Nonlinear Alfvén wave
= Nonlinear Alfvén wave
{title2=$v_s=u_x+sB_x/\sqrt{\mu_0\rho}$}
A finite-amplitude ideal-MHD Alfvén wave can rotate the transverse <magnetic field> at constant magnitude, with constant <mass density>, <pressure> and longitudinal components. Its transverse velocity obeys $\mathbf u_\perp=\mathbf C-s\mathbf B_\perp/\sqrt{\mu_0\rho}$ and its speed is constant along the wave. The constant <magnetic pressure> prevents compressive acceleration.