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, 2009, Volume 159, Number 3, Pages 515–526
DOI: https://doi.org/10.4213/tmf6369 (Mi tmf6369) 		 
This article is cited in 24 scientific papers (total in 24 papers)

Padé approximations for Painlevé I and II transcendents

V. Yu. Novokshenov

Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences
Full-text PDF (721 kB) Citations (24)
References:
PDF
HTML
DOI: https://doi.org/10.4213/tmf6369
Abstract: We use a version of the Fair–Luke algorithm to find the Padé approximate solutions of the Painlevé I and II equations. We find the distributions of poles for the well-known Ablowitz–Segur and Hastings–McLeod solutions of the Painlevé II equation. We show that the Boutroux tritronquée solution of the Painleé I equation has poles only in the critical sector of the complex plane. The algorithm allows checking other analytic properties of the Painlevé transcendents, such as the asymptotic behavior at infinity in the complex plane.
Keywords: Painlevé equation, meromorphic solution, distribution of poles, Padé approximation, continued fraction, Riemann–Hilbert problem.
English version:
Theoretical and Mathematical Physics, 2009, Volume 159, Issue 3, Pages 853–862
DOI: https://doi.org/10.1007/s11232-009-0073-8
Bibliographic databases:
Language: Russian
Citation: V. Yu. Novokshenov, “Padé approximations for Painlevé I and II transcendents”, TMF, 159:3 (2009), 515–526; Theoret. and Math. Phys., 159:3 (2009), 853–862
Citation in format AMSBIB
\Bibitem{Nov09}
\by V.~Yu.~Novokshenov
\paper Pad\'e approximations for Painlev\'e I and II transcendents
\jour TMF
\yr 2009
\vol 159
\issue 3
\pages 515--526
\mathnet{http://mi.mathnet.ru/tmf6369}
\crossref{https://doi.org/10.4213/tmf6369}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2568568}
\zmath{https://zbmath.org/?q=an:1185.34139}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2009TMP...159..853N}
\transl
\jour Theoret. and Math. Phys.
\yr 2009
\vol 159
\issue 3
\pages 853--862
\crossref{https://doi.org/10.1007/s11232-009-0073-8}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000269118800018}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-70350035894}
Linking options:
  • https://www.mathnet.ru/eng/tmf6369
  • https://doi.org/10.4213/tmf6369
  • https://www.mathnet.ru/eng/tmf/v159/i3/p515
    • This publication is cited in the following 24 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:589
    Full-text PDF :232
    References:65
    First page:24
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024