Relations of al Functions over Subvarieties in a Hyperelliptic Jacobian

Shigeki Matsutani

Relations of al Functions over Subvarieties in a Hyperelliptic Jacobian

Authors

Shigeki Matsutani 8-21-1 Higashi-Linkan, Sagamihara, 228-0811, Japan.

Keywords:

sine-Gordon equation, nonlinear integrable differential equation, hyperelliptic functions, a subvariety in a 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.