Evolution of weak discontinuity in a van der Waals gas

In this article, the Lie symmetries analysis that leaves the system of partial differential equations (PDEs), governed by the one dimensional unsteady flow of an isentropic, inviscid and perfectly conducting compressible fluid obeying the van der Waals equation of state invariant, is presented. Using these symmetries the governing system of PDEs is reduced into system of ordinary differential equations (ODEs). Then the reduced system of ODEs is solved analytically which in turn produces the exact solution for the governing PDEs. Further, the influence of the van der Waals excluded volume in the behavior of evolution of weak discontinuity is studied extensively.