Ah. Khater et al., BACKLUND-TRANSFORMATIONS AND PAINLEVE ANALYSIS - EXACT-SOLUTIONS FOR THE NONLINEAR ISOTHERMAL MAGNETOSTATIC ATMOSPHERES, Physics of plasmas, 4(8), 1997, pp. 2853-2863
The equations of magnetohydrostatic equilibria for a plasma in a gravi
tational field are investigated analytically. For equilibria with one
ignorable spatial coordinate, the equations reduce to a single nonline
ar elliptic equation for the magnetic potential <(mu)over tilde>, know
n as the Grad-Shafranov equation. Specifying the arbitrary functions i
n the latter equation, one gets the nonlinear elliptic equation. Analy
tical solutions of the elliptic equation are obtained for the case of
a nonlinear isothermal atmosphere in a uniform gravitational field. Th
e solutions are obtained by using the Backlund transformations techniq
ue and Painleve analysis, which are adequate for describing parallel f
ilaments of diffuse, magnetized plasma suspended horizontally in equil
ibrium in a uniform gravitational field. (C) 1997 American Institute o
f Physics.