Similarity solutions for the two-dimensional non-stationary ideal MHD equations

A similarity analysis of the non-linear two-dimensional non-stationary ideal magnetohydrodynamic (MHD) equations is presented. In the case of a magnetic field perpendicular to the isentropic motion of the plasma, the complete Lie algebra of infinitesimal symmetries is given. The laws of conservation are mentioned. The similarity method for partial differential equations as a procedure for reducing the number of independent variables is applied repeatedly. Finally systems of ordinary differential equations are obtained for similarity solutions of the MHD equations considered. (author)