On the Riemann-Hilbert problem for a \(q\)-difference Painlevé equation

DOI10.1007/s00220-021-04024-yzbMath1476.39004arXiv1911.05854OpenAlexW3133223495WikidataQ114230944 ScholiaQ114230944MaRDI QIDQ2025637

Pieter Roffelsen, Nalini Joshi

Publication date: 14 May 2021

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

Full work available at URL: https://arxiv.org/abs/1911.05854

zbMATH Keywords

transcendental solutions\(q\)-difference Painlevé equation\(q\)-monodromy surface

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) Difference equations, scaling ((q)-differences) (39A13) Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.) for ordinary differential equations in the complex domain (34M50) Teichmüller theory; moduli spaces of holomorphic dynamical systems (37F34) Integrable difference and lattice equations; integrability tests (39A36)

Related Items (2)

On symmetric solutions of the fourth q-Painlevé equation ⋮ On the monodromy manifold of \(q\)-Painlevé VI and its Riemann-Hilbert problem

Cites Work

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• An isomonodromy interpretation of the hypergeometric solution of the elliptic Painlevé equation (and generalizations)
• Moduli spaces for linear differential equations and the Painlevé equations
• Density matrix of an impenetrable Bose gas and the fifth Painlevé transcendent
• Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. I: General theory and \(\tau \)-function
• Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. II
• Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. III
• Discrete Painlevé equations and their appearance in quantum gravity
• Matrix models of two-dimensional quantum gravity and isomonodromic solutions of ``discrete Painlevé equations
• Rational surfaces associated with affine root systems and geometry of the Painlevé equations
• Galois theory of difference equations
• Poles of Painlevé IV rationals and their distribution
• A \(q\)-analog of the sixth Painlevé equation
• Quantised Painlevé monodromy manifolds, Sklyanin and Calabi-Yau algebras
• A steepest descent method for oscillatory Riemann-Hilbert problems. Asymptotics for the MKdV equation
• Isomonodromy transformations of linear systems of difference equations
• A differential equation for orthogonal polynomials
• Analytic solutions ofq-P(A₁) near its critical points
• Geometric aspects of Painlevé equations
• Connection preserving deformations andq-semi-classical orthogonal polynomials
• Asymptotic behaviour around a boundary point of theq-Painlevé VI equation and its connection problem
• Lax forms of theq-Painlevé equations
• The isomonodromy approach in the theory of two-dimensional quantum gravitation
• On the solvability of Painleve I, III and V
• Method for Solving the Korteweg-deVries Equation
• Painlevé Monodromy Manifolds, Decorated Character Varieties, and Cluster Algebras
• CFT approach to the q-Painlevé VI equation
• Large-Degree Asymptotics of Rational Painlevé-IV Functions Associated to Generalized Hermite Polynomials
• Discrete Painlevé Equations
• Lax pairs of discrete Painlevé equations: (A₂+A₁)⁽¹⁾case
• Local analytic classification of q-difference equations
• Roots of generalised Hermite polynomials when both parameters are large

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