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.