  The problem of propagating nonlinear acoustic waves is considered; the
solution to which, both with and without damping, having been obtained to-date
starting from the Navier-Stokes-Duhem equations together with the continuity
and thermal conduction equation. The novel approach reported here adopts
instead, a discontinuous Lagrangian approach, i.e. from Hamilton's principle
together with a discontinuous Lagrangian for the case of a general viscous
flow. It is shown that ensemble averaging of the equation of motion resulting
from the Euler-Lagrange equations, under the assumption of irrotational flow,
leads to a weakly nonlinear wave equation for the velocity potential: in effect
a generalisation of Kuznetsov's well known equation with an additional term due
to thermodynamic non-equilibrium effects.
