(G′/G)-expansion method for two-dimensional force-free magnetic fields described by some nonlinear equations

Abstract

In this paper three nonlinear force-free magnetic field equations such as the Liouville equation, Sine-Poisson equation and Sinh-Poisson equation are studied by (G′/G)-expansion method and exact periodic solutions are extracted. In all these cases the ratio of the current density and the magnetic field is not constant e.g. as happens in the solar atmosphere.