Abstract
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.
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Lindblom, O., Euler, N. Solutions of Discrete-Velocity Boltzmann Equations via Bateman and Riccati Equations. Theoretical and Mathematical Physics 131, 595–608 (2002). https://doi.org/10.1023/A:1015428229008
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DOI: https://doi.org/10.1023/A:1015428229008