The generation of plasma density fluctuations by nonlinear Alfve´n waves is considered. Of particular interest is the modification to the ‘‘static approximation,’’ describing the relationship between wave intensity and plasma density, when the Alfve´n wave packet is rapidly steepening. The study concentrates on a forced wave equation for the plasma density, which yields the static approximation in a select approximation. An analytic solution to this equation is obtained for a reasonable model of a steeping wave packet. The principal results are (a) the static approximation should give a surprisingly robust description of the coupling between Alfve´n wave intensity and plasma density, (b) departures of the plasma density perturbation from the static approximation result are determined by a parameter that is a simple function of the wave amplitude and plasma &bgr;, (c) for rapidly evolving wave packets, the position of maximum density change is displaced from that of maximum wave intensity, and (d) the magnitude of the density fluctuation will not be much different than the static approximation estimate of (b2/B20)n0.