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This article is cited in 12 scientific papers (total in 12 papers)
Special polynomials and rational solutions of the hierarchy of the second Painlevé equation
M. V. Demina, N. A. Kudryashov Moscow Engineering Physics Institute (State University)
Abstract:
We study special polynomials used to represent rational solutions of
the hierarchy of the second Painlevé equation. We find several recursion
relations satisfied by these polynomials. In particular, we obtain
a differential–difference relation that allows finding any polynomial
recursively. This relation is an analogue of the Toda chain equations.
Keywords:
Painlevé equations, hierarchy of the second Painlevé equation, rational solution, special polynomial, Toda chain.
Received: 27.12.2006
Citation:
M. V. Demina, N. A. Kudryashov, “Special polynomials and rational solutions of the hierarchy of the second Painlevé equation”, TMF, 153:1 (2007), 58–67; Theoret. and Math. Phys., 153:1 (2007), 1398–1406
Linking options:
https://www.mathnet.ru/eng/tmf6121https://doi.org/10.4213/tmf6121 https://www.mathnet.ru/eng/tmf/v153/i1/p58
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Abstract page: | 699 | Full-text PDF : | 303 | References: | 69 | First page: | 2 |
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