The formalism of Borderies, Goldreich, and Tremaine (1984), as simplified by Shu and Stewart (1985), is used to develop a theory for the viscous damping of nonlinear density waves in particulate disks of moderate collision frequency. The specific application is to Saturn's rings, but the development is general enough to allow application to a wider context (e.g., to gas clouds in a spiral galaxy). A Krook formulation is used rather than a Boltzmann formulation to treat the statistical effects of inelastic collisions. Issues that have arisen as a result of the study include a self-induced Q barrier in the first wavelength or two of the Mimas 5:3 density wave train and the surprising discovery that Saturn's B ring may behave almost as a superfluid, with hardly any viscous losses.