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 4πρ ≈ 2πh, where ρ is the mean epicycle radius of the particle and h is the typical thickness of the system under study. In Saturn's rings, ρ ≲ 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 ∼ 100 m or so structure in low and moderately high optical depth regions of the rings.