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TMF, 2010, Volume 162, Number 1, Pages 69–74 (Mi tmf6455)  

This article is cited in 3 scientific papers (total in 3 papers)

Hamiltonians associated with the third and fifth Painlevé equations

V. V. Tsegel'nik

Belarusian State University of Informatics and Radioelectronics, Minsk, Belarus

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

DOI: https://doi.org/10.4213/tmf6455

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English version:
Theoretical and Mathematical Physics, 2010, 162:1, 57–62

Bibliographic databases:

Received: 26.12.2008
Revised: 25.05.2009

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

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Askhabov S.N., “Nelineinye uravneniya s vesovymi yadrami tipa potentsiala v kompleksnykh prostranstvakh lebega”, Nauchnye vedomosti belgorodskogo gosudarstvennogo universiteta, 25:23 (2011), 5–20  elib
    2. B. I. Suleimanov, ““Kvantovaya” linearizatsiya uravnenii Penleve kak komponenta ikh $L,A$ par”, Ufimsk. matem. zhurn., 4:2 (2012), 127–135  mathnet
    3. B. I. Suleimanov, “Quantum aspects of the integrability of the third Painlevé equation and a non-stationary time Schrödinger equation with the Morse potential”, Ufa Math. J., 8:3 (2016), 136–154  mathnet  crossref  mathscinet  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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