Nonlinear wave equations, covariant exterior derivative, Painlevé test, and integrability

DOI10.1007/BF00672246zbMath0641.35048OpenAlexW1964723528MaRDI QIDQ1100631

A. Bringer, J. A. Louw, Willi-Hans Steeb

Publication date: 1987

Published in: International Journal of Theoretical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00672246

zbMATH Keywords

integrabilityPainlevé testnonlinear wave equationscovariant exterior derivative

Mathematics Subject Classification ID

Second-order nonlinear hyperbolic equations (35L70) Partial differential equations of mathematical physics and other areas of application (35Q99)

Cites Work

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• Remarks on the two-dimensional sine-Gordon equation and the Painlevé tests
• On the geometric origin of the equation \(\phi_{11}-\phi_{22} = \exp(\phi)-\exp(-2\phi)\)
• The soliton connection
• The sine-Gordon equations: Complete and partial integrability
• On the integrability of nonlinear Dirac equations
• The Painlevé property for partial differential equations
• On Lie–Bäcklund vector fields of the evolution equations ∂2u/∂x ∂t=f(u) and ∂u/∂t=∂2u/∂x2+f(u)
• The Bäcklund problem for the equation ∂2z/∂x1∂x2= f (z)
• Necessary condition for the existence of algebraic first integrals
• Necessary condition for the existence of algebraic first integrals

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