10E9 solution to the elliptic Painlevé equation

Kenji Kajiwara; Tetsu Masuda; Masatoshi Noumi; Yasuhiro Ohta; Yasuhiko Yamada

doi:10.1088/0305-4470/36/17/102

10E9 solution to the elliptic Painlevé equation

Kenji Kajiwara, Tetsu Masuda, Masatoshi Noumi, Yasuhiro Ohta, Yasuhiko Yamada

応用理論研究部門

研究成果: ジャーナルへの寄稿 › 学術誌 › 査読

48 被引用数 (Scopus)

抄録

A τ function formalism for Sakai's elliptic Painlevé equation is presented. This establishes the equivalence between the two formulations by Sakai and by Ohta-Ramani-Grammaticos. We also give a simple geometric description of the elliptic Painlevé equation as a non-autonomous deformation of the addition formula on elliptic curves. By using these formulations, we construct a particular solution of die elliptic Painlevé equation expressed in terms of the elliptic hypergeometric function ₁₀E₉.

本文言語	英語
ページ（範囲）	L263-L272
ジャーナル	Journal of Physics A: Mathematical and General
巻	36
号	17
DOI	https://doi.org/10.1088/0305-4470/36/17/102
出版ステータス	出版済み - 5月 2 2003

All Science Journal Classification (ASJC) codes

統計物理学および非線形物理学
数理物理学
物理学および天文学（全般）

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10.1088/0305-4470/36/17/102

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author = "Kenji Kajiwara and Tetsu Masuda and Masatoshi Noumi and Yasuhiro Ohta and Yasuhiko Yamada",

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T1 - 10E9 solution to the elliptic Painlevé equation

AU - Kajiwara, Kenji

AU - Masuda, Tetsu

AU - Noumi, Masatoshi

AU - Ohta, Yasuhiro

AU - Yamada, Yasuhiko

PY - 2003/5/2

Y1 - 2003/5/2

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AB - A τ function formalism for Sakai's elliptic Painlevé equation is presented. This establishes the equivalence between the two formulations by Sakai and by Ohta-Ramani-Grammaticos. We also give a simple geometric description of the elliptic Painlevé equation as a non-autonomous deformation of the addition formula on elliptic curves. By using these formulations, we construct a particular solution of die elliptic Painlevé equation expressed in terms of the elliptic hypergeometric function 10E9.

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JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 17

ER -

10E9 solution to the elliptic Painlevé equation

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