Potential symmetry and invariant solutions of Fokker–Planck equation modelling magnetic field diffusion in magnetohydrodynamics including the Hall current
✍ Scribed by A.H Khater; D.K Callebaut; S.F Abdul-Aziz; T.N Abdelhameed
- Publisher
- Elsevier Science
- Year
- 2004
- Tongue
- English
- Weight
- 277 KB
- Volume
- 341
- Category
- Article
- ISSN
- 0378-4371
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✦ Synopsis
Lie groups involving potential symmetries are exposed in view of applications to physics. The system of magnetohydrodynamic equations for incompressible matter with Ohm's law for ÿnite resistivity and Hall current is studied in Cartesian geometry. The equations for the evolution of the plasma ow and the magnetic ÿeld decouple. The latter one reduces to a Fokker-Planck type equation. Invariant solutions are obtained involving the e ects of time-dependent ows 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.