B{umlt a}cklund transformations and Painlev{acute e} analysis: Exact solutions for the nonlinear isothermal magnetostatic atmospheres

Journal Article · Fri Aug 01 04:00:00 EDT 1997 · Physics of Plasmas

DOI:https://doi.org/10.1063/1.872418· OSTI ID:526917

Khater, A H ^[1]; Callebaut, D K ^[2]; Ibrahim, R S ^[1]

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1. Mathematics Department, Faculty of Science, Cairo University, Beni-Suef (Egypt)
2. Physics Department, U I A, University of Antwerp, B-2610 Antwerp (Belgium)

The equations of magnetohydrostatic equilibria for a plasma in a gravitational field are investigated analytically. For equilibria with one ignorable spatial coordinate, the equations reduce to a single nonlinear elliptic equation for the magnetic potential {tilde {mu}}, known as the Grad{endash}Shafranov equation. Specifying the arbitrary functions in the latter equation, one gets the nonlinear elliptic equation. Analytical solutions of the elliptic equation are obtained for the case of a nonlinear isothermal atmosphere in a uniform gravitational field. The solutions are obtained by using the B{umlt a}cklund transformations technique and Painlev{acute e} analysis, which are adequate for describing parallel filaments of diffuse, magnetized plasma suspended horizontally in equilibrium in a uniform gravitational field. {copyright} {ital 1997 American Institute of Physics.}

• OSTI ID: 526917
• Journal Information: Physics of Plasmas, Journal Name: Physics of Plasmas Journal Issue: 8 Vol. 4; ISSN PHPAEN; ISSN 1070-664X
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
ANALYTICAL SOLUTION
GRAVITATIONAL FIELDS
MAGNETOHYDRODYNAMICS
PLASMA