  We study the evolution of non-linear circularly polarised Alfven waves by
solving numerically the time-dependent equations of magnetohydrodynamics (MHD)
in one dimension. We examine the behaviour of the waves and find that different
physical mechanisms are relevant in different ranges of beta. In a low beta
plasma the wave may undergo a parametric decay. This is because the wave
excites a density enhancement that travels slower than the wave itself and thus
interacts with the wave. When beta is greater or equal to one the density
enhancement does not interact with the wave and no decay takes place, instead
the Alfven wave is reflected against the density enhancement. The reflection
zone propagates with the speed 1/n of the Alfven speed. Because of that the
magnetic flux is conserved which results in an amplification of the oscillating
magnetic field by a factor 1/n. We find that n depends on beta, and that in
particular it is less or equal to one for values of beta ~ 1 and is greater or
equal to one for beta >> 1. We discuss the relevance of these mechanisms to the
acceleration of the solar wind, and the triggering of MHD turbulence in the
polar wind region. In particular these simulations can explain the presence of
inward propagating Alfven waves in the solar corona.
