The propagation of disturbances through a non-ideal medium, where of relati
vely undistorted waves is used to study the situations when the disturbance
amplitude is finite, arbitrarily small, and not so small. The effects of t
he solid particles and that of the non-planar wave front configuration on t
he distortion attenuation, and shock formation of propagating pulses are de
scribed in detail. The resonant multiwave theory of weakly nonlinear geomet
rical optics, which takes into consideration systems where many waves coexi
st and interact with one another resonantly, is applied to derive transport
equations for signals having all possible wave modes which are mutually co
upled and interact resonantly among themselves.