DOI: 10.1063/1.525721. The Painlevé property for partial differential equations

The Painlevé property for partial differential equations

10.1063/1.525721

Crossref journal-article

AIP Publishing

Journal of Mathematical Physics (317)

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.

Bibliography

Weiss, J., Tabor, M., & Carnevale, G. (1983). The PainlevÃ© property for partial differential equations. Journal of Mathematical Physics, 24(3), 522â526.

Authors 3

John Weiss (first)
M. Tabor (additional)
George Carnevale (additional)

References 17 Referenced 1,887

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10.1007/BF02413316 / Acta Math. (1890)
10.1063/1.525389 / J. Math. Phys. / Analytic structure of the Henon-Heiles Hamiltonian in integrable and nonintegrable regimes (1982)
10.1103/PhysRevA.25.1257 / Phys. Rev. A / Integrable Hamiltonian systems and the Painlevé property (1982)
10.1063/1.524491 / J. Math. Phys. (1980)
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{'key': '2024021014425296000_r12', 'first-page': '674', 'article-title': 'Integrals of Nonlinear Equations of Evolution and Solitary Waves', 'volume': '21', 'year': '1968', 'journal-title': 'Commun. Pure Appl. Math.'} / Commun. Pure Appl. Math. / Integrals of Nonlinear Equations of Evolution and Solitary Waves (1968)
{'key': '2024021014425296000_r13'}
{'key': '2024021014425296000_r14'}
{'key': '2024021014425296000_r15', 'first-page': '753', 'article-title': 'Analytic Solutions of the Two-Dimensional Kortwegde Vries Equation', 'volume': '19', 'year': '1974', 'journal-title': 'Pis’ma Zh. Eksp. Teor. Fiz.'} / Pis’ma Zh. Eksp. Teor. Fiz. / Analytic Solutions of the Two-Dimensional Kortwegde Vries Equation (1974)
{'key': '2024021014425296000_r15a', 'first-page': '387', 'volume': '19', 'year': '1974', 'journal-title': 'JETP Lett.'} / JETP Lett. (1974)

Dates

Type	When
Created	22 years, 5 months ago (March 7, 2003, 12:50 p.m.)
Deposited	1 year, 6 months ago (Feb. 10, 2024, 10:56 a.m.)
Indexed	4 hours, 17 minutes ago (Aug. 28, 2025, 8:34 a.m.)
Issued	42 years, 5 months ago (March 1, 1983)
Published	42 years, 5 months ago (March 1, 1983)
Published Print	42 years, 5 months ago (March 1, 1983)

Funders 0

None

BibTeX

@article{Weiss_1983, title={The Painlevé property for partial differential equations}, volume={24}, ISSN={1089-7658}, url={http://dx.doi.org/10.1063/1.525721}, DOI={10.1063/1.525721}, number={3}, journal={Journal of Mathematical Physics}, publisher={AIP Publishing}, author={Weiss, John and Tabor, M. and Carnevale, George}, year={1983}, month=mar, pages={522–526} }

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