  I show that when non-linearities are taken into account the Landau theory of
Fermi liquids predicts the existence of hyperbolic waves in fermionic systems.
The zero sound is described by a infinite set of coupled non-linear partial
differential equations, one for each harmonic of oscillation of the Fermi
surface. When just a few harmonics are included it is possible to describe the
dynamics of the first sound in a very simple way. These results lead to the
interesting experimental possibility of having non-linear effects in quantum
liquids. In particular I discuss the problem of generation of second harmonic
in a Fermi system.
