Cover Image

A Fully Noncommutative Painlevé II Hierarchy: Lax Pair and Solutions Related to Fredholm Determinants

We consider Fredholm determinants of matrix Hankel operators associated with matrix versions of the -th Airy functions. Using the theory of integrable operators, we relate them to a fully noncommutative Painlevé II hierarchy, defined through a matrix-valued version of the Lenard operators. In partic...

Full description

Saved in:

Bibliographic Details
Published in:	Symmetry, Integrability and Geometry: Methods and Applications
Date:	2021
Main Author:	Tarricone, Sofia
Format:	Article
Language:	English
Published:	Інститут математики НАН України 2021
Online Access:	https://nasplib.isofts.kiev.ua/handle/123456789/211186
Tags:	Add Tag No Tags, Be the first to tag this record!
Journal Title:	Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:	A Fully Noncommutative Painlevé II Hierarchy: Lax Pair and Solutions Related to Fredholm Determinants. Sofia Tarricone. SIGMA 17 (2021), 002, 25 pages

Institution

Digital Library of Periodicals of National Academy of Sciences of Ukraine

Similar Items

Recursion Relation for Toeplitz Determinants and the Discrete Painlevé II Hierarchy
by: Chouteau, Thomas, et al.
Published: (2023)

Construction of a Lax Pair for the E₆⁽¹⁾ q-Painlevé System
by: Witte, N.S., et al.
Published: (2012)

Simple Lax Description of the ILW Hierarchy
by: Buryak, A., et al.
Published: (2018)

A Lax Formalism for the Elliptic Difference Painlevé Equation
by: Yamada, Y.
Published: (2009)

A 3 × 3 Lax Form for the -Painlevé Equation of Type ₆
by: Park, Kanam
Published: (2023)

Bäcklund Transformations for First and Second Painlevé Hierarchies
by: Sakka, A.H.
Published: (2009)

Lax Integrable Supersymmetric Hierarchies on Extended Phase Spaces
by: Hentosh, O.Ye.
Published: (2006)

Rational Solutions of the Painlevé-II Equation Revisited
by: Miller, P.D., et al.
Published: (2017)

On the Increasing Tritronquée Solutions of the Painlevé-II Equation
by: Miller, P.D.
Published: (2018)

Lax Pair for a Novel Two-Dimensional Lattice
by: Kuznetsova, Maria N.
Published: (2021)

The Elliptic Painlevé Lax Equation vs. van Diejen's 8-Coupling Elliptic Hamiltonian
by: Noumi, Masatoshi, et al.
Published: (2020)

A Class of Special Solutions for the Ultradiscrete Painlevé II Equation
by: Isojima, Sh., et al.
Published: (2011)

On Spectral Properties of the L Operator in the Lax Pair of the sine-Gordon Equation
by: Kappeler, Thomas, et al.
Published: (2018)

On Spectral Properties of the L Operator in the Lax Pair of the sine-Gordon Equation
by: Th. Kappeler, et al.
Published: (2018)

On Spectral Properties of the L Operator in the Lax Pair of the sine-Gordon Equation
by: Kappeler, T., et al.
Published: (2018)

Bargmann type finite-dimensional reductions of the Lax integrable supersymmetric Boussinesq hierarchy and their integrability
by: Ye. Hentosh
Published: (2015)

Bargmann type finite-dimensional reductions of the Lax integrable supersymmetric Boussinesq hierarchy and their integrability
by: Hentosh, O.E.
Published: (2015)

The Malgrange Form and Fredholm Determinants
by: Bertola, M.
Published: (2017)

On the fredholm theory of a planar problem with shift for a pair of functions
by: Lysenko, Z. M., et al.
Published: (2011)

Large z Asymptotics for Special Function Solutions of Painlevé II in the Complex Plane
by: Deaño, A.
Published: (2018)

A Completeness Study on Certain 2×2 Lax Pairs Including Zero Terms
by: Hay, M.C.
Published: (2011)

Quantization of Calogero-Painlevé System and Multi-Particle Quantum Painlevé Equations II-VI
by: Mobasheramini, Fatane, et al.
Published: (2021)

Rational Solutions of Painlevé V from Hankel Determinants and the Asymptotics of Their Pole Locations
by: Balogoun, Malik, et al.
Published: (2025)

Information complexity of projection algorithms for the solution of Fredholm equations of the first kind. II
by: Solodkii, S. G., et al.
Published: (1998)

Differential Equations for Approximate Solutions of Painlevé Equations: Application to the Algebraic Solutions of the Painlevé-III (D₇) Equation
by: Buckingham, Robert J., et al.
Published: (2024)

Truncated Solutions of Painlevé Equation Pv
by: Costin, R.D.
Published: (2018)

Hierarchy and asymmetry in international relations
by: I. P. Derevianko
Published: (2021)

Lax-integrable Laberge–Mathieu hierarchy of supersymmetric nonlinear dynamical systems and its finite-dimensional reduction of Neumann type
by: Hentosh, О. Ye., et al.
Published: (2009)

Tronquée Solutions of the Third and Fourth Painlevé Equations
by: Xia, X.
Published: (2018)

Stochastic dynamics and Boltzmann hierarchy. II
by: Petrina, D. Ya., et al.
Published: (1998)

On fully wild categories of representations of posets
by: Kasjan, Stanislaw
Published: (2018)

On fully wild categories of representations of posets
by: Kasjan, S.
Published: (2006)

Evolutionary Hirota Type (2+1)-Dimensional Equations: Lax Pairs, Recursion Operators and Bi-Hamiltonian Structures
by: Sheftel, M.B., et al.
Published: (2018)

Improved analytic hierarchy process on the basis of clarification of formation procedures for matrix of paired comparisons
by: M. M. Potomkin, et al.
Published: (2020)

On topological approach to fully nonlinear parabolic problems
by: Skrypnik, I.V., et al.
Published: (2002)

Description of bilateral ideals in a class of noncommutative rings. II
by: Bavula, V. V., et al.
Published: (1993)

Ermakov-Painlevé II Symmetry Reduction of a Korteweg Capillarity System
by: Rogers, C., et al.
Published: (2017)

Hypergeometric Solutions of the A₄⁽¹⁾-Surface q-Painlevé IV Equation
by: Nakazono, N.
Published: (2014)

An Isomonodromy Interpretation of the Hypergeometric Solution of the Elliptic Painlevé Equation (and Generalizations)
by: Rains, E.M.
Published: (2011)

Meromorphic Solution of the Degenerate Third Painlevé Equation Vanishing at the Origin
by: Kitaev, A.V.
Published: (2019)