The equations of magnetohydrostatic equilibria for a plasma in a gravitational field are investigated analytically. An investigation of a family of isothermal magnetostatic atmospheres with oneignorable coordinate corresponding to a uniform gravitational field in a plane geometry is carried out. These equations transform to a single nonlinear elliptic equation for the magnetic vector potential . This equation depends on an arbitrary function of that must be specified. With choices of the different arbitrary functions, we obtain analytical solutions of elliptic equation using the Fan subequation method.
"Exact Travelling Wave Solutions for Isothermal Magnetostatic Atmospheres by Fan Subequation Method." Abstr. Appl. Anal. 2012 (SI03) 1 - 11, 2012. https://doi.org/10.1155/2012/962789