Discrete Painlevé equations and their Lax pairs as reductions of integrable lattice equations

DOI10.1088/1751-8113/46/9/095204zbMath1266.39012arXiv1209.4721OpenAlexW3103955698MaRDI QIDQ4920445

Peter H. van der Kamp, Gilles Reinout Willem Quispel, Christopher Michael Ormerod

Publication date: 17 May 2013

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

Full work available at URL: https://arxiv.org/abs/1209.4721

zbMATH Keywords

fourth Painlevé equationLax pairssixth Painlevé equationpartial difference equationsperiodic reductions\(q\)-Painlevé equation with a symmetry group of affine Weyl type \(E^{(1)}_6\)integrable non-autonomous lattice equationsnon-autonomous discrete Korteweg-de Vries equationnon-autonomous discrete Schwarzian Korteweg-de Vries equation

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Discrete version of topics in analysis (39A12) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15) Partial difference equations (39A14)

Related Items (5)

Quantizing the discrete Painlevé VI equation: the Lax formalism ⋮ Lattice equations arising from discrete Painlevé systems: II. ${A}_{4}^{(1)}$ case ⋮ Hierarchies of q-discrete Painlevé equations ⋮ Commutation relations and discrete garnier systems ⋮ Super-QRT and 4D-mappings reduced from the lattice super-KdV equation

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