  The Alfv\'en waves are fundamental wave phenomena in magnetized plasmas and
the dynamics of Alfv\'en waves are governed by a system of nonlinear partial
differential equations called the MHD system. In this paper, we study the
rigidity aspect of the scattering problem for the MHD equations: We prove that
the Alfv\'en waves must vanish if their scattering fields vanish at infinities.
The proof is based on a careful study of the null structure and a family of
weighted energy estimates.
