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Symmetry, Integrability and Geometry: Methods and Applications, 2007, Volume 3, 073, 6 pp.
DOI: https://doi.org/10.3842/SIGMA.2007.073 (Mi sigma199) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Do All Integrable Evolution Equations Have the Painlevé Property?

K. M. Tamizhmania, Basil Grammaticosbc, Alfred Ramanid

a Departement of Mathematics, Pondicherry University, Kalapet, 605014 Puducherry, India
b Paris XI, CNRS, UMR 8165, Bât. 104, 91406 Orsay, France
c IMNC, Université Paris VII
d Centre de Physique Théorique, Ecole Polytechnique, CNRS, 91128 Palaiseau, France
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DOI: https://doi.org/10.3842/SIGMA.2007.073
Abstract: We examine whether the Painlevé property is necessary for the integrability of partial differential equations (PDEs). We show that in analogy to what happens in the case of ordinary differential equations (ODEs) there exists a class of PDEs, integrable through linearisation, which do not possess the Painlevé property. The same question is addressed in a discrete setting where we show that there exist linearisable lattice equations which do not possess the singularity confinement property (again in analogy to the one-dimensional case).
Keywords: integrability; linearisability; Painlevé property; singularity confinement.
Received: June 12, 2007; Published online June 19, 2007
Bibliographic databases:
Document Type: Article
MSC: 34A99; 35A21; 39A12
Language: English
Citation: K. M. Tamizhmani, Basil Grammaticos, Alfred Ramani, “Do All Integrable Evolution Equations Have the Painlevé Property?”, SIGMA, 3 (2007), 073, 6 pp.
Citation in format AMSBIB
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\by K.~M.~Tamizhmani, Basil Grammaticos, Alfred Ramani
\paper Do All Integrable Evolution Equations Have the Painlev\'e Property?
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    		Symmetry, Integrability and Geometry: Methods and Applications
     
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