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Relations of al Functions over Subvarieties in a Hyperelliptic Jacobian

Shigeki Matsutani
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Abstract

The sine-Gordon equation has hyperelliptic al function solutions over a hyperelliptic Jacobian for $y^2 = f(x)$ of arbitrary genus $g$. This article gives an extension of the sine-Gordon equation to that over subvarieties of the hyperelliptic Jacobian. We also obtain the condition that the sine-Gordon equation in a proper subvariety of the Jacobian is defined.

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Shigeki Matsutani. 2004-11-21. Relations of al Functions over Subvarieties in a Hyperelliptic Jacobian. https://arxiv.org/abs/nlin/0202035

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