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Teoreticheskaya i Matematicheskaya Fizika, 2010, Volume 162, Number 1, Pages 69–74
DOI: https://doi.org/10.4213/tmf6455 (Mi tmf6455) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Hamiltonians associated with the third and fifth Painlevé equations

V. V. Tsegel'nik

Belarusian State University of Informatics and Radioelectronics, Minsk, Belarus
Full-text PDF (372 kB) Citations (5)
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DOI: https://doi.org/10.4213/tmf6455
Abstract: We obtain a Painlevé-type differential equation for the simplest rational Hamiltonian associated with the fifth Painlevé equation in the case $\gamma\ne0$, $\delta=0$. We prove the existence of Hamiltonians of a nonrational type associated with the fifth Painlevé equation in the case $\gamma\ne0$, $\delta=0$. We obtain a generalization of the Garnier and Okamoto formulas for rational Hamiltonians associated with the third Painlevé equation.
Keywords: third Painlevé equation, fifth Painlevé equation, Hamiltonian.
Received: 26.12.2008
Revised: 25.05.2009
English version:
Theoretical and Mathematical Physics, 2010, Volume 162, Issue 1, Pages 57–62
DOI: https://doi.org/10.1007/s11232-010-0003-9
Bibliographic databases:
Language: Russian
Citation: V. V. Tsegel'nik, “Hamiltonians associated with the third and fifth Painlevé equations”, TMF, 162:1 (2010), 69–74; Theoret. and Math. Phys., 162:1 (2010), 57–62
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf/v162/i1/p69
    • This publication is cited in the following 5 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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