  We study the properties of classical and quantum compacton chains by means of
extensive numerical simulations. Such chains are strongly nonlinear and their
classical dynamics remains chaotic at arbitrarily low energies. We show that
the collective excitations of classical chains are described by sound waves
which decay rate scales algebraically with the wave number with a generic
exponent value. The properties of the quantum chains are studied by the quantum
Monte Carlo method and it is found that the low energy excitations are well
described by effective phonon modes with the sound velocity dependent on an
effective Planck constant. Our results show that at low energies the quantum
effects lead to a suppression of chaos and drive the system to a
quasi-integrable regime of effective phonon modes.
