  Large-amplitude Alfv\'en waves are ubiquitous in space plasmas and a main
component of magnetohydrodynamic (MHD) turbulence in the heliosphere. As pump
waves they are prone to parametric instability by which they can generate
cyclotron and acoustic daughter waves. Here we revisit a related process within
the framework of the multi-fluid equations for a plasma consisting of many
species. The nonlinear coupling of the Alfv\'en wave to acoustic waves is
studied, and a set of compressive and coupled wave equations for the transverse
magnetic field and longitudinal electric field is derived for waves propagating
along the mean-field direction. It turns out that slightly compressive Alfv\'en
waves exert, through induced gyro-radius and kinetic-energy modulations, an
electromotive force on the particles in association with a longitudinal
electric field, which has a potential that is given by the gradient of the
transverse kinetic energy of the particles gyrating about the mean field. This
in turn drives electric fluctuations (sound and ion-acoustic waves) along the
mean magnetic field, which can nonlinearly react back on the transverse
magnetic field. Mutually coupled Alfv\'en-cyclotron-acoustic waves are thus
excited, a nonlinear process that can drive a cascade of wave energy in the
plasma and may generate compressive microturbulence. These driven electric
fluctuations might have consequences for the dissipation of MHD turbulence and,
thus, for the heating and acceleration of particles in the solar wind.
