Special polynomials and rational solutions of the hierarchy of the second Painlevé equation

DOI10.1007/s11232-007-0123-zzbMath1138.35388OpenAlexW1978954081MaRDI QIDQ2480101

Nikolay A. Kudryashov, Maria V. Demina

Publication date: 31 March 2008

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

Full work available at URL: https://doi.org/10.1007/s11232-007-0123-z

zbMATH Keywords

Painlevé equationsToda chainrational solutionspecial polynomialhierarchy of the second Painlevé equation

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) Other special orthogonal polynomials and functions (33C47)

Related Items (12)

On the properties of solutions of the equations in the generalized hierarchy of the equation \(P_{34}\) ⋮ Multi-particle dynamical systems and polynomials ⋮ Soliton, rational and special solutions of the Korteweg-de Vries hierarchy ⋮ Electrostatic partners and zeros of orthogonal and multiple orthogonal polynomials ⋮ Analytic properties of solutions to equations in the generalized hierarchy of the second Painlevé equation ⋮ From Laurent series to exact meromorphic solutions: The Kawahara equation ⋮ Point vortices and polynomials of the Sawada-Kotera and Kaup-Kupershmidt equations ⋮ Point vortices and classical orthogonal polynomials ⋮ Modified method of simplest equation and its application to nonlinear PDEs ⋮ Hankel determinant approach to generalized Vorob'ev-Yablonski polynomials and their roots ⋮ Solutions of the fourth-order equation in the generalized hierarchy of the second Painlevé equation ⋮ Unnamed Item

Cites Work

• Symmetry approach to the integrability problem
• Studies on the Painlevé equations. III: Second and fourth Painlevé equations, \(P_{II}\) and \(P_{IV}\)
• Remarks on the Yablonskii-Vorob'ev polynomials
• Integrable lattices
• Painlevé differential equations in the complex plane
• Uniformization and transcendence of solutions for the first and second Painlevé hierarchies
• Non-autonomous Hénon-Heiles systems
• The first and second Painlevé equations of higher order and some relations between them
• The Yablonskii-Vorob'ev polynomials for the second Painlevé hierarchy
• The second Painlev  equation, its hierarchy and associated special polynomials
• Unnamed Item
• Unnamed Item

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