Exact Travelling Wave Solutions for Isothermal Magnetostatic Atmospheres by Fan Subequation Method

Abstract

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 $u$. This equation depends on an arbitrary function of $u$ that must be specified. With choices of the different arbitrary functions, we obtain analytical solutions of elliptic equation using the Fan subequation method.