The non-self-similar Riemann solutions to a compressible fluid described by the generalized Chaplygin gas

In this paper, we concern with the Riemann solutions to a compressible fluid described by the generalized Chaplygin gas, where the external force is a constant. Five exact solutions are given. In particular, the delta shock wave with a Dirac delta function in density and internal energy occurs in some solutions, and the location, velocity and weights of the delta shock wave are explicitly described. It is also noticed that because of the effect of the external force, these exact solutions are not self-similar.