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

Division of Applied Mathematics

Research output: Contribution to journal › Article › peer-review

49 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	L263-L272
Journal	Journal of Physics A: Mathematical and General
Volume	36
Issue number	17
DOIs	https://doi.org/10.1088/0305-4470/36/17/102
Publication status	Published - May 2 2003

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics
Physics and Astronomy(all)

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10.1088/0305-4470/36/17/102

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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

N2 - 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.

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

IS - 17

ER -

10E9 solution to the elliptic Painlevé equation

Abstract

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