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An alternate approach to finding and using the Lie group of the Vlasov equation

Authors :
Dana Roberts
Source :
Journal of Mathematical Physics. 26:1529-1533
Publication Year :
1985
Publisher :
AIP Publishing, 1985.

Abstract

Two recent methods for finding exact solutions to the Vlasov–Maxwell equations using Lie group theory are compared by the introduction of an ‘‘intermediate’’ approach. In the latter, the Lie group and general similarity solutions of the Vlasov equation are found through a method which treats independent and dependent variables as forms that are on an essentially equal footing. A Maxwell equation is then used to constrain the solutions further. The procedure is shown to illustrate a more general theorem that implies that the reduction of the number of variables in a set of equations through the use of canonical variables generated from the Lie group invariance of one equation in the set leads to the same solutions as are found by considering the invariance of the entire set.

Details

ISSN :
10897658 and 00222488
Volume :
26
Database :
OpenAIRE
Journal :
Journal of Mathematical Physics
Accession number :
edsair.doi...........3ffd10d1828a322c9294bcef033b8d1a
Full Text :
https://doi.org/10.1063/1.526912