Exact Solutions to the Beltrami Equation with a Non-constant $\alpha (\mathbf{x})$

Infinite families of new exact solutions to the Beltrami equation with a non-constant $\alpha (\mathbf{x})$ are derived. Differential operators connecting the steady axisymmetric Klein – Gordon equation and a special case of the Grad – Shafranov equation are constructed. A Lie semi-group of nonlinear transformations of the Grad – Shafranov equation is found.