Similarity solutions of 2-velocity models of the extended Boltzmann equation

We analyse, in the frame of the extended kinetic theory, travelling wave solutions for the 2-velocity discrete models of the Boltzmann equation. The extended formalism allows for absorption, creation, due to scattering with a background as well as for the existence of external sources of test particles. As a preliminary step, existence, uniqueness and stability of equilibrium states are investigated. We find new, soliton-like solutions, and analyse their dependence of the physical parameters of the model.