Embedded delta shocks

In 1977 Korchinski presented a new type of shock discontinuity in conservation laws. These singular solutions were coined δ-shocks since there is a time dependent Dirac delta involved. A naive description is that such δ-shock is of the overcompressive type: a single shock wave belonging to both families, the four characteristic lines of which impinge into the shock itself. In this work, we open the fan of solutions by studying two-family waves without intermediate constant states but possessing central rarefactions or comprising δ-shocks.