Ah. Khater et al., BACKLUND-TRANSFORMATIONS AND PAINLEVE ANALYSIS - EXACT-SOLUTIONS FOR A GRAD-SHAFRANOV-TYPE MAGNETOHYDRODYNAMIC EQUILIBRIUM, IMA journal of applied mathematics, 58(1), 1997, pp. 51-69
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.