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Teoreticheskaya i Matematicheskaya Fizika, 2007, Volume 153, Number 1, Pages 58–67
DOI: https://doi.org/10.4213/tmf6121 (Mi tmf6121) 		 
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)
Full-text PDF (395 kB) Citations (12)
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DOI: https://doi.org/10.4213/tmf6121
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
English version:
Theoretical and Mathematical Physics, 2007, Volume 153, Issue 1, Pages 1398–1406
DOI: https://doi.org/10.1007/s11232-007-0123-z
Bibliographic databases:
Language: Russian
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
Citation in format AMSBIB
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    • This publication is cited in the following 12 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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