  In this paper, we characterize a class of solutions to the unsteady
2-dimensional flow of a van der Waals fluid involving shock waves, and derive
an asymptotic amplitude equation exhibiting quadratic and cubic nonlinearities
including dissipation and diffraction. We exploit the theory of nonclassical
symmetry reduction to obtain some exact solutions. Because of the
nonlinearities present in the evolution equation, one expects that the wave
profile will eventually encounter distortion and steepening which in the limit
of vanishing dissipation culminates into a shock wave; and once shock is
formed, it will propagate by separating the portions of the continuous region.
Here we have shown how the real gas effects, which manifest themselves through
the van der Waals parameters $\tilde{a}$ and $\tilde{b}$ influence the wave
characteristics, namely the shape, strength, and decay behavior of shocks.
