Solitonic solutions for the generalized two-velocity Boltzmann equation

We obtain solitonic solutions for an inhomogeneous model Boltzmann equation which describes a two velocity one-dimensional gas diffusing in a background when remotion and regeneration processes are allowed. These solutions are obtained as a series expansion in the similarity variable, whose coefficients can be exactly found within a recursive scheme. The solitons describe a shape-preserving distribution function which approaches a stationary value as time elapses. The particular case in which remotion and regeneration events are neglected can be solved in a closed form.