  The Riemann problem of one dimensional shallow water equations with
discontinuous topography has been constructed recently. The elementary waves
include shock waves, rarefaction waves, and the stationary wave. The stationary
wave appears when the water depth changes, especially when there exists a
bottom step. In this paper, we are mainly concerned with the interaction
between a stationary wave with either a shock wave or a rarefaction wave. By
using the characteristic analysis methods, the evolution of waves is described
during the interaction process. The solution in large time scale is also
presented in each case. The results may contribute to research on more
complicated wave interaction problems.
