= Isothermal perpendicular magnetosonic simple wave
{title2=$B_y=K\rho,\ c_f^2=c_s^2+K^2\rho/\mu_0$}
With $B_x=0$, a fast <simple wave in magnetohydrodynamics> has constant $u_y$ and $B_y/\rho=K$. Its longitudinal velocity satisfies $du_x/d\rho=\pm c_f/\rho$, and $\rho_t+(u_x\pm c_f)\rho_x=0$. Along this state curve the speed derivative is $\pm[c_f/\rho+K^2/(2\mu_0c_f)]$, which is nonzero. Compressive profiles therefore exhibit <shock formation by characteristic intersection>, unlike a <linearly degenerate characteristic field>.
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