Exact nonlinear solutions for three-dimensional Alfvén-wave packets in relativistic magnetohydrodynamics

We show that large-amplitude, non-planar, Alfvén-wave (AW) packets are exact nonlinear solutions of the relativistic magnetohydrodynamic equations when total magnetic-field strength in local fluid rest frame ( $b$ ) is a constant. derive analytic expressions relating components fluctuating velocity and magnetic field. also these constant- AWs propagate without distortion at Alfvén never steepen into shocks. These findings observed abundance solar wind suggest such waves may be present outflows around compact astrophysical objects.