A similarity reduction of the Grad–Shafranov equation | Zendy

Yuri E. Litvinenko | Zendy

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A similarity reduction of the Grad–Shafranov equation

Author(s) -

Yuri E. Litvinenko

Publication year - 2010

Publication title -

physics of plasmas

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.75

H-Index - 160

eISSN - 1089-7674

pISSN - 1070-664X

DOI - 10.1063/1.3456519

Subject(s) - physics , invariant (physics) , homogeneous space , partial differential equation , similarity (geometry) , lie group , differential equation , reduction (mathematics) , similarity solution , mathematics , mathematical analysis , mathematical physics , pure mathematics , quantum mechanics , mechanics , artificial intelligence , geometry , image (mathematics) , computer science , boundary layer

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

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