  The propagation of intense acoustic waves in a one-dimensional phononic
crystal is studied. The medium consists in a structured fluid, formed by a
periodic array of fluid layers with alternating linear acoustic properties and
quadratic nonlinearity coefficient. The spacing between layers is of the order
of the wavelength, therefore Bragg effects such as band-gaps appear. We show
that the interplay between strong dispersion and nonlinearity leads to new
scenarios of wave propagation. The classical waveform distortion process
typical of intense acoustic waves in homogeneous media can be strongly altered
when nonlinearly generated harmonics lie inside or close to band gaps. This
allows the possibility of engineer a medium in order to get a particular
waveform. Examples of this include the design of media with effective (e.g.
cubic) nonlinearities, or extremely linear media (where distortion can be
cancelled). The presented ideas open a way towards the control of acoustic wave
propagation in nonlinear regime.
