discussed. Here we give a rigorous sense to these solutions by introduction of
a special regularization of the delta-functions. The crucial observation is
that the collision integral of the Boltzmann-Enskog equation coincides with
that of the first equation of the BBGKY hierarchy for hard spheres if the
special regularization to the delta-functions is applied. This allows to reduce
the nonlinear Boltzmann-Enskog equation to the BBGKY hierarchy of linear
equations in this particular case.
  Also we show that similar functions are exact smooth solutions for the
recently proposed generalized Enskog equation. They can be referred to as
"particle-like" or "soliton-like" solutions and are analogues of multisoliton
solutions of the Korteweg-de Vries equation.
