Mathematics
Scientific paper
Feb 1997
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1997ima....58...51k&link_type=abstract
IMA J. Appl. Math., Vol. 58, No. 1, p. 51 - 69
Mathematics
Solar Flares: Magnetohydrodynamics
Scientific paper
The problem of plasma equilibrium in a gravitational field is investigated analytically. For the two-dimensional problem, the system of ideal magnetohydrodynamic equations is reduced to a single nonlinear elliptic equation of the magnetic potential as a Grad-Shafranov-type equation. By specifying the arbitrary functions in this equation, the sinh-Poisson equation can be obtained. Using the Backlund-transformation technique and Painlevé analysis, a set of exact solutions are obtained which adequately describe force-free models for solar flares and plane-parallel filaments of a diffuse magnetized plasma suspended horizontally in equilibrium in a uniform gravitational field.
Callebaut Dirk K.
Ibrahim S. R.
Khater A. H.
Shamardan A. B.
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