Remarks on the two-dimensional sine-Gordon equation and the Painlevé tests

DOI10.1007/BF00420570zbMath0591.35061OpenAlexW2052118245MaRDI QIDQ1074783

Peter A. Clarkson

Publication date: 1985

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

Full work available at URL: https://doi.org/10.1007/bf00420570

zbMATH Keywords

sine-Gordon equationinverse scatteringmovable logarithmic branch pointPainlevé conjecture

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Partial differential equations of mathematical physics and other areas of application (35Q99)

Related Items (3)

Nonlinear wave equations, covariant exterior derivative, Painlevé test, and integrability ⋮ Nonlinear quantum-mechanical system associated with Sine-Gordon equation in (1 + 2) dimensions ⋮ Static solitons, Lorentz invariance, and a new perspective on the integrability of the sine Gordon equation in (1+2) dimensions

Cites Work

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• A boundary value problem associated with the second Painleve transcendent and the Korteweg-de Vries equation
• Lie transformations, nonlinear evolution equations, and Painlevé forms
• The sine-Gordon equations: Complete and partial integrability
• The Painlevé property for partial differential equations. II: Bäcklund transformation, Lax pairs, and the Schwarzian derivative
• The Painlevé property for partial differential equations
• The Connection between Partial Differential Equations Soluble by Inverse Scattering and Ordinary Differential Equations of Painlevé Type
• Nonlinear Diffusion Equations, Integrability and the Painlevé Property

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