Self-similiar solutions of the two-dimensional non-stationary 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.