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A Nonlinear Differential Equation Related to the Jacobi Elliptic Functions
Author
Source
International Journal of Differential Equations
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-09-11
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
A nonlinear differential equation for the polar angle of a point of an ellipse is derived.
The solution of this differential equation can be expressed in terms of the Jacobi elliptic function dn(u,k).
If the polar angle is extended to the complex plane, the Jacobi imaginary transformation properties and the dependence on the real and complex quarter periods can be described.
From the differential equation of the polar angle, exact solutions of the Poisson Boltzmann and the sinh-Poisson equations are found in terms of the Jacobi elliptic functions.
American Psychological Association (APA)
Johannessen, Kim. 2012. A Nonlinear Differential Equation Related to the Jacobi Elliptic Functions. International Journal of Differential Equations،Vol. 2012, no. 2012, pp.1-9.
https://search.emarefa.net/detail/BIM-470070
Modern Language Association (MLA)
Johannessen, Kim. A Nonlinear Differential Equation Related to the Jacobi Elliptic Functions. International Journal of Differential Equations No. 2012 (2012), pp.1-9.
https://search.emarefa.net/detail/BIM-470070
American Medical Association (AMA)
Johannessen, Kim. A Nonlinear Differential Equation Related to the Jacobi Elliptic Functions. International Journal of Differential Equations. 2012. Vol. 2012, no. 2012, pp.1-9.
https://search.emarefa.net/detail/BIM-470070
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-470070