On Relations of Hyperelliptic Weierstrass al Functions

Abstract

We study relations of the Weierstrass's hyperelliptic al-functions over a non-degenerated hyperelliptic curve $y^2=f(x)$ of arbitrary genus $g$ as solutions of sine-Gordon equation using Weierstrass's local parameters, which are characterized by two ramified points. Though the hyperelliptic solutions of the sine-Gordon equation had already obtained, our derivations of them are simple; they need only residual computations over the curve and primitive matrix computations.

AMS-Tex, 10 pages