  A wave equation, that governs finite amplitude acoustic disturbances in a
thermoviscous Newtonian fluid, and includes nonlinear terms up to second order,
is proposed. In contrast to the model known as the Kuznetsov equation, the
proposed nonlinear wave equation preserves the Hamiltonian structure of the
fundamental fluid dynamical equations in the non-dissipative limit. An exact
traveling front solution is obtained from a generalized traveling wave
assumption. This solution is, in an overall sense, equivalent to the Taylor
shock solution of the Burgers equation. However, in contrast to the Burgers
equation, the model equation considered here is capable to describe waves
propagating in opposite directions. Owing to the Hamiltonian structure of the
proposed model equation, the front solution is in agreement with the classical
Rankine-Hugoniot relations. The exact front solution propagates at supersonic
speed with respect to the fluid ahead of it, and subsonic speed with respect to
the fluid behind it, similarly to the fluid dynamical shock. Linear stability
analysis reveals that the front is stable when the acoustic pressure belongs to
a critical interval, and is otherwise unstable. These results are verified
numerically. Studies of head-on colliding fronts demonstrate that the front
propagation speed changes upon collision.
