Kinetics of Bose Condensation

The process of condensation in the system of scalar bosons with weak $\lambda {\phi }^4$ interaction is considered. The Boltzmann kinetic equation is solved numerically. We consider two kinetic stages. At the first stage condensate is still absent but there is nonzero inflow of particles towards $\mathbf{p}=0$ and the distribution function at $\mathbf{p}=0$ grows from finite values to infinity. At the second stage there are two components, 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.