Solutions of Discrete-Velocity Boltzmann Equations via Bateman and Riccati Equations

We propose several approaches for solving two discrete-velocity Boltzmann equations using the rescaling ansatz and the truncated Painlev'e 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.