On fourth-order nonlinear differential equations with the Painlevé property

DOI10.1134/S0012266106080027zbMath1148.34057OpenAlexW1988501446MaRDI QIDQ2480406

V. I. Gromak

Publication date: 31 March 2008

Published in: Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0012266106080027

zbMATH Keywords

Painlevé propertyHamiltonian systemsBäcklund transformationsspecial solutions

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55)

Related Items

Special polynomials associated with some hierarchies ⋮ “Quantizations” of isomonodromic Hamilton system $H^{\frac{7}{2}+1}$ ⋮ Application of symmetry and singularity analyses to mathematical models of biological systems ⋮ The Symmetric Fourth Painlevé Hierarchy and Associated Special Polynomials ⋮ Special polynomials associated with rational solutions of some hierarchies

Cites Work

• Unnamed Item
• Unnamed Item
• Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. I: General theory and \(\tau \)-function
• Double Bäcklund transformations and special integrals for the \(K_{II}\) hierarchy
• Studies on the Painlevé equations. III: Second and fourth Painlevé equations, \(P_{II}\) and \(P_{IV}\)
• Monodromy- and spectrum-preserving deformations. I
• Bäcklund transformations and their applications
• The Hénon-Heiles system revisited
• Painlevé differential equations in the complex plane
• Non-autonomous Hénon-Heiles systems
• The first and second Painlevé equations of higher order and some relations between them
• First-degree birational transformations of the Painlevé equations and their contiguity relations
• Discrete equations corresponding to fourth-order differential equations of the P₂ and K₂ hierarchies
• Bäcklund transformations for the second Painlevé hierarchy: a modified truncation approach
• Higher‐order Painlevé Equations in the Polynomial Class I. Bureau Symbol P2
• Rational Solutions of Painlevé Equations
• Solutions of the first and second Painlevé equations are meromorphic