Nonlinear Landau Damping of Alfvén Waves

It is shown that large-amplitude linearly or elliptically polarized Alfvén waves propagating parallel to ${\overrightarrow{\mathrm{B}}}_0$ can be dissipated by nonlinear Landau damping. The damping is due to the longitudinal electric field associated with the ion sound wave which is driven (in second order) by the Alfvén wave. The damping rate can be large even in a cold plasma ($\beta \ll 1$, but not zero), and the mechanism which we propose may be the dominant one in many plasmas of astrophysical interest.