Family of self-similiar solutions of the nonstationary ideal MHD equations

The aim of the paper is to construct the self-similiar solutions of the non-steady ideal MHD equations. It is assumed that the flow is axisymmetric, the matter has only radial component in the poloidal plane. 2D nonstationary problem is reduced to the Grad–Shafranof equation solution. As a result it is shown that there are the family of self-similiar solutions and they depend on adiabatic exponent.