A Nonlinear Differential Equation Related to the Jacobi Elliptic Functions. (8th September 2012)

• Record Type: Journal Article
• Authors: Johannessen, Kim
• Other Names: Rogovchenko Yuriy Academic Editor.
• Is Part Of: International journal of differential equations. Volume 2012(2012)
• Publication Date: 2012-09-08
• Subjects: Differential equations -- Periodicals; Differential equations; Periodicals; 515.35
• DOI: 10.1155/2012/412569
• Languages: English
• ISSNs: 1687-9643

Abstract

Abstract : 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.