A Nonlinear Differential Equation Related to the Jacobi Elliptic Functions
Copyright policy )A Nonlinear Differential Equation Related to the Jacobi Elliptic Functions
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.
- University of Southern Denmark Denmark
Boltzmann equations, Elliptic functions and integrals, Explicit solutions, first integrals of ordinary differential equations, QA1-939, Poisson Boltzmann, Nonlinear ordinary differential equations and systems, Jacobi elliptic functions, Mathematics
Boltzmann equations, Elliptic functions and integrals, Explicit solutions, first integrals of ordinary differential equations, QA1-939, Poisson Boltzmann, Nonlinear ordinary differential equations and systems, Jacobi elliptic functions, Mathematics
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