  Dynamic plasma equilibrium systems, both in isotropic and anisotropic
framework, possess infinite-dimensional Lie groups of point symmetries, which
depend on solution topology and lead to construction of infinite families of
new physical solutions.
  By performing the complete classification, we show that in the static
isotropic case no infinite point symmetries arise, whereas static anisotropic
plasma equilibria still possess a Lie group of symmetries depending on one free
function defined on the set of magnetic field lines. The finite form of the
symmetries is found and used to obtain new exact solutions. We demonstrate how
anisotropic axially- and helically-symmetric equilibria are obtained using
conventional Grad-Shafranov and JFKO equations.
  A recently developed multifunctional automated Maple-based software package
for symmetry and conservation law analysis is presented and used in this work.
