A note on a Discrete Boltzmann Equation with multiple collisions

We compute a non-trivial explicit solution for the one-dimensional plane 6-velocity discrete Boltzmann model with multiple collisions introduced in [E. Longo, R. Monaco, On the discrete kinetic theory with multiple collisions: Plane six-velocity and unsteady Couette flow, in: Muntz, et al. (Eds.), The Proceedings of Rarefied Gas Dynamics, in: AIAA Publ., vol. 118, 1989, pp. 118–130] which asymptotically connects two particular equilibrium states. We prove that such a solution exists provided that a suitable condition on the differential elastic cross sections holds.