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This article is cited in 20 scientific papers (total in 21 papers)
Higher Painlevé Transcendents as Special Solutions of Some Nonlinear Integrable Hierarchies
Nikolay A. Kudryashov Department of Applied Mathematics,
National Research Nuclear University “MEPhI”,
Kashirskoe sh. 31, Moscow, 115409 Russia
Abstract:
It is well known that the self-similar solutions of the Korteweg–de Vries equation and the modified Korteweg–de Vries equation are expressed via the solutions of the first and second Painlevé equations. In this paper we solve this problem for all equations from the Korteveg–de Vries, modified Korteweg–de Vries, Kaup–Kupershmidt, Caudrey–Dodd–Gibbon and Fordy–Gibbons hierarchies. We show that the self-similar solutions of equations corresponding to hierarchies mentioned above can be found by means of the general solutions of higher-order Painlevé hierarchies introduced more than ten years ago.
Keywords:
Painlevé equation, Painlevé transcendent, Korteweg–de Vries hierarchy, modified Korteveg–de Vries hierarchy, Kaup–Kupershmidt hierarchy, Caudrey–Dodd–Cibbon hierarchy.
Received: 02.12.2013 Accepted: 22.12.2013
Citation:
Nikolay A. Kudryashov, “Higher Painlevé Transcendents as Special Solutions of Some Nonlinear Integrable Hierarchies”, Regul. Chaotic Dyn., 19:1 (2014), 48–63
Linking options:
https://www.mathnet.ru/eng/rcd140 https://www.mathnet.ru/eng/rcd/v19/i1/p48
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Abstract page: | 257 | References: | 70 |
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