  We have developed a three-dimensional manifold that greatly facilitates
finding the solution of Riemann Problems. Here, we illustrate this feature in
the context of a system of two conservation laws with quadratic flux functions
and their perturbations. Points in this manifold represent potential shock
waves, hence its name, wave manifold. We calculate and display graphically
significant surfaces within this manifold. We also construct shock,
rarefaction, and composite curves, combine them to form wave curves, and
intersect them with the surfaces to solve Riemann problems. This manifold is
divided into regions. Using these non-overlapping three-dimensional regions,
rather than overlapping two-dimensional regions, dramatically simplifies the
search for Riemann solutions. We present the solution of the Riemann Problems
for a few illustrative cases.
