Symmetries, weak symmetries and related solutions of the Grad-Shafranov equation

Abstract

We discuss a new family of solutions of the Grad--Shafranov (GS) equation that describe D-shaped toroidal plasma equilibria with sharp gradients at the plasma edge. These solutions have been derived by exploiting the continuous Lie symmetry properties of the GS equation and in particular a special type of "weak" symmetries. In addition, we review the continuous Lie symmetry properties of the GS equation and present a short but exhaustive survey of the possible choices for the arbitrary flux functions that yield GS equations admitting some continuous Lie symmetry. Particular solutions related to these symmetries are also discussed.

8 pages, 4 figures

References in corpus (1)

• On the notion of conditional symmetry of differential equations

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• Symmetry Classification of quasi-linear PDE's. II: an exceptional case