Group analysis of the one-dimensional boltzmann equation: II. Equivalence groups and symmetry groups in the special case

Abstract

We obtain relations that define the equivalence algebra of the family of one-dimensional Boltzmann equations f_t + cf_x + F(t, x, c)f_c = 0 and show that all equations of that form are locally equivalent. We carry out the group classification of the equation with respect to the function F in the special case where the function F and the transformations of the variables t and x are assumed to be independent of c. We show that, under such constraints for the transformation and the family of equations, the maximum possible symmetry algebra is eight-dimensional, which corresponds to an equation with a linear function F.