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Backlund transformations and exact solutions for a nonlinear elliptic equation modelling isothermal magnetostatic atmosphere
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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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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 : 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 (Publishers DOI) |
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