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Title
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Backlund transformations and exact solutions for a nonlinear elliptic equation modelling isothermal magnetostatic atmosphere
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Author
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Abstract
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| The equations of magnetostatic equilibria for a plasma in a gravitational field are investigated analytically. For equilibria with an ignorable spatial coordinate, the equations reduce to a single nonlinear elliptic equation for the magnetic potential u known as the Grad-Shafranov equation. By specifying the arbitrary functions in this equation, a Liouville equation is obtained. Backlund transformations are described and applied to obtain exact solutions for the Liouville equation modelling an isothermal magnetostatic atmosphere, in which the current density J is proportional to the exponential of the magnetic potential and moreover falls off exponentially with distance vertical to the base with an e-folding distance equal to the gravitational scale height. |
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Language
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English
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Source (journal)
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IMA journal of applied mathematics. - London, 1981, currens
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Publication
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London
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2000
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ISSN
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0272-4960
[print]
1464-3634
[online]
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Volume/pages
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65
:1
(2000)
, p. 97-108
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ISI
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000088400000004
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Full text (Publisher's DOI)
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