The first and second Painlevé equations of higher order and some relations between them

DOI10.1016/S0375-9601(96)00795-5zbMath0962.35504OpenAlexW1993598611MaRDI QIDQ1968117

Publication date: 7 March 2000

Published in: Physics Letters. A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0375-9601(96)00795-5

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) Nonlinear ordinary differential equations and systems (34A34)

Related Items

Painlevé Test and Higher Order Differential Equations, Nonisospectral scattering problems and similarity reductions, On matrix Painlevé hierarchies, Poles and \(\alpha\)-points of meromorphic solutions of the first Painlevé hierarchy, Solution classes of the matrix second Painlevé hierarchy, On the properties of solutions of equations in the \(K_{2}\) hierarchy, Lax pairs and special polynomials associated with self-similar reductions of Sawada -- Kotera and Kupershmidt equations, Soliton, rational and special solutions of the Korteweg-de Vries hierarchy, Hierarchies of Difference Equations and Bäcklund Transformations, Paul Painlevé and his contribution to science, Higher Painlevé transcendents as special solutions of some nonlinear integrable hierarchies, Pole-free solutions of the first Painlevé hierarchy and non-generic critical behavior for the KdV equation, Systematic construction of nonautonomous Hamiltonian equations of Painlevé type. I. Frobenius integrability, Non-autonomous reductions of the KdV equation and multi-component analogs of the Painlevé equations P34 and P3, Multicomponent Painlevé ODEs and related nonautonomous KdV stationary hierarchies, Systematic construction of nonautonomous Hamiltonian equations of Painlevé‐type. II. Isomonodromic Lax representation, Unnamed Item, Hamiltonians and conjugate Hamiltonians of some fourth-order nonlinear ODEs, Rational solutions of equations associated with the second Painlevé equation, Integrability properties of a generalized reduction of the KdV6 equation, A new derivation of Painlevé hierarchies, On Lagrangians and Hamiltonians of some fourth-order nonlinear Kudryashov ODEs, Bäcklund transformations for a new extended Painlevé hierarchy, Traveling wave reduction of the modified KdV hierarchy: the Lax pair and the first integrals, On the nesting of Painlevé hierarchies: a Hamiltonian approach, Nonlinear differential equations of the second, third and fourth order with exact solutions, Higher‐Order Painlevé Equations in the Polynomial Class II: Bureau Symbol P1, On matrix fourth Painlevé hierarchies, A Lagrangian description of the higher-order Painlevé equations, On symmetries of the non-stationary PIIn hierarchy and their applications, Non-autonomous Hénon-Heiles systems, Nonlinear differential equations associated with the first Painlevé hierarchy, Global meromorphy of solutions of the Painlevé equations and their hierarchies, On the Stokes geometry of a unified family of \(P_{\mathrm{J}}\)-hierarchies (J=I, II, IV, 34), Power expansions for solution of the fourth-order analog to the first Painlevé equation, Non-autonomous Hénon-Heiles system from Painlevé class, Unnamed Item, Rational and special solutions for some Painlevé hierarchies, Instanton-type solutions for the second and the fourth Painlevé hierarchies with a large parameter, A generalized sextic Freud weight, Polygons of differential equations for finding exact solutions, Lower estimates of the growth order of solutions to the second Painlevé hierarchy, Third order differential equations with fixed critical points, Multi-Poisson approach to the Painlevé equations: from the isospectral deformation to the isomonodromic deformation, Power and non-power expansions of the solutions for the fourth-order analogue to the second Painlevé equation, Special polynomials and rational solutions of the hierarchy of the second Painlevé equation, On fourth-order nonlinear differential equations with the Painlevé property, The Yablonskii-Vorob'ev polynomials for the second Painlevé hierarchy, The Prelle-Singer method and Painlevé hierarchies, A certain expression of the first Painlevé hierarchy, Lax pair and first integrals of the traveling wave reduction for the KdV hierarchy, On tronquée solutions of the first Painlevé hierarchy, On an extended second Painlevé hierarchy, Special polynomials associated with rational solutions of some hierarchies, Lax pairs for one of hierarchies similar to the first Painlevé hierarchy, A note on solutions of the Korteweg-de Vries hierarchy, On the mKdV-Liouville hierarchy and its self-similarity reduction, Bäcklund transformations for new fourth Painlevé hierarchies, Lax pairs and rational solutions of similarity reductions for Kupershmidt and Sawada-Kotera hierarchies, General formal solutions for a unified family of \(P_{\mathrm{J}}\)-hierarchies (J=I, II, IV, 34), Existence of a global solution of the Whitham equations, Nonisospectral scattering problems: A key to integrable hierarchies, Auxiliary differential polynomials for the first Painlevé hierarchy, Discrete equations corresponding to fourth-order differential equations of the P₂ and K₂ hierarchies

Cites Work