Teoreticheskaya i Matematicheskaya Fizika
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


TMF:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

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)
References:
PDF
HTML
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 (hh-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
\Bibitem{Tse07}
\by V.~V.~Tsegel'nik
\paper Hamiltonians associated with the~sixth Painlev\'e equation
\jour TMF
\yr 2007
\vol 151
\issue 1
\pages 54--65
\mathnet{http://mi.mathnet.ru/tmf6011}
\crossref{https://doi.org/10.4213/tmf6011}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2347302}
\zmath{https://zbmath.org/?q=an:1189.35292}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2007TMP...151..482T}
\elib{https://elibrary.ru/item.asp?id=9521571}
\transl
\jour Theoret. and Math. Phys.
\yr 2007
\vol 151
\issue 1
\pages 482--491
\crossref{https://doi.org/10.1007/s11232-007-0036-x}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000245809000004}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-34247209066}
Linking options:
  • https://www.mathnet.ru/eng/tmf6011
  • https://doi.org/10.4213/tmf6011
  • https://www.mathnet.ru/eng/tmf/v151/i1/p54
    • This publication is cited in the following 3 articles:
    1. V. V. Tsegel'nik, “Properties of solutions of two second-order differential equations with the Painlevé property”, Theoret. and Math. Phys., 206:3 (2021), 315–320  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    2. Conte R., “Generalized Bonnet Surfaces and Lax pairs of P-Vi”, J. Math. Phys., 58:10 (2017), 103508  crossref  mathscinet  zmath  isi  scopus
    3. V. V. Tsegel'nik, “Hamiltonians associated with the third and fifth Painlevé equations”, Theoret. and Math. Phys., 162:1 (2010), 57–62  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    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
    Statistics & downloads:
    Abstract page:471
    Full-text PDF :288
    References:80
    First page:1
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025