Title
Backlund transformations and exact solutions for a nonlinear elliptic equation modelling isothermal magnetostatic atmosphere Backlund transformations and exact solutions for a nonlinear elliptic equation modelling isothermal magnetostatic atmosphere
Author
Faculty/Department
Faculty of Sciences. Physics
Publication type
article
Publication
London ,
Subject
Mathematics
Source (journal)
IMA journal of applied mathematics. - London, 1981, currens
Volume/pages
65(2000) :1 , p. 97-108
ISSN
0272-4960
1464-3634
ISI
000088400000004
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
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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