  Local solutions of Riemann problems for quadratic systems of two conservation
laws were constructed in the geometric context. In this paper, also for
quadratic systems, we decompose the characteristic and sonic' surfaces in their
slow and fast components.These decompositions allow to decompose the wave
manifold in regions called admissible region and non admissible region.There
are admissible regions having local shock curve arcs and non local shock curve
arcs. Such regions are important to construct non local solutions of Riemann
problems. Our study is restricted to the symmetric Case IV in the
Sheaffer-Shearer classification.

Analysis of PDEs