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On Relations of Hyperelliptic Weierstrass al Functions

Shigeki Matsutani
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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.

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Shigeki Matsutani. 2003-06-28. On Relations of Hyperelliptic Weierstrass al Functions. https://arxiv.org/abs/nlin/0201019

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