Condensation of bosons in the kinetic regime

We study the kinetic regime of the Bose condensation of scalar particles. The Boltzmann equation is solved numerically. We consider two kinetic stages. At the first stage the condensate is absent but there is a nonzero inflow of particles towards $\mathbf{p}=0$ and the distribution function at $\mathbf{p}=0$ grows from finite values to infinity in a finite time. We observe a profound similarity between Bose condensation and Kolmogorov turbulence. At the second stage there are two components, the condensate and particles, reaching their equilibrium values. We show that the evolution in both stages proceeds in a self-similar way and find the time needed for condensation. We do not consider a phase transition from the first stage to the second. Condensation of self-interacting bosons is compared to the condensation driven by interaction with a cold gas of fermions; the latter turns out to be self-similar too. Exploiting the self-similarity we obtain a number of analytical results in all cases.