Delta shock wave solution for a symmetric Keyfitz-Kranzer system

The Riemann solutions for a symmetric Keyfitz-Kranzer system are constructed explicitly, in which some singular hyperbolic waves are discovered such as the delta shock wave and the composite wave JR. The global solutions to the double Riemann problem are achieved when the delta shock wave is involved. It is shown that a delta shock wave is separated into a delta contact discontinuity and a shock wave during the process of constructing solutions.