Abstract
A 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.
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