Equivalence group and exact solutions of the system of nonhomogeneous Boltzmann equations

The article is devoted to the construction of exact solutions of a system of two Boltzmann kinetic inhomogeneous equations. The source functions in the equations simulate the integrals of double and triple inelastic collisions. An extension of the Lie group L4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_4$$\end{document} admitted by the system of homogeneous equations is carried out. In the present paper, the Lie group L4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_4$$\end{document} is considered as an equivalence group for inhomogeneous equations. Conditions are found under which transformations from the extended group vanish the sources in the transformed equations. A class of sources linear in the distribution functions is obtained for which the generalized Bobylev–Krook–Wu solutions hold in explicit form. Physical interpretations are also presented.