Bäcklund transformation and the Painlevé property

DOI10.1063/1.527134zbMath0617.35118OpenAlexW2565154731MaRDI QIDQ4726749

John Weiss

Publication date: 1986

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.527134

zbMATH Keywords

integrabilityuniformizationBäcklund transformationsmeromorphic functionsfactorizations of operatorsgeneralized Painlevé test

Mathematics Subject Classification ID

Partial differential equations of mathematical physics and other areas of application (35Q99) Geometric theory, characteristics, transformations in context of PDEs (35A30)

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Cites Work

• The reduction problem and the inverse scattering method
• The Schwarzian derivative and uniformization
• Integrable nonlinear Klein-Gordon equations and Toda lattices
• Conservation laws and symmetries of generalized sine-Gordon equations
• Monodromy groups and linearly polymorphic functions
• A Method for Finding N-Soliton Solutions of the K.d.V. Equation and K.d.V.-Like Equation
• The Lie Algebra Structure of Degenerate Hamiltonian and Bi-Hamiltonian Systems
• The sine-Gordon equations: Complete and partial integrability
• Sir Edmund Whittaker's Work on Automorphic Functions
• The Painlevé property for partial differential equations. II: Bäcklund transformation, Lax pairs, and the Schwarzian derivative
• The Painlevé property for partial differential equations
• On classes of integrable systems and the Painlevé property
• The Painlevé property and Bäcklund transformations for the sequence of Boussinesq equations
• On the one- and two-dimensional Toda lattices and the Painlevé property
• The Painlevé Property and Hirota's Method
• Modified equations, rational solutions, and the Painlevé property for the Kadomtsev–Petviashvili and Hirota–Satsuma equations
• The weak-Painlevé property as a criterion for the integrability of dynamical systems
• Quasiconformal mappings, with applications to differential equations, function theory and topology
• A new hierarchy of Korteweg–de Vries equations
• Bäcklund transformations for the sine–Gordon equations
• The Schwarzian Derivative and Disconjugacy of nth order Linear Differential Equations
• Uniformization, Moduli, and Kleinian Groups†
• Necessary condition for the existence of algebraic first integrals

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