Backlund transformations and Painleve analysis: exact solutions for a Grad-Shafranov-type magnetohydrodynamic equilibrium
- 1 February 1997
- journal article
- research article
- Published by Oxford University Press (OUP) in IMA Journal of Applied Mathematics
- Vol. 58 (1) , 51-69
- https://doi.org/10.1093/imamat/58.1.51
Abstract
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 Bäcklund-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.Keywords
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