Discrete integrable systems from continuous Painlevé equations through limiting procedures

DOI10.1088/0951-7715/13/4/305zbMath0963.37069OpenAlexW2048094346MaRDI QIDQ4508709

Yasuhiro Ohta, Basile Grammaticos, Alfred Ramani

Publication date: 5 July 2001

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/0951-7715/13/4/305

zbMATH Keywords

integrable systemsdiscrete Painlevé equations

Mathematics Subject Classification ID

Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Soliton equations (35Q51) Discrete version of topics in analysis (39A12) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15) Lattice dynamics; integrable lattice equations (37K60)

Related Items (12)

Application of the τ‐function theory of Painlevé equations to random matrices: P_V, P_III, the LUE, JUE, and CUE ⋮ Application of theτ-function theory of Painlevé equations to random matrices:P_VI, the JUE, CyUE, cJUE and scaled limits ⋮ Hierarchies of Difference Equations and Bäcklund Transformations ⋮ Multiplicative equations related to the affine Weyl group E8 ⋮ Gambier lattices and other linearisable systems ⋮ Do all integrable equations satisfy integrability criteria? ⋮ Linearisable ultradiscrete systems with sign variables and the confinement of singularities ⋮ Strongly asymmetric discrete Painlevé equations: The additive case ⋮ A note on minimization of rational surfaces obtained from birational dynamical systems ⋮ Linearisable mappings, revisited ⋮ Special solutions of discrete Painlevé equations through direct linearisation ⋮ Discretising the Painlevé equations à la Hirota-Mickens

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