On group classification of the spatially homogeneous and isotropic Boltzmann equation with sources

In Nonenmacher (1984) [1] an admitted Lie group of transformations for the spatially homogeneous and isotropic Boltzmann equation with sources was studied. In fact, the author is Nonenmacher (1984) [1] considered the equation for a generating function of the power moments of the Boltzmann equation solution. However, this equation is still a non-local partial differential equation, and this property was not taken into account there. In the present paper the admitted Lie group of this equation is studied, using our original method developed for group analysis of equations with non-local operators (Grigoriev and Meleshko, 1986; Meleshko, 2005; Grigoriev et al., 2010 [2], [3] and [4]). The Lie groups obtained are compared with Nonenmacher (1984) [1]. The deficiency of Nonenmacher (1984) [1] is corrected.

► The spatially homogeneous and isotropic Boltzmann equation with sources is studied. ► Complete group classification of the equation for the generating moment function is presented. ► The method developed for group analysis of equations with non-local operators is used. ► Comparisons with previous results and their corrections are performed.