# Exact Solutions to the Beltrami Equation with a Non-constant \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha({\bf x})$$\end{document}

Exact Solutions to the Beltrami Equation with a Non-constant \documentclass[12pt]{minimal}... Infinite families of new exact solutions to the Beltrami equationwith a non-constant \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\alpha({\bf x})$$\end{document} 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Regular and Chaotic Dynamics Springer Journals

# Exact Solutions to the Beltrami Equation with a Non-constant \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha({\bf x})$$\end{document}

, Volume 26 (6) – Nov 1, 2021
8 pages

/lp/springer-journals/exact-solutions-to-the-beltrami-equation-with-a-non-constant-0AgM5WtndZ
Publisher
Springer Journals
ISSN
1560-3547
eISSN
1468-4845
DOI
10.1134/s1560354721060071
Publisher site
See Article on Publisher Site

### Abstract

Infinite families of new exact solutions to the Beltrami equationwith a non-constant \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\alpha({\bf x})$$\end{document} 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.

### Journal

Regular and Chaotic DynamicsSpringer Journals

Published: Nov 1, 2021

Keywords: ideal fluid equilibria; force-free plasma equilibria; Klein – Gordon equation; Yukawa potential; Beltrami equation

### References

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