Potential symmetry and invariant solutions of Fokker–Planck equation modelling magnetic field diffusion in magnetohydrodynamics including the Hall current

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 finite resistivity and Hall current is studied in Cartesian geometry. The equations for the evolution of the plasma flow and the magnetic field decouple. The latter one reduces to a Fokker–Planck type equation. Invariant solutions are obtained involving the effects of time-dependent flows 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.