RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Ufimsk. Mat. Zh.:
Year:
Volume:
Issue:
Page:
Find






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


Ufimsk. Mat. Zh., 2017, Volume 9, Issue 3, Pages 63–77 (Mi ufa387)  

Adiabatic approximation in a resonance capture problem

L. A. Kalyakin

Institute of Mathematics, Ufa Scientific Center, RAS, Chernyshevsky str. 112, 450008, Ufa, Russia

Abstract: By means of the averaging method, we analyze two model problems on capture into resonance that leads us to the adiabatic approximation in the leading term in the asymptotics. The main aim is an approximate (by using a small parameter) description of the domain of capture into resonance. This domain is in the phase plane and it is formed by the initial points for the resonance solutions with an unboundedly increasing energy. The capture domain depends on an additional parameter involved in the equation. We show that the adiabatic approximation fails as the capture domain becomes narrow. In this case we have to modify substantially the averaging method. As a result, a system of nonlinear differential equations arises for the leading term in the asymptotics and this system is not always integrable.

Keywords: nonlinear oscillations, small parameter, asymptotics, capture into a resonance, adiabatic approximation.

Funding Agency Grant Number
Russian Science Foundation 17-11-01004
The research is supported by the grant of Russian Science Foundation (project no. 17-11-01004).


Full text: PDF file (886 kB)
References: PDF file   HTML file

English version:
Ufa Mathematical Journal, 2017, 9:3, 61–75 (PDF, 837 kB); https://doi.org/10.13108/2017-9-3-61

Bibliographic databases:

UDC: 517.956.226
MSC: 34D10, 34D20, 37J25, 34E13
Received: 02.04.2017

Citation: L. A. Kalyakin, “Adiabatic approximation in a resonance capture problem”, Ufimsk. Mat. Zh., 9:3 (2017), 63–77; Ufa Math. J., 9:3 (2017), 61–75

Citation in format AMSBIB
\Bibitem{Kal17}
\by L.~A.~Kalyakin
\paper Adiabatic approximation in a resonance capture problem
\jour Ufimsk. Mat. Zh.
\yr 2017
\vol 9
\issue 3
\pages 63--77
\mathnet{http://mi.mathnet.ru/ufa387}
\elib{http://elibrary.ru/item.asp?id=30022852}
\transl
\jour Ufa Math. J.
\yr 2017
\vol 9
\issue 3
\pages 61--75
\crossref{https://doi.org/10.13108/2017-9-3-61}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000411740000007}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85030034266}


Linking options:
  • http://mi.mathnet.ru/eng/ufa387
  • http://mi.mathnet.ru/eng/ufa/v9/i3/p63

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Уфимский математический журнал
    Number of views:
    This page:98
    Full text:25
    References:10

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019