Symmetry analysis of the Grad-Shafranov equation

Lie's technique of computing symmetries of differential equations is applied to a specific case of the Grad-Shafranov equation. The case considered contains the majority of exact solutions from literature. The full symmetry group is computed and new group-invariant solutions are obtained from these symmetries. The basic results and methods behind this technique are given to allow the reader who is unfamiliar with the subject to use the results given in this paper. Several plots of the level sets or flux surfaces of the new solutions are given.