We use a method based on a separation of variables for solving
a first order partial differential equations system, using a very
simple modelling of MHD. The method consists in introducing three
unknown variables Φ1, Φ2, Φ3 in addition
to the time variable t and then in searching a solution which
is separated with respect to Φ1 and t only. This is
allowed by a very simple relation, called a “metric separation
equation”, which governs the type of solutions with respect to
time. The families of solutions for the system of equations thus
obtained, correspond to a radial evolution of the fluid. Solving
the MHD equations is then reduced to find the transverse component
H∑ of the magnetic field on the unit sphere Σ by
solving a non linear partial equation on Σ. Thus, we generalize
ideas of Courant-Friedrichs [7] and of Sedov [11],
on dimensional analysis and self-similar solutions.