Equations are a 2-D partiell hyperbolic nonlinear PDE System of Equations in
preserving-form

describing nonlinear acoustic waves in any kind of media.

System can be extracted out of Euler Equations of Hydrodynamics by assuming
some acoustic stuff.

It cant be solved analytically, but is very convinient for modelling nonlinear
acoustics on a digital

computer, using a modern adapted finite differenzies Algorithm in time domain.

Preserving form garanties, proofed by theorem of LAX WENDROFF. a convergation
of the

numerical solution to a weak physical solution, fullfiling Entropie condition,
and therefore excluding

nonphysical solutions. ( consistent numerical Algorithm as trivial condition
)

A powerful FDTD Algorithm for hyperbolic eqation systems is for example

Dispersion-Relation-Preserving-Algorithm of Tam:

Including central optimized ( both in time and wavenumber ) Differential - Operators
of 4. th order,

together with a well tuned , in time and wavenumber optimized , Integraloperatorof
4. th Order

(Adams Bashford), especially designed for nonlinear hyperbolc Systemes in Preservingform:.

Integraloperator ist implemented onesided. Therefore algorithm can be computed
explizit.

Equations on my startpage containing additional a special transformation of
room and time variables.