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, 2012, Volume 173, Number 2, Pages 245–267
DOI: https://doi.org/10.4213/tmf8320 (Mi tmf8320) 		 
This article is cited in 8 scientific papers (total in 8 papers)

Solution of the equivalence problem for the Painlevé IV equation

V. V. Kartakab

a Ufa State Aviation Technical University, Ufa, Russia
b Bashkir State University, Ufa, Russia
Full-text PDF (484 kB) Citations (8)
References:
PDF
HTML
DOI: https://doi.org/10.4213/tmf8320
Abstract: We solve the equivalence problem for the Painlevé IV equation, formulating the necessary and sufficient conditions in terms of the invariants of point transformations for an arbitrary second-order differential equation to be equivalent to the Painlevé IV equation. We separately consider three pairwise nonequivalent cases: both equation parameters are zero, $a=b=0$; only one parameter is zero, $b=0$; and the parameter $b\ne0$. In all cases, we give an explicit point substitution transforming an equation satisfying the described test into the Painlevé IV equation and also give expressions for the equation parameters in terms of invariants.
Keywords: Painlevé equation, point transformation, equivalence problem, invariant.
Received: 29.12.2011
Revised: 13.06.2012
English version:
Theoretical and Mathematical Physics, 2012, Volume 173, Issue 2, Pages 1541–1564
DOI: https://doi.org/10.1007/s11232-012-0132-4
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: V. V. Kartak, “Solution of the equivalence problem for the Painlevé IV equation”, TMF, 173:2 (2012), 245–267; Theoret. and Math. Phys., 173:2 (2012), 1541–1564
Citation in format AMSBIB
\Bibitem{Kar12}
\by V.~V.~Kartak
\paper Solution of the~equivalence problem for the~Painlev\'e IV equation
\jour TMF
\yr 2012
\vol 173
\issue 2
\pages 245--267
\mathnet{http://mi.mathnet.ru/tmf8320}
\crossref{https://doi.org/10.4213/tmf8320}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3172195}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2012TMP...173.1541K}
\elib{https://elibrary.ru/item.asp?id=20732546}
\transl
\jour Theoret. and Math. Phys.
\yr 2012
\vol 173
\issue 2
\pages 1541--1564
\crossref{https://doi.org/10.1007/s11232-012-0132-4}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000312081200005}
\elib{https://elibrary.ru/item.asp?id=20486604}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84870760347}
Linking options:
  • https://www.mathnet.ru/eng/tmf8320
  • https://doi.org/10.4213/tmf8320
  • https://www.mathnet.ru/eng/tmf/v173/i2/p245
    • This publication is cited in the following 8 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
    Statistics & downloads:
    Abstract page:490
    Full-text PDF :201
    References:94
    First page:29
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024