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