Meromorphic functions in a first-order system

Abstract

We consider the differential equations $s^{\prime }=c^5$ and $c^{\prime }=-s^5$ with initial conditions $s(0)=0$ and $c(0)=1$. We show that $s^2{c}^2$ extends to the reciprocal of the Weierstrass elliptic function with invariants $g_2=0$ and $g_3=16$. We also show that powers of $s^2{c}^2$ are the only functions of the form $s^m{c}^n$ that extend meromorphically in the plane.

References in corpus (1)

• The Elliptic Functions in a First-Order System

Cited by in corpus (1)

• Higher Trigonometry: A Class Of Nonlinear Systems