In this article, we study the nonlinear resistive magnetohydrodynamic (MHD) equations based on the symmetry analysis. Through the process, the symmetry generators and their corresponding symmetry group of transformations are obtained. In order to determine the group-invariant solutions using the symmetry generators and invariants of the Lie algebra, a two-dimensional optimal system of subalgebras is determined. Subsequently, for each member of the optimal system, the symmetry variables are derived, leading to the reduction of the MHD equations to a system of linear ordinary differential equations. By solving the symmetry reductions, some new group-invariant solutions for the MHD equations are found, including spiral, circular, and hyperbolic types of flow. Moreover, we address the earlier studies and provide a comparison with their results.
Mondal et al. (Sun,) studied this question.