Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 2 (2006), 017, 17 pages      math-ph/0602008      http://dx.doi.org/10.3842/SIGMA.2006.017

Applications of Symmetry Methods to the Theory of Plasma Physics

Giampaolo Cicogna a, Francesco Ceccherini b and Francesco Pegoraro b
a) Dip. di Fisica and INFN, Largo B. Pontecorvo 3, Ed. B-C, 56127 - Pisa, Italy
b) Dip. di Fisica, INFM and CNISM, Largo B. Pontecorvo 3, Ed. B-C, 56127 - Pisa, Italy

Received October 17, 2005, in final form January 20, 2006; Published online February 02, 2006

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.

Key words: Lie point symmetries; partial differential equations; plasma physics.

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