  We study propagating Alfven waves by solving the time-dependent equations of
magnetohydrodynamics (MHD) in one dimension numerically. In a homogeneous
medium the circularly polarized Alfven wave is an exact solution of the ideal
MHD equations, and therefore it does not suffer from any dissipation. A
high-amplitude linearly polarized Alfven wave, on the other hand, steepens and
form current sheets, in which the Poynting flux is lost. In a stratified
medium, however, a high-amplitude circularly polarized Alfven wave can also
lose a significant fraction of its Poynting flux.
