One-dimensional ultrasound propagation at stratified gas: Gross-Jackson   model
  The system of hydrodynamic-type equations, derived by two-side distribution function for a stratified gas in gravity field is applied to a problem of ultrasound. The theory is based on Gross-Jackson kinetic equation, which solution is built by means of locally equilibrium distribution function with different local parameters for molecules moving "up"and "down". The linearized version of the obtained system is studied and compared with other results and experiments at arbitrary Knudsen numbers. The problem of a generation by a moving plane in a rarefied gas is explored. The WKB solutions for ultrasound in a stratified medium are constructed in explicit form, evaluated and plotted. 
Sergey Leble, Maxim Solovchuk