Complete classification of rational solutions of \(A_{2n}\)-Painlevé systems

DOI10.1016/j.aim.2021.107770zbMath1472.37067arXiv2010.00076OpenAlexW3162175594MaRDI QIDQ2032945

Robert Milson, Yves Grandati, Daivd Gómez-Ullate

Publication date: 14 June 2021

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2010.00076

zbMATH Keywords

Hermite polynomialsrational solutionsPainlevé equationsMaya diagramsWronskian determinantsDarboux dressing chains

Mathematics Subject Classification ID

Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Entire and meromorphic solutions to ordinary differential equations in the complex domain (34M05) Nonautonomous Hamiltonian dynamical systems (Painlevé equations, etc.) (37J65)

Related Items

An affine Weyl group characterization of polynomial Heisenberg algebras ⋮ Exceptional Gegenbauer polynomials via isospectral deformation ⋮ The expansion of Wronskian Hermite polynomials in the Hermite basis ⋮ On the general family of third-order shape-invariant Hamiltonians related to generalized Hermite polynomials

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Complex SUSY transformations and the Painlevé IV equation
• A conjecture on exceptional orthogonal polynomials
• The relationship between semiclassical Laguerre polynomials and the fourth Painlevé equation
• Oscillation theorems for the Wronskian of an arbitrary sequence of eigenfunctions of Schrödinger's equation
• Supersymmetric quantum mechanics and Painlevé IV equation
• Differential equations in the spectral parameter
• Algebraic solutions of the sixth Painlevé equation
• Universal characters and an extension of the KP hierarchy
• Extended affine root systems. I: Coxeter transformations
• Studies on the Painlevé equations. III: Second and fourth Painlevé equations, \(P_{II}\) and \(P_{IV}\)
• Rational solutions of the fifth Painlevé equation
• Dressing chains and the spectral theory of the Schrödinger operator
• Recuttings of polygons
• Nonlinear chains and Painlevé equations
• Generalized Hermite polynomials and monodromy-free Schrödinger operators
• Poles of Painlevé IV rationals and their distribution
• Painlevé equations -- nonlinear special functions.
• A modification of Crum's method
• Exceptional Legendre polynomials and confluent Darboux Transformations
• Corrigendum on the proof of completeness for exceptional Hermite polynomials: ``Rational extensions of the quantum harmonic oscillator and exceptional Hermite polynomials
• A Bochner type characterization theorem for exceptional orthogonal polynomials
• Universal characters, integrable chains and the Painlevé equations
• On Stieltjes relations, Painlevé-IV hierarchy and complex monodromy
• Connection between quantum systems involving the fourth Painlevé transcendent and k-step rational extensions of the harmonic oscillator related to Hermite exceptional orthogonal polynomial
• Rational solutions of the Noumi and Yamada system of type $A_4^{(1)}$A4(1)
• FROM KP/UC HIERARCHIES TO PAINLEVÉ EQUATIONS
• Painlevé IV and degenerate Gaussian unitary ensembles
• Special polynomials associated with rational solutions of the defocusing nonlinear Schrödinger equation and the fourth Painlevé equation
• The Symmetric Fourth Painlevé Hierarchy and Associated Special Polynomials
• On the linearization of the first and second Painlevé equations
• Vortices and Polynomials
• Determinant structure of the rational solutions for the Painlevé IV equation
• Symmetries in the fourth Painlevé equation and Okamoto polynomials
• Painlevé equations from Darboux chains: I.P_III–P_V
• Special polynomials and the Hirota Bilinear relations of the second and the fourth Painlevé equations
• Orthogonal Polynomials and Painlevé Equations
• Durfee Rectangles and Pseudo‐Wronskian Equivalences for Hermite Polynomials
• The fourth Painlevé equation and associated special polynomials
• Cyclic Maya diagrams and rational solutions of higher order Painlevé systems
• Large-Degree Asymptotics of Rational Painlevé-IV Functions Associated to Generalized Hermite Polynomials
• Rational extensions of the quantum harmonic oscillator and exceptional Hermite polynomials
• The Factorization Method
• ASSOCIATED STURM-LIOUVILLE SYSTEMS
• Roots of generalised Hermite polynomials when both parameters are large
• Monodromy-free Schrödinger operators with quadratically increasing potentials
• Application of the \(\tau\)-function theory of Painlevé equations to random matrices: PIV, PII and the GUE.

This page was built for publication: Complete classification of rational solutions of \(A_{2n}\)-Painlevé systems