  Measurements and simulations of inertial compressive turbulence in the solar
wind are characterized by anti-correlated magnetic fluctuations parallel to the
mean field and density structures. This signature has been interpreted as
observational evidence for non-propagating pressure balanced structures (PBS),
kinetic ion acoustic waves, as well as the MHD slow-mode. Given the high
damping rates of parallel propagating compressive fluctuations, their ubiquity
in satellite observations is surprising, and suggestive of a local driving
process. One possible candidate for the generation of compressive fluctuations
in the solar wind is Alfv\'en wave parametric instability. Here we test the
parametric decay process as a source of compressive waves in the solar wind by
comparing the collisionless damping rates of compressive fluctuations with the
growth rates of the parametric decay instability daughter waves. Our results
suggest that generation of compressive waves through parametric decay is
overdamped at 1 AU, but that the presence of slow-mode like density
fluctuations is correlated with the parametric decay of Alfv\'en waves.
