Compressible MHD simulations in one dimension with three-dimensional vectors are used to investigate a number of processes relevant to problems in interplanetary physics. The simulations indicate that a large-amplitude nonequilibrium (e.g., linearly polarized) Alfv¿nic wave, which always starts with small relative fluctuations in the magnitude B of the magnetic field, typically evolves to flatten the magnetic profile in most regions. Under a wide variety of conditions B and the density &rgr; become anticorrelated on average. If the mean magnetic field is allowed to decrease in time, the point where the transverse magnetic fluctuation amplitude ΔBT is greater than the mean field B0 is not special, and large values of ΔBT/B0 do not cause the compressive thermal energy to increase remarkably or the wave energy to dissipate at an unusually high rate. Nor does the ''backscatter'' of the waves that occurs when the sound speed is less than the Alfv¿n speed result, in itself, in substantial energy dissipation, but rather primarily in a phase change between the magnetic and velocity fields. For isolated wave packets the backscatter does not occur for any of the parameters examined; an initial radation of acoustic waves away from the packet establishes a stable traveling structure. Thus these simulations, although greatly idealized compared to reality, suggest a picture in which the interplanetary fluctuations should have small ΔB and increasingly quasi-pressure balanced compressive fluctuations, as observed, and in which the dissipation and ''saturation'' as ΔBT/B0≈1 required by some theories of wave acceleration of the solar wind do not occur. The simulations also provide simple ways to understand the processes of nonlinear steepening and backscattering of Alfv¿n waves and demonstrate the existence of previously unreported types of quasi-steady MHD states. ¿ American Geophysical Union 1995