Riccati solutions of discrete Painlevé equations with Weyl group symmetry of type E8(1)

DOI10.1063/1.1531216zbMath1062.34102arXivnlin/0210040OpenAlexW3098592340MaRDI QIDQ4832949

Mikio Murata, Hidetaka Sakai, Jin Yoneda

Publication date: 14 December 2004

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

Full work available at URL: https://arxiv.org/abs/nlin/0210040

Mathematics Subject Classification ID

Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Discrete version of topics in analysis (39A12) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions (37K20)

Related Items (13)

Theory and applications of the elliptic Painlevé equation ⋮ Semiclassical orthogonal polynomial systems on nonuniform lattices, deformations of the Askey table, and analogues of isomonodromy ⋮ Geometry of an elliptic difference equation related to Q4 ⋮ Special functions arising from discrete Painlevé equations: a survey ⋮ On a novel representation of discrete Painlevé equations ⋮ Multiplicative equations related to the affine Weyl group E8 ⋮ Hypergeometric \(\tau \)-functions of the \(q\)-Painlevé system of type \(E_{8}^{(1)}\) ⋮ Singularity analysis for difference Painlevé equations associated with the affine Weyl groupE₈ ⋮ Geometric aspects of Painlevé equations ⋮ Full-parameter discrete Painlevé systems from non-translational Cremona isometries ⋮ Elliptic Painlevé equations from next-nearest-neighbor translations on the $E_8^{(1)}$ lattice ⋮ A geometric approach to tau-functions of difference Painlevé equations ⋮ Padé Interpolation for Elliptic Painlevé Equation

Cites Work

• Studies on the Painlevé equations. III: Second and fourth Painlevé equations, \(P_{II}\) and \(P_{IV}\)
• Rational surfaces associated with affine root systems and geometry of the Painlevé equations
• Special function solutions of the discrete Painlevé equations
• A \(q\)-analog of the sixth Painlevé equation
• An affine Weyl group approach to the eight-parameter discrete Painlevé equation
• Degeneration through coalescence of theq-Painlevé VI equation
• Discrete versions of the Painlevé equations
• Do integrable mappings have the Painlevé property?

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