Bilinear discrete Painleve-II and its particular solutions

DOI10.1088/0305-4470/28/12/025zbMath0859.34073arXivsolv-int/9412007OpenAlexW1973118188MaRDI QIDQ4716529

Kenji Kajiwara, Junkichi Satsuma, Jarmo Hietarinta, Basile Grammaticos, Alfred Ramani

Publication date: 25 March 1997

Published in: Journal of Physics A: Mathematical and General (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/solv-int/9412007

zbMATH Keywords

gauge transformationdiscrete Painlevé II (d-P\(_{\text{II}}\)) equation

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Applications of dynamical systems (37N99) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10)

Related Items (10)

Determinant structure of the rational solutions for the Painlevé II equation ⋮ 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 ⋮ A bilinear approach to discrete Miura transformations. ⋮ Rational solutions for the discrete Painlevé II equation. ⋮ Strongly asymmetric discrete Painlevé equations: The additive case ⋮ Strongly asymmetric discrete Painlevé equations: The multiplicative case ⋮ 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

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