We propose several approaches for solving two discrete-velocity Boltzmann equations using the rescaling ansatz and the truncated Painlevé expansions. We use solutions of the two- and three-dimensional Bateman equations for the singularity manifold conditions to reduce the problem to Riccati equations. Both equations fail the Painlevé test.
Validerad; 2002; 20061005 (evan);
Also published in russian: O. Lindblom, N. Euler, Solutions of Discrete-Velocity Boltzmann Equations via Bateman and Riccati Equations, Theoretical and Mathematical Physics, 2002, Volume 131, Number 2, 179–193 DOI: 10.4213/tmf322