Similarity solutions for the two-dimensional nonstationary ideal MHD equations

Abstract

A similarity analysis of the non-linear two-dimensional non-stationary ideal MHD equations is presented. In the case of a magnetic field perpendicular to the isentropic motion of the plasma, the authors establish the complete Lie algebra of infinitesimal symmetries. 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, they obtain systems of ordinary differential equations for similarity solutions of the MHD equations considered.