Applications of Symmetry Methods to the Theory of Plasma Physics

Abstract

The theory of plasma physics offers a number of nontrivial examples of partial differential equations, which can be successfully treated with symmetry methods. We propose three different examples which may illustrate the reciprocal advantage of this "interaction" between plasma physics and symmetry techniques. The examples include, in particular, the complete symmetry analysis of system of two PDE's, with the determination of some conditional and partial symmetries, the construction of group-invariant solutions, and the symmetry classification of a nonlinear PDE.

arXiv commentPublished in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/

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Cited by in corpus (7)

• Group invariant transformations for the Klein-Gordon equation in three dimensional flat spaces
• MHD equilibria with incompressible flows: symmetry approach
• Reduction of non-linear d'Alembert equations to two-dimensional equations
• Symmetry Extensions and Their Physical Reasons in the Kinetic and Hydrodynamic Plasma Models
• Symmetry classification of quasi-linear PDE's containing arbitrary functions
• Lie symmetry analysis of the Grad-Shafranov equation
• Reduction of multidimensional non-linear d'Alembert equations to two-dimensional equations: ansatzes, compatibility of reduction conditions