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This article is cited in 2 scientific papers (total in 2 papers)
Second-degree Painlevé Equations and Their Contiguity Relations
Basil Grammaticosa, Alfred Ramanib, Partha Guhacd a IMNC, Université Paris VII & XI, CNRS,UMR 8165, Bât. 440, 91406 Orsay, France
b Centre de Physique Théorique, Ecole Polytechnique, CNRS,
91128 Palaiseau, France
c Satyendranath Nath Bose National Centre for Basic Sciences,
JD Block, Sector III, Kolkata — 700098, India
d Institut des Hautes Etudes Scientifiques, 35 route de Chartres, 91440 Bures sur Yvette, France
Abstract:
We study second-order, second-degree systems related to the Painlevé equations which possess one and two parameters. In every case we show that by introducing a quantity related to the canonical Hamiltonian variables it is possible to derive such a second-degree equation. We investigate also the contiguity relations of the solutions of these higher-degree equations. In most cases these relations have the form of correspondences, which would make them non-integrable in general. However, as we show, in our case these contiguity relations are indeed integrable mappings, with a single ambiguity in their evolution (due to the sign of a square root).
Keywords:
Painlevé equations, contiguity relations, second-degree differential equations, Hamiltonian formalism.
Received: 03.10.2013 Accepted: 04.12.2013
Citation:
Basil Grammaticos, Alfred Ramani, Partha Guha, “Second-degree Painlevé Equations and Their Contiguity Relations”, Regul. Chaotic Dyn., 19:1 (2014), 37–47
Linking options:
https://www.mathnet.ru/eng/rcd139 https://www.mathnet.ru/eng/rcd/v19/i1/p37
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Abstract page: | 130 | References: | 32 |
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