Autotransforms for Some Differential Equations and Their Physical Applications

Oleg I. Bogoyavlenskij, Yuyang Peng

Department of Mathematics and Statistics, Queen’s University, Kingston, K7L 3N6 ON, Canada

Abstract: General constructions of differential equations with autotransforms are presented. Differential operators connecting a linear case of the Grad – Shafranov equation and the axisymmetric Helmholtz equation are found. Infinite families of exact solutions to both equations are derived.

Keywords: differential operators, Grad – Shafranov equation, force-free plasma equilibria, exact solutions, Helmholtz equation.

MSC: 35Q35

Received: 09.07.2020
Accepted: 07.09.2020

Language: English

DOI: 10.1134/S1560354720060040

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