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
Faculty of Sciences. Physics

article

2000
London
, 2000

Mathematics

IMA journal of applied mathematics. - London, 1981, currens

65(2000)
:1
, p. 97-108

0272-4960

1464-3634

000088400000004

E

English (eng)

University of Antwerp

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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