We study both theoretically and experimentally the nonlinear interaction be
tween an intense surface acoustic wave and a two-dimensional electron plasm
a in semiconductor-piezocrystal hybrid structures. The experiments on hybri
d systems exhibit strongly nonlinear acoustoelectric effects. The plasma tu
rns into moving electron stripes, the acoustoelectric current reaches its m
aximum, and the sound absorption strongly decreases. To describe the nonlin
ear phenomena, we develop a coupled-amplitude method for a two-dimensional
system in the strongly nonlinear regime of interaction. At low electron den
sities the absorption coefficient decreases with increasing sound intensity
, whereas at high electron density the absorption coefficient is not a mono
tonous function of the sound intensity. High-harmonic generation coefficien
ts as a function of the sound intensity have a nontrivial behavior. Theory
and experiment are found to be in a good agreement.