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Painleve Analysis and Nonlinear Periodic Solutions For Isothermal Magnetostatic Atmospheres.

Author name : Eid Sayed K Sayed
Publication Date : 1998-03-25
Journal Name : Solar Physics

Abstract

The equations of magnetohydrodynamic equilibria for a plasma in a gravitational field are investigated analytically. For equilibria with one ignorable spatial coordinate, the equations reduce to a single nonlinear elliptic equation for the magnetic potential ψ, known as the Grad–Shafranov equation. Specifying the arbitrary functions in the latter equation, one gets a nonlinear elliptic equation. Analytical solutions of the elliptic equation are obtained for the case of a nonlinear isothermal atmosphere in a uniform gravitational field. The solutions are obtained by using the Painlevé analysis, and are adequate for describing parallel filaments of diffuse, magnetized plasma suspended horizontally in equilibrium in a uniform gravitational field.

Keywords

Atmospheres , Periodic Solutions , Elliptic Equation , Arbitrary Functions , Gravitational Field.

Publication Link

https://doi.org/10.1023/A:1005046607282

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