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

*2021, Volume 26, Number 6, pp. 692-699*

Author(s):

**Bogoyavlenskij O. I., Peng Y.**

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.

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