Solving Boltzmann Equations by Bateman and Riccati Equations
Ove Lindblom · 2001
Abstract: Propositions for solutions of two discrete-velocity Boltzmann equa-tions are given by rescaling Ansätze using truncated Painleve expansions. So-lutions of the two- and three-dimensional Bateman equations for the singu-larity manifold conditions are used to reduce the problem to Riccati equations. This enables us to extend, essentially, the solutions obtainable by truncated Painleve expansions for a two-dimensional and a three-dimensional Boltz-mann equation. Both equations do not pass the Painleve test.