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The Painlevé property for partial differential equations
Abstract
In this paper we define the Painlevé property for partial differential equations and show how it determines, in a remarkably simple manner, the integrability, the Bäcklund transforms, the linearizing transforms, and the Lax pairs of three well-known partial differential equations (Burgers’ equation, KdV equation, and the modified KdV equation). This indicates that the Painlevé property may provide a unified description of integrable behavior in dynamical systems (ordinary and partial differential equations), while, at the same time, providing an efficient method for determining the integrability of particular systems.
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Citations
Cited by
Pattern formation outside of equilibrium
Cross, M. C., & Hohenberg, P. C. (1993) · Reviews of Modern Physics · doi:10.1103/revmodphys.65.851 · Cited by 7,859
Chaotic streamlines in the ABC flows
Dombre, T., Frisch, U., Greene, J. M., Hénon, M., Mehr, A., & Soward, A. M. (1986) · Journal of Fluid Mechanics · doi:10.1017/s0022112086002859 · Cited by 744
Metadata
- Authors
- Weiss, J., Tabor, M., & Carnevale, G.
- Venue
- Journal of Mathematical Physics
- Publisher
- AIP Publishing
- Published
- 1983-03-01
- Volume
- 24
- Issue
- 3
- Pages
- 522-526
- ISSN
- 0022-2488 (ISSN-L)
- 1089-7658
- OpenAlex
- W2083332431
- Cited by
- 2,157
- References
- 0
- FWCI
- 35.30
- Type
- journal article
- Language
- en
- Open access
- closed
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- CoChat. (2026). Citation check: The Painlevé property for partial differential equations. https://app.cochat.ai/papers/10.1063/1.525721
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- Weiss, J., Tabor, M., & Carnevale, G. (1983). The Painlevé property for partial differential equations. Journal of Mathematical Physics. https://doi.org/10.1063/1.525721
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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