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) Alfvenic 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 rho become anticorrelated on average, If the mean magnetic field is allowed to decrease in time, the point where the transverse magnetic fluctuation amplitude delta B-T is greater than the mean field B-0 is not special, and large values of delta B-T/B-0 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 Alfven 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 radiation 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 delta B and increasingly quasi-pressure balanced compressive fluctuations, as observed, and in which the dissipation and ''saturation'' at delta B-T/B-0 approximate to 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 of Alfven waves and demonstrate the existence of previously unreported types of quasi-steady MHD states.