FROM KP/UC HIERARCHIES TO PAINLEVÉ EQUATIONS

DOI10.1142/S0129167X11007537zbMath1248.34138arXiv1004.1347OpenAlexW2963734224MaRDI QIDQ2885368

Teruhisa Tsuda

Publication date: 23 May 2012

Published in: International Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1004.1347

zbMATH Keywords

Painlevé equationmonodromy preserving deformationinfinite-dimensional integrable system

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Isomonodromic deformations for ordinary differential equations in the complex domain (34M56)

Related Items (19)

Multiparameter universal characters of B-type and integrable hierarchy ⋮ Plethystic B-type KP and universal character hierarchies ⋮ Six-dimensional Painlevé systems and their particular solutions in terms of rigid systems ⋮ Multi-component universal character hierarchy and its polynomial tau-functions ⋮ Strongly coupled B-type universal characters and hierarchies ⋮ Supersymmetric quantum spin chains and modified universal characters ⋮ Polynomial tau-functions of the orthogonal KP, multicomponent orthogonal KP and BUC hierarchies ⋮ The symmetric KP hierarchy and affine Yangian of \(\mathfrak{gl}(1)\) ⋮ Solutions of the universal character hierarchy and BUC hierarchy by fermionic approach ⋮ Two types of universal characters and the integrable hierarchies ⋮ Linear transformations of vertex operators presentations of coupled Hall-Littlewood functions ⋮ Virasoro symmetries of multicomponent Gelfand-Dickey systems ⋮ Quantum Gaudin model, spin chains, and universal characters ⋮ Hermite-Padé approximation, isomonodromic deformation and hypergeometric integral ⋮ On solutions of the Fuji-Suzuki-Tsuda system ⋮ Complete classification of rational solutions of \(A_{2n}\)-Painlevé systems ⋮ Finite-dimensional tau functions of the universal character hierarchy ⋮ \(q\)-universal characters and an extension of the lattice \(q\)-universal characters ⋮ Two-component symplectic universal characters and integrable hierarchies

Cites Work

• Unnamed Item
• Symmetry approach to the integrability problem
• Solitons and infinite dimensional Lie algebras
• Universal character and \(q\)-difference Painlevé equations
• Toda equation and special polynomials associated with the Garnier system
• Moduli spaces for linear differential equations and the Painlevé equations
• Universal characters and an extension of the KP hierarchy
• Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. II
• Studies of the Painlevé equations. I: Sixth Painlevé equation \(P_{VI}\)
• Monodromy- and spectrum-preserving deformations. I
• Infinite dimensional Grassmannian structure of two-dimensional quantum gravity
• Intersection theory on the moduli space of curves and the matrix Airy function
• A matrix integral solution to two-dimensional \(W_ p\)-gravity
• Dressing chains and the spectral theory of the Schrödinger operator
• Nonlinear chains and Painlevé equations
• Rational surfaces associated with affine root systems and geometry of the Painlevé equations
• Spectral curve, Darboux coordinates and Hamiltonian structure of periodic dressing chains
• Folding transformations of the Painlevé equations
• On the decomposition of tensor products of the representations of the classical groups: By means of the universal characters
• On the Umemura polynomials for the Painlevé III equation
• The sixth Painlevé equation as similarity reduction of \({\widehat{\mathfrak{gl}}_3}\) generalized Drinfel'd-Sokolov hierarchy
• Universal characters, integrable chains and the Painlevé equations
• Relativistic Toda systems
• The sixth Painlevé equation arising fromD⁽¹⁾₄hierarchy
• A coalescent diagram of the Painlevé equations from the viewpoint of isomonodromic deformations
• Determinant structure of the rational solutions for the Painlevé IV equation
• Symmetries in the fourth Painlevé equation and Okamoto polynomials
• A determinant formula for a class of rational solutions of Painlevé V equation
• Painlevé equations from Darboux chains: I.P_III–P_V
• On a Class of Algebraic Solutions to the Painlevé VI Equation, Its Determinant Formula and Coalescence Cascade
• Explicit auto-transformations of integrable chains
• Backlund transformations of MKdV and Painleve equations
• Determinant structure of the rational solutions for the Painlevé II equation
• ON THE BILINEAR FORMS OF PAINLEVé'S 4TH EQUATION
• Third version of the dressing method

This page was built for publication: FROM KP/UC HIERARCHIES TO PAINLEVÉ EQUATIONS