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      A similarity reduction of the Grad-Shafranov equation

      Litvinenko, Yuri E.
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      A similarity reduction.pdf
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      DOI
       10.1063/1.3456519
      Link
       pop.aip.org
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      Litvinenko, 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
      2010
      Type
      Journal Article
      Publisher
      American Institute of Physics
      Rights
      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.
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      • Computing and Mathematical Sciences Papers [1455]
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