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Zapiski Nauchnykh Seminarov POMI, 2012, Volume 398, Pages 145–161
(Mi znsl5200)
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This article is cited in 1 scientific paper (total in 1 paper)
Parametric Painlevé equations
A. V. Kitaev St. Petersburg Department of the Steklov Mathematical Institute, St. Petersburg, Russia
Abstract:
The parametric Painlevé equations are those ODEs whose general solutions can be presented in the parametric form in terms of the Painlevé functions. Most of these ODEs do not possess the Painlevé property. By considering similarity solutions of the short pulse equation and its decoupled generalization we derive a non-trivial example of the parametric Painlevé equation related with the third Painlevé equation. We also discuss some analytic properties of this equation describing the structure of movable singularities.
Key words and phrases:
the Painlevé equations, isomonodromy deformations, Lax pair, short pulse equation.
Received: 19.03.2012
Citation:
A. V. Kitaev, “Parametric Painlevé equations”, Questions of quantum field theory and statistical physics. Part 22, Zap. Nauchn. Sem. POMI, 398, POMI, St. Petersburg, 2012, 145–161; J. Math. Sci. (N. Y.), 192:1 (2013), 81–90
Linking options:
https://www.mathnet.ru/eng/znsl5200 https://www.mathnet.ru/eng/znsl/v398/p145
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Abstract page: | 201 | Full-text PDF : | 65 | References: | 29 |
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