Title 



Backlund transformations and exact solutions for a nonlinear elliptic equation modelling isothermal magnetostatic atmosphere


Author 





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 GradShafranov 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 efolding distance equal to the gravitational scale height.  

Language 



English


Source (journal) 



IMA journal of applied mathematics.  London, 1981, currens 

Publication 



London : 2000


ISSN 



02724960 [print]
14643634 [online]


Volume/pages 



65:1(2000), p. 97108


ISI 



000088400000004


Full text (Publisher's DOI) 


 
