  We derive a number of solution for one-dimensional dynamics of relativistic
magnetized plasma that can be used as benchmark estimates in relativistic
hydrodynamic and magnetohydrodynamic numerical codes.
  First, we analyze the properties of simple waves of fast modes propagating
orthogonally to the magnetic field in relativistically hot plasma. The magnetic
and kinetic pressures obey different equations of state, so that the system
behaves as a mixture of gases with different polytropic indices. We find the
self-similar solutions for the expansion of hot strongly magnetized plasma into
vacuum.
  Second, we derive linear hodograph and Darboux equations for the relativistic
Khalatnikov potential, which describe arbitrary one-dimensional isentropic
relativistic motion of cold magnetized plasma and find their general and
particular solutions. The obtained hodograph and Darboux equations are very
powerful: system of highly non-linear, relativistic, time dependent equations
describing arbitrary (not necessarily self-similar) dynamics of highly
magnetized plasma reduces to a single linear differential equation.
