Geodesic
Solutions of Discrete-Velocity Boltzmann Equations via Bateman and Riccati Equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 131 (2002) no. 2, pp. 179-193

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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. 
@article{TMF_2002_131_2_a0,
     author = {O. Lindblom and N. Euler},
     title = {Solutions of {Discrete-Velocity} {Boltzmann} {Equations} via {Bateman} and {Riccati} {Equations}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {179--193},
     publisher = {mathdoc},
     volume = {131},
     number = {2},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2002_131_2_a0/}
}
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O. Lindblom; N. Euler. Solutions of Discrete-Velocity Boltzmann Equations via Bateman and Riccati Equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 131 (2002) no. 2, pp. 179-193. http://geodesic.mathdoc.fr/item/TMF_2002_131_2_a0/