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Zh. Vychisl. Mat. Mat. Fiz., 2006, Volume 46, Number 9, Pages 1605–1616 (Mi zvmmf413)  

This article is cited in 6 scientific papers (total in 6 papers)

Asymptotic solution to the problem of autoresonance: Outer expansion

R. N. Garifullin

Institute of Mathematics and Computing Center, Ufa Science Center, Russian Academy of Sciences, ul. Chernyshevskogo 112, Ufa, 450077, Russia

Abstract: The autoresonance phenomenon (phase locking) is studied for a nonlinear second-order ordinary differential equation. Using the matching method and the multiple scale method, a two-parameter asymptotic solution to this equation is constructed.

Key words: second-order ordinary differential equation, autoresonance phenomenon, asymptotic method.

Full text: PDF file (1572 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2006, 46:9, 1526–1538

Bibliographic databases:

UDC: 519.634
Received: 18.03.2005

Citation: R. N. Garifullin, “Asymptotic solution to the problem of autoresonance: Outer expansion”, Zh. Vychisl. Mat. Mat. Fiz., 46:9 (2006), 1605–1616; Comput. Math. Math. Phys., 46:9 (2006), 1526–1538

Citation in format AMSBIB
\Bibitem{Gar06}
\by R.~N.~Garifullin
\paper Asymptotic solution to the problem of autoresonance: Outer expansion
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2006
\vol 46
\issue 9
\pages 1605--1616
\mathnet{http://mi.mathnet.ru/zvmmf413}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2287661}
\transl
\jour Comput. Math. Math. Phys.
\yr 2006
\vol 46
\issue 9
\pages 1526--1538
\crossref{https://doi.org/10.1134/S0965542506090065}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33748996486}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. E. M. Maslov, L. A. Kalyakin, A. G. Shagalov, “Breather resonant phase locking by an external perturbation”, Theoret. and Math. Phys., 152:2 (2007), 1173–1182  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. L. A. Kalyakin, “Asymptotic analysis of autoresonance models”, Russian Math. Surveys, 63:5 (2008), 791–857  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    3. O. A. Sultanov, “Stability of autoresonance in dissipative systems”, Ufa Math. J., 7:1 (2015), 58–69  mathnet  crossref  isi  elib
    4. L. A. Kalyakin, “Asymptotic analysis of the model of gyromagnetic autoresonance”, Comput. Math. Math. Phys., 57:2 (2017), 281–296  mathnet  crossref  crossref  isi  elib
    5. L. A. Kalyakin, “Resonance capture in a system of two oscillators near equilibrium”, Theoret. and Math. Phys., 194:3 (2018), 331–346  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    6. Kalyakin L.A., “Capture and Keeping of a Resonance Near Equilibrium”, Russ. J. Math. Phys., 26:2 (2019), 152–167  crossref  isi
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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