BACKLUND-TRANSFORMATIONS AND PAINLEVE ANALYSIS - EXACT-SOLUTIONS FOR A GRAD-SHAFRANOV-TYPE MAGNETOHYDRODYNAMIC EQUILIBRIUM

The problem of plasma equilibrium in a gravitational field is investig ated analytically. For the two-dimensional problem, the system of idea l magnetohydrodynamic equations is reduced to a single nonlinear ellip tic equation of the magnetic potential as a Grad-Shafranov-type equati on. By specifying the arbitrary functions in this equation, the sinh-P oisson equation can be obtained. Using the Backlund-transformation tec hnique and Painleve analysis, a set of exact solutions are obtained wh ich adequately describe force-free models for solar flares and plane-p arallel filaments of a diffuse magnetized plasma suspended horizontall y in equilibrium in a uniform gravitational field.