Non-Abelian integrable hierarchies: matrix biorthogonal polynomials and perturbations

DOI10.1088/1751-8121/aab9cazbMath1401.37073OpenAlexW2794543352MaRDI QIDQ4581252

Gerardo Ariznabarreta, Juan Carlos García-Ardila, Manuel Mañas, Francisco Marcellán

Publication date: 16 August 2018

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

Full work available at URL: https://doi.org/10.1088/1751-8121/aab9ca

zbMATH Keywords

quasideterminantsbilinear identitiesmatrix biorthogonal polynomialsChristoffel-type formulasnon-abelian Toda lattice hierarchynoncommutative KP hierarchy

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions (37K20) Other special orthogonal polynomials and functions (33C47)

Related Items (12)

Multivariate orthogonal Laurent polynomials and integrable systems ⋮ Multivariate Toda hierarchies and biorthogonal polynomials ⋮ Revisiting biorthogonal polynomials: an \(LU\) factorization discussion ⋮ Pearson equations for discrete orthogonal polynomials: I. Generalized hypergeometric functions and Toda equations ⋮ Laguerre–Freud equations for three families of hypergeometric discrete orthogonal polynomials ⋮ Duality and difference operators for matrix valued discrete polynomials on the nonnegative integers ⋮ Matrix biorthogonal polynomials: eigenvalue problems and non-Abelian discrete Painlevé equations. A Riemann-Hilbert problem perspective ⋮ Christoffel transformation for a matrix of bi-variate measures ⋮ Ratio asymptotics for biorthogonal matrix polynomials with unbounded recurrence coefficients ⋮ Pearson equations for discrete orthogonal polynomials. III: Christoffel and Geronimus transformations ⋮ Matrix biorthogonal polynomials on the real line: Geronimus transformations ⋮ Multiple orthogonal polynomials: Pearson equations and Christoffel formulas

Uses Software

• OPQ

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