The G′/G-expansion method for solutions of evolution equations from isothermal magnetostatic atmospheres

Abstract

The equations of magnetohydrostatic equilibria for plasma in a gravitational field are investigated analytically. An investigation of a family of isothermal magneto static atmospheres with one ignorable coordinate corresponding to a uniform gravitational field in a plane geometry is carried out. The distributed current in the model J is directed along the x-axis where x is the horizontal ignorable coordinate. 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 different arbitrary functions, we obtain analytical nonlinear solutions of the elliptic equation using the G′G-expansion method. Finally, the hyperbolic versions of these equations will be solved by the travelling wave hypothesis method.