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This chapter shows some applications of the sigma function theory constructed in the previous chapter to integrable systems. We investigate the differential and difference relations among Abelian functions on \(J_X\) which are expressed by the sigma function. They correspond to some solutions of integrable equations in terms of the sigma function and their related functions.

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Application of the Sigma Function Theory to Integrable Systems

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  • 发表日期：

    2025年

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  • Shigeki Matsutani

摘要

This chapter shows some applications of the sigma function theory constructed in the previous chapter to integrable systems. We investigate the differential and difference relations among Abelian functions on \(J_X\) which are expressed by the sigma function. They correspond to some solutions of integrable equations in terms of the sigma function and their related functions.