https://doi.org/10.1140/epjb/e2006-00138-5
Potential symmetry and invariant solutions of Fokker-Planck equation in cylindrical coordinates related to magnetic field diffusion in magnetohydrodynamics including the Hall current
1
Mathematics Departement, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt
2
Departement Natuurkunde, CDE, University of Antwerp, B-2610 Antwerp, Belgium
Corresponding author: a khater_ah@yahoo.com
Received:
19
October
2005
Revised:
8
December
2005
Published online:
12
April
2006
Lie groups involving potential symmetries are applied in connection with the system of magnetohydrodynamic equations for incompressible matter with Ohm's law for finite resistivity and Hall current in cylindrical geometry. Some simplifications allow to obtain a Fokker-Planck type equation. Invariant solutions are obtained involving the effects of time-dependent flow and the Hall-current. Some interesting side results of this approach are new exact solutions that do not seem to have been reported in the literature.
PACS: 05.10.Gg – Stochastic analysis methods (Fokker-Planck, Langevin, etc.) / 52.30.Cv – Magnetohydrodynamics (including electron magnetohydrodynamics) / 02.30.Jr – Partial differential equations / 52.65.Ff – Fokker-Planck and Vlasov equation
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2006
