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Backlund transformations and Painleve analysis: Exact solutions for a Grad--Shafranov-type magnetohydrodynamic equilibrium |
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| Authors: | KHATER, A. H. IBRAHIM, R. S. SHAMARDAN, A. B. CALLEBAUT, D. K. |
| Affiliation: | Mathematics Department, Faculty of Science, Beni-Suef, Cairo University Beni-Suef, Egypt Mathematics Department, Faculty of Science, El-Minya University El-Minya, Egypt Physics Department, UIA, University of Antwerp B-2610 Antwerp, Belgium |
| Abstract: | The problem of plasma equilibrium in a gravitational field isinvestigated analytically. For the two-dimensional problem,the system of ideal magnetohydrodynamic equations is reducedto a single nonlinear elliptic equation of the magnetic potentialas a Grad-Shafranov-type equation. By specifying the arbitraryfunctions in this equation, the sinh-Poisson equation can beobtained. Using the Bäcklund-transformation technique andPainlevé analysis, a set of exact solutions are obtainedwhich adequately describe force-free models for solar flaresand plane-parallel filaments of a diffuse magnetized plasmasuspended horizontally in equilibrium in a uniform gravitationalfield. |
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