Soluble Boltzmann equations for internal state and Maxwell models II. Similarity solutions

Abstract

We continue our study of the nonlinear Boltzmann equation for “diffuse” binary scattering between subsystems in a microcanonical ensemble. Exact similarity solutions of Bobylev-Krook-Wu type are found for systems of arbitrary dimensionality and in both continuous and discrete state variables. Additional similarity solutions are also derivable as expansions in Laguerre or Meixner polynomials, the required Fourier coefficients following from algebraic recursion relations.