A phase-space asymptotic approach to wave propagation in homogeneous dispersive media is discussed which has several advantages by comparison to conventional techniques, such as the stationary phase method, ordinary ray tracing, etc. This approach, which is based on the wave-kinetic theory, ^7/8 is used to examine in detail three types of one-dimensional canonic dispersive media: cubic, quintic and sinusoidal. The analysis is also carried out using standard Fourier techniques for comparison purposes. Lastly, a link is made between the wave-kinetic method and integrals appearing in catastrophe theory. ^10/11 / M.S.