Properties of solutions of two second-order differential equations with the Painlevé property

DOI10.1134/S0040577921030041zbMath1476.37079OpenAlexW3176453974WikidataQ115248080 ScholiaQ115248080MaRDI QIDQ2036345

V. V. Tsegel'nik

Publication date: 29 June 2021

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

Full work available at URL: https://doi.org/10.1134/s0040577921030041

zbMATH Keywords

Painlevé equationPainlevé propertyHamiltonian systemdirect Bäcklund transformationinverse Bäcklund transformation

Mathematics Subject Classification ID

Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Formal solutions and transform techniques for ordinary differential equations in the complex domain (34M25) Nonautonomous Hamiltonian dynamical systems (Painlevé equations, etc.) (37J65)

Related Items (1)

On Bäcklund transformations for some second-order nonlinear differential equations

Cites Work

• ``Quantizations of the second Painlevé equation and the problem of the equivalence of its \(L-A\) pairs
• The isomonodromic deformation method in the theory of Painlevé equations
• Polynomial Hamiltonians associated with Painleve equations. II: Differential equations satisfied by polynomial Hamiltonians
• Random unitary matrices, permutations and Painlevé
• Hamiltonians associated with the third and fifth Painlevé equations
• ``Quantizations of higher Hamiltonian analogues of the Painlevé I and Painlevé II equations with two degrees of freedom
• Hamiltonians associated with the sixth Painlevé equation
• ON A NOVEL CLASS OF INTEGRABLE ODEs RELATED TO THE PAINLEVÉ EQUATIONS
• A Hirota bilinear equation for Painlevé transcendents PIV, PII and PI
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