Relations of al Functions over Subvarieties in a Hyperelliptic Jacobian
Abstract
The sine-Gordon equation has hyperelliptic al function solutions over a hyperelliptic Jacobian for y2 = 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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