Litvinenko, Yuri E.2010-11-302010-11-302010Litvinenko, Y.E. (2010). A similarity reduction of the Grad-Shafranov equation. Physics of Plasmas, 17(7), 074502.https://hdl.handle.net/10289/4828A direct method for finding similarity reductions of partial differential equations is applied to a specific case of the Grad–Shafranov equation. As an illustration of the method, the frequently used Solov’ev equilibrium is derived. The method is employed to obtain a new family of exact analytical solutions, which contain both the classical and nonclassical group-invariant solutions of the Grad–Shafranov equation and thus greatly extends the range of the available analytical solutions. All the group-invariant solutions based on the classical Lie symmetries are shown to be particular cases in the new family of solutions.application/pdfenCopyright (2010) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.mathematicsmathsGrad–Shafranov equationJournal Article10.1063/1.3456519