Ah. Khater et al., PAINLEVE ANALYSIS AND NONLINEAR PERIODIC-SOLUTIONS FOR ISOTHERMAL MAGNETOSTATIC ATMOSPHERES, Solar physics, 178(2), 1998, pp. 285-315
The equations of magnetohydrodynamic equilibria for a plasma in a grav
itational field are investigated analytically. For equilibria with one
ignorable spatial coordinate, the equations reduce to a single nonlin
ear elliptic equation for the magnetic potential psi, known as the Gra
d-Shafranov equation. Specifying the arbitrary functions in the latter
equation, one gets a nonlinear elliptic equation. Analytical solution
s of the elliptic equation are obtained for the case of a nonlinear is
othermal atmosphere in a uniform gravitational field. The solutions ar
e obtained by using the Painleve analysis, and are adequate for descri
bing parallel filaments of diffuse, magnetized plasma suspended horizo
ntally in equilibrium in a uniform gravitational field.