Group analysis of the one-dimensional Boltzmann equation. I: Symmetry groups (Q2399394)

In this article the author considers the one-dimensional Boltzmann equation for the distribution function of a system of particles on which a force field, depending on the position, velocity and time, acts. The symmetry algebra of this equation is obtained in the general case and under the requirement that in the new variables one of, or both the relations for the velocity and the force are conserved. It is shown that the algebra is infinite-dimensional, and that its structure does not depend on the form of the force.