  The Kompaneets theory of photon kinetic evolution due to the Compton effect
in the absence of absorption and emission is extended to the case of the Vlasov
plasma wave oscillations. Under the assumption that the electron distribution
function at equilibrium is perturbed by a solution of the linearised Vlasov
equation in the long-wavelength limit, a solution of the Kompaneets kinetic
equation for the photon distribution function is found and discussed.
