Simple wave in magnetohydrodynamics (source code)

= Simple wave in magnetohydrodynamics
{title2=$A_x\mathbf U_q=v(q)\mathbf U_q$}

An ideal-MHD simple wave traces a one-parameter state-space curve whose tangent is a right <eigenvector> of the characteristic matrix. Its parameter obeys $q_t+v(q)q_x=0$ and its characteristic speed obeys the <Inviscid Burgers equation>. <Nonlinear Alfvén waves> are a linearly degenerate example.