On Relations of Hyperelliptic Weierstrass al Functions
Shigeki Matsutani
Abstract
We study relations of the Weierstrass's hyperelliptic al-functions over a non-degenerated hyperelliptic curve y2 = 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.
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