Hamiltonians associated with the third and fifth Painlevé equations
type: Item
instance of: scholarly article
title: Hamiltonians associated with the third and fifth Painlevé equations
zbMATH Open document ID: 1216.34098
published in: Theoretical and Mathematical Physics
publication date: 2010-09-24T00:00:00Z
review text: The Painlevé equations are nonlinear second order differential equations, solutions of which have numerous applications in modern mathematics. It is known from the works of K. Okamoto that the Painlevé equations can be written in a Hamiltonian form with polynomial Hamiltonians. The author investigates Painlevé type differential equations with rational Hamiltonians which are related to the third and fifth Painlevé equation.
reviewed by: Galina Filipuk
Mathematics Subject Classification ID: 34M55
zbMATH DE Number: 5790837
zbMATH Keywords: Painlevé equations
zbMATH Keywords: Hamiltonians
author: V. V. Tsegel'nik
MaRDI profile type: Publication
full work available at URL: s11232-010-0003-9
OpenAlex ID: W2050455102
cites work: Density matrix of an impenetrable Bose gas and the fifth Painlevé transcendent
cites work: Painlevé functions of the third kind
cites work: Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder Transition
cites work: Holonomic quantum fields. V
cites work: Polynomial Hamiltonians associated with Painleve equations. II: Differential equations satisfied by polynomial Hamiltonians
cites work: Polynomial Hamiltonians associated with Painleve equations. I
cites work: Hamiltonians associated with the sixth Painlevé equation
cites work: Level spacing distributions and the Bessel kernel
cites work: Integrable lattices: Random matrices and random permutations
cites work: Painlevé equations as classical analogues of Heun equations
cites work: Painlevé equations and isomonodromic deformations of equations of the Heun class
cites work: Q4490853
cites work: ``Quantizations'' of the second Painlevé equation and the problem of the equivalence of its \(L-A\) pairs
cites work: Q3999049
DOI: 10.1007/S11232-010-0003-9
description: scientific article; zbMATH DE number 5790837