Thursday, July 18, 2013

1307.4741 (A. S. Trushechkin)

Soliton-like solutions of the Boltzmann-Enskog kinetic equation for
elastic and inelastic hard spheres

A. S. Trushechkin
We find explicit soliton-like solutions for the nonlinear integro-differential Boltzmann-Enskog kinetic equation (for both elastic and inelastic hard spheres). They are analogues of multisoliton solutions of the Korteweg-de Vries equation. To our awareness, these are the first classical explicit solutions of the Boltzmann-Enskog equation. The constructed solutions are regularized versions of the so called microscopic solutions of the Boltzmann-Enskog equation discovered by N.N.Bogolyubov. The microscopic solutions have the form of sums of delta-functions and correspond to trajectories of individual hard spheres. Our soliton-like solutions have the form of sums of regularized delta-functions. Finally, we give some comments on the reversibility paradox and entropy production.
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