Nonlinear dynamics of directed acoustic waves in stratified and homogeneous liquids and gases with~arbitrary equation of state

A method of separating one-dimensional disturbances into components propagating upwards and downwards and the stationary one in a stratified medium was developed. The system of equations is split into three coupled nonlinear equations of interacting components. Weak nonlinear evolution formulae for the directed and stationary components of a medium with an arbitrary equation of state were obtained. The wave components treated by the numerical calculations keep their propagation direction, even for quite large initial amplitudes. The results of the numerical simulation are presented. The examples demonstrate a nonlinear evolution of the wave propagating downwards for both the models of the atmosphere: the exponentially stratified model and the homogeneous one.