Abstract
In this paper, we analytically investigated the possibility of parametric resonance of acoustic and optical phonons. We obtained a general dispersion equation for parametric amplification and transformation of phonons. The dispersions of the resonant acoustic phonon modes and the threshold amplitude of the field for acoustic phonon parametric amplification are obtained. The parametric amplification for acoustic phonons in a doped semiconductor superlattice can occur under the condition that the amplitude of the external electromagnetic field is higher than the threshold amplitude.