Geometric aspects of Painlevé equations

Kenji Kajiwara, Masatoshi Noumi, Yasuhiko Yamada

研究成果: Contribution to journalReview article査読

44 被引用数 (Scopus)

抄録

In this paper a comprehensive review is given on the current status of achievements in the geometric aspects of the Painlev equations, with a particular emphasis on the discrete Painlevé equations. The theory is controlled by the geometry of certain rational surfaces called the spaces of initial values, which are characterized by eight point configuration on P1 P1 and classified according to the degeneration of points. We give a systematic description of the equations and their various properties, such as affine Weyl group symmetries, hypergeometric solutions and Lax pairs under this framework, by using the language of Picard lattice and root systems. We also provide with a collection of basic data; equations, point configurations/root data, Weyl group representations, Lax pairs, and hypergeometric solutions of all possible cases.

本文言語英語
論文番号073001
ジャーナルJournal of Physics A: Mathematical and Theoretical
50
7
DOI
出版ステータス出版済み - 1 12 2017

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modelling and Simulation
  • Mathematical Physics
  • Physics and Astronomy(all)

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