팽르베 미분방정식(Painlevé Equations)

개요

• Painlevé I-VI
• II\[\frac{d^2y}{dt^2} = 2 y^3 + ty + \alpha \]

 

메모

• \(q''(s)=sq(s)+2q(s)^3\)
• 에어리 (Airy) 함수와 미분방정식

사전 형태의 자료

• http://ko.wikipedia.org/wiki/팽르베_방정식
• http://en.wikipedia.org/wiki/Painlevé_transcendents

관련링크 및 웹페이지

• Painlevé Equations

리뷰, 에세이, 강의노트

• Guzzetti, Davide. “A Review on The Sixth Painleve’ Equation.” Constructive Approximation 41, no. 3 (June 2015): 495–527. doi:10.1007/s00365-014-9250-6.

관련논문

• Takao Suzuki, A generalization of the $q$-Painlevé VI equation from a viewpoint of a particular solution in terms of the $q$-hypergeometric function, arXiv:1602.01573[math-ph], February 04 2016, http://arxiv.org/abs/1602.01573v4
• Brezhnev, Yurii V. “The Sixth Painleve Transcendent and Uniformization of Algebraic Curves.” Journal of Differential Equations 260, no. 3 (February 2016): 2507–56. doi:10.1016/j.jde.2015.10.009.
• Kajiwara, Kenji, Masatoshi Noumi, and Yasuhiko Yamada. “Geometric Aspects of Painlev’e Equations.” arXiv:1509.08186 [math-Ph, Physics:nlin], September 27, 2015. http://arxiv.org/abs/1509.08186.