- A self-consistent system of the Boltzmann equation and the Poisson equation is used to study the-dynamical evolution of Saturn's main A, B, and C rings. The, theory, as applied to the Saturnian ring system, predicts for several features, such as numerous irregular density wakes, with size and spacing between them of the order 4pirho approximate to 2pih, where rho is the mean epicycle radius of, the particle and h is the typical thickness of the system under study. In Saturn's rings, rho less than or similar to 10 m. Computer N-body experiments are desribed which test the validities of the theory. Use of the 112-processor SGI Origin 2000 supercomputer is enabled us to make long runs using a large number of particles in the direct simulation code and thus simulate phenomena not. previously studied numerically. We predict that forthcoming in 2004 Cassini spacecraft high-resolution images will reveal this recurrent fine-scale similar to 100 in or so structure in low and moderately high optical depth regions of the rings.