In a recent work I have derived a higher order nonlinear acoustic equation for the case of weak dissipation. It will be published as

On the Kuznetsov Equation and Higher Order Nonlinear Acoustics Equations,
15th International Symposium in Nonlinear Acoustics, Göttingen 1999

Abstract:
Compressible flow of a Newtonian fluid is studied in the fully nonlinear
approximation and to lowest order in the dissipation, neglecting cross terms
MaKn (Ma is the Mach number, Kn the Knudsen number). An initially
vorticity free flow is shown to remain vorticity free. An acoustic equation
is derived. If Kn=Ma^n, the equation obtained is correct to order Ma^n.
- For n=1, it reduces to the Kuznetsov equation
 

Last updated November 29, 1999.