Sbornik: Mathematics
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
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


Mat. Sb.:
Year:
Volume:
Issue:
Page:
Find




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

Sbornik: Mathematics, 2006, Volume 197, Issue 1, Pages 53–67
DOI: https://doi.org/10.1070/SM2006v197n01ABEH003746 (Mi sm1119) 		 
This article is cited in 2 scientific papers (total in 4 papers)

Asymptotic behaviour of a special solution of Abel's equation relating to a cusp catastrophe

A. M. Il'ina, B. I. Suleimanovb

a Chelyabinsk State University
b Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences
English version PDF (260 kB) Citations (4) Russian version article
References:
PDF
HTML
DOI: https://doi.org/10.1070/SM2006v197n01ABEH003746
Abstract: A special solution of Abel's ordinary differential equation of the first kind $u'_{x}+u^3-tu-x=0$ is considered, which describes the behaviour of a broad spectrum of solutions of partial differential equations with a small parameter in the neighbourhood of cusp points of their slowly varying equilibrium positions. The existence of this special solution is demonstrated; an asymptotic formula for it as $|x|\to\infty$, $t\to-\infty$ is constructed and substantiated.
Bibliography: 4 titles.
Keywords: asymptotics, singular perturbations, small parameter, cusp catastrophe.
Received: 20.06.2005
Bibliographic databases:
UDC: 517.928
MSC: Primary 34E05, 35B40; Secondary 35B25
Language: English
Original paper language: Russian
Citation: A. M. Il'in, B. I. Suleimanov, “Asymptotic behaviour of a special solution of Abel's equation relating to a cusp catastrophe”, Sb. Math., 197:1 (2006), 53–67
Citation in format AMSBIB
\Bibitem{IliSul06}
\by A.~M.~Il'in, B.~I.~Suleimanov
\paper Asymptotic behaviour of a special solution of Abel's equation relating to a cusp catastrophe
\jour Sb. Math.
\yr 2006
\vol 197
\issue 1
\pages 53--67
\mathnet{http://mi.mathnet.ru//eng/sm1119}
\crossref{https://doi.org/10.1070/SM2006v197n01ABEH003746}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2230132}
\zmath{https://zbmath.org/?q=an:1144.34035}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000237780600004}
\elib{https://elibrary.ru/item.asp?id=9188971}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33744762772}
Linking options:
  • https://www.mathnet.ru/eng/sm1119
  • https://doi.org/10.1070/SM2006v197n01ABEH003746
  • https://www.mathnet.ru/eng/sm/v197/i1/p55
    Cycle of papers
    This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математический сборник Sbornik: Mathematics
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024