Nonlinear periodic solutions for isothermal magnetostatic atmospheres

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:242

Article

Khater, A. H.¹  Callebaut, D. K.²  Bhrawy, A. H.^1,3  Abdelkawy, M. A.¹ 

[1] Beni Suef Univ, Fac Sci, Dept Math, Bani Suwayf, Egypt

[2] Univ Antwerp, Dept Phys, CDE, B-2610 Antwerp, Belgium

[3] King Abdulaziz Univ, Fac Sci, Dept Math, Jeddah, Saudi Arabia

关键词: Nonlinear equations;    Magnetohydrostatic equilibria;    Grad-Shafranov equation;    Backlund transformations;    Solar atmosphere;   

DOI  :  10.1016/j.cam.2012.10.012

来源: Elsevier

【 摘 要 】

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 known as the Grad-Shafranov equation. Specifying the arbitrary function in the latter equation, yields a nonlinear elliptic equation. Analytical nonlinear periodic solutions of this elliptic equation are obtained for the case of an isothermal atmosphere in a uniform gravitational field: e.g. a model for the solar atmosphere. We obtained several classes of exact solutions of five nonlinear evolution equations (Liouville, sinh-Poisson, double sinh-Poisson, sine-Poisson and double sine-Poisson) using the generalized tanh method. Moreover, the Backlund transformations are used to generate further new classes of solutions. The final results may be used to investigate some models in solar physics. (C) 2012 Published by Elsevier B.V.

【 授权许可】

Free