Simple waves and pressure delta waves for a Chaplygin gas in two-dimensions

We present two new types of self-similar solutions to the Chaplygin gas model in two space dimensions:Simple waves and pressure delta waves, which are absent in one space dimension, butappear in the solutions to the two-dimensional Riemann problems. A simple wave is a flow in aphysical region whose image in the state space is a one-dimensional curve. The solutions to theinteraction of two rarefaction simple waves are constructed. Comparisons with polytropic gasesare made. Pressure delta waves are Dirac type concentration in the pressure variable,or impulses of the pressure on discontinuities. They appear in the study of Riemann problemsof four rarefaction shocks. This type of discontinuities and concentrations are different fromdelta waves for the pressureless gas flow model, for which the delta waves are associated withconvection and concentration of mass. By re-interpreting the terms in the Chaplygin gas system into newforms we are able to define distributional solutions that include the pressure delta waves.Generalized Rankine-Hugoniot conditions for pressure delta waves are derived.