Rational solutions for the discrete Painlevé II equation.

DOI10.1016/S0375-9601(97)00397-6zbMath1053.39500arXivsolv-int/9702001MaRDI QIDQ1968369

Kazushi Yamamoto, Kenji Kajiwara, Yasuhiro Ohta

Publication date: 7 March 2000

Published in: Physics Letters. A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/solv-int/9702001

Mathematics Subject Classification ID

Other functions defined by series and integrals (33E20) Discrete version of topics in analysis (39A12)

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Geometric aspects of Painlevé equations ⋮ Random ballistic growth and diffusion in symmetric spaces ⋮ Rational solutions of difference Painlevé equations ⋮ Continuous limit of the difference second Painlevé equation and its asymptotic solutions ⋮ Umemura polynomials for the Painlevé V equation ⋮ Hypergeometric Solutions to an Ultradiscrete Painlevé Equation ⋮ Discriminants of Umemura polynomials associated to Painlevé III ⋮ On a q-Difference Painlevé III Equation: II. Rational Solutions ⋮ Proceedings of the 12th international workshop on nonlinear evolution equations and dynamical systems (NEEDS '98), Leeds, UK, June 21--28, 1998. Transl. from the Russian ⋮ A simplified version of higher covariant derivative regularization ⋮ Special function solutions of the discrete Painlevé equations ⋮ Bäcklund transformations for discrete Painlevé equations: discrete P\(_{\text{II}}\)-P\(_{\text{V}}\)

Cites Work

• Studies on the Painlevé equations. III: Second and fourth Painlevé equations, \(P_{II}\) and \(P_{IV}\)
• From continuous to discrete Painlevé equations
• Casorati determinant solutions for the discrete Painleve-II equation
• Solutions of the second and fourth Painlevé equations, I
• Do integrable mappings have the Painlevé property?
• A study of the alternate discrete Painlevé II equation
• Bilinear discrete Painleve-II and its particular solutions
• On a unified approach to transformations and elementary solutions of Painlevé equations
• Casorati determinant solutions for the discrete Painlevé III equation
• Determinant structure of the rational solutions for the Painlevé II equation
• Cellular automata and ultra-discrete Painlevé equations
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