A similarity reduction of the Grad-Shafranov equation
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Export citationLitvinenko, Y.E. (2010). A similarity reduction of the Grad-Shafranov equation. Physics of Plasmas, 17(7), 074502.
Permanent Research Commons link: https://hdl.handle.net/10289/4828
Abstract
A direct method for finding similarity reductions of partial differential equations is applied to a specific case of the Grad–Shafranov equation. As an illustration of the method, the frequently used Solov’ev equilibrium is derived. The method is employed to obtain a new family of exact analytical solutions, which contain both the classical and nonclassical group-invariant solutions of the Grad–Shafranov equation and thus greatly extends the range of the available analytical solutions. All the group-invariant solutions based on the classical Lie symmetries are shown to be particular cases in the new family of solutions.
Date
2010Type
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American Institute of Physics
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Copyright (2010) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.