Geodesic
Painlev\'e test and a self-similar solution of the kinetic model
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the XVII All-Russian Youth School-Conference «Lobachevsky Readings-2018», November 23-28, 2018, Kazan. Part 2, Tome 176 (2020), pp. 91-94.

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We study a one-dimensional system of equations for a discrete gas model (McKean system). The McKean system is the Boltzmann kinetic equation of a model one-dimensional gas consisting of two groups of particles. Under certain conditions on a singularity variety, the system passes the Painlevé test. In addition, the kinetic system admits a reduction to a system of ordinary differential equations for which the Painlevé test is performed and it becomes possible to find a solution.
Keywords: Painlevé test, self-similar solution, McKean system. 
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S. A. Dukhnovskii. Painlev\'e test and a self-similar solution of the kinetic model. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the XVII All-Russian Youth School-Conference «Lobachevsky Readings-2018», November 23-28, 2018, Kazan. Part 2, Tome 176 (2020), pp. 91-94. http://geodesic.mathdoc.fr/item/INTO_2020_176_a8/

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