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Teoreticheskaya i Matematicheskaya Fizika, 2007, Volume 151, Number 1, Pages 54–65
DOI: https://doi.org/10.4213/tmf6011 (Mi tmf6011) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Hamiltonians associated with the sixth Painlevé equation

V. V. Tsegel'nik

Belarussian State University of Computer Science and Radioelectronic Engineering
Full-text PDF (420 kB) Citations (3)
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DOI: https://doi.org/10.4213/tmf6011
Abstract: We obtain the formula determining the general form of polynomial Hamiltonians associated with the sixth Painlevé equation and prove its uniqueness. We prove the existence of nonpolynomial Hamiltonians associated with this equation. We identify the Hamiltonian class for which the defining differential equation coincides with the equation ($h$-equation) for the simplest polynomial Hamiltonian (the Okamoto Hamiltonian).
Keywords: Painlevé equation, Hamiltonian, family of solutions, Bäcklund transformation, Heun equation.
Received: 06.07.2006
Revised: 08.09.2006
English version:
Theoretical and Mathematical Physics, 2007, Volume 151, Issue 1, Pages 482–491
DOI: https://doi.org/10.1007/s11232-007-0036-x
Bibliographic databases:
Language: Russian
Citation: V. V. Tsegel'nik, “Hamiltonians associated with the sixth Painlevé equation”, TMF, 151:1 (2007), 54–65; Theoret. and Math. Phys., 151:1 (2007), 482–491
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf/v151/i1/p54
    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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    References:70
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