The Boltzmann equation for persistent scattering models

The nonlinear Boltzmann equation (N.L.B.E.) for the persistent scattering model of Futcher and Hoare can be completely solved by a straightforward application of the Fourier transform method for general Maxwell models. It then follows: (i) that the N.L.B.E. for this model possesses the Bobylev-Krook-Wu mode as a special similarity solution; (ii) that all solutions lying inside a certain Hilbert space can be given in the form of an expansion in eigenfunctions of the linearized Boltzmann equation, the coefficients of which can be determined recursively; (iii) that the Cornille-Gervois solutions-lying outside the above Hilbert space-can be constructed not only for the persistent scattering model, but also for a general class of Maxwell models.