  We give a Lax description for the system of polytropic gas equations. The
special structure of the Lax function naturally leads to the two infinite sets
of conserved charges associated with this system. We obtain closed form
expressions for the conserved charges as well as the generating functions for
them. We show how the study of these generating functions can naturally lead to
the recursion relation between the conserved quantities as well as the higher
order Hamiltonian structures.
