BACKLUND-TRANSFORMATIONS AND PAINLEVE ANALYSIS - EXACT-SOLUTIONS FOR THE NONLINEAR ISOTHERMAL MAGNETOSTATIC ATMOSPHERES

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.