Nonlinear couplings among kinetic Alfv en waves are investigated for a three-component plasma consisting of electrons, protons, and heavy ions. The parametric instability is investigated, and the growth rate is obtained. In the kinetic regime, the growth rate for the parallel decay instability increases with the heavy ion content, but the growth rate for the reverse decay is independent of the latter since the perpendicular wavelength is much larger than the ion gyroradius. It decreases with the heavy ion content when the perpendicular wavelength is of the order of the ion gyroradius. It is also found that in the short perpendicular wavelength limit, the growth rate is only weakly affected by the heavy ions. On the other hand, in the inertial regime, for both parallel and reverse decay cases, the growth rate decreases as the number of heavy ions becomes large. V C 2013 American Institute of Physics. [http://dx.