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TMF, 1999, Volume 118, Number 3, Pages 383–389 (Mi tmf710)  

This article is cited in 8 scientific papers (total in 9 papers)

On the two-scale method for the problem of perturbed one-frequency oscillations

A. M. Il'in

Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences

Abstract: We consider the asymptotic behavior with respect to time of the solution to the initial problem for an ordinary differential equation with a small parameter $\varepsilon$. We construct an asymptotic approximation that is valid for time values $t\gg\varepsilon$ up to any order in $\varepsilon$.

DOI: https://doi.org/10.4213/tmf710

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English version:
Theoretical and Mathematical Physics, 1999, 118:3, 301–306

Bibliographic databases:


Citation: A. M. Il'in, “On the two-scale method for the problem of perturbed one-frequency oscillations”, TMF, 118:3 (1999), 383–389; Theoret. and Math. Phys., 118:3 (1999), 301–306

Citation in format AMSBIB
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\paper On the two-scale method for the problem of perturbed one-frequency oscillations
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\jour Theoret. and Math. Phys.
\yr 1999
\vol 118
\issue 3
\pages 301--306
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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. V. M. Babich, L. A. Kalyakin, M. D. Ramazanov, N. Kh. Rozov, “Arlen Mikhailovich Il'in (on the occasion of the 70th anniversary)”, Proc. Steklov Inst. Math. (Suppl.), 2003no. , suppl. 1, S1–S7  mathnet  mathscinet  zmath  elib
    2. A. M. Il'in, M. A. Melentsov, “The asymptotics of solutions of systems of differential equations with a small parameter for large times”, Proc. Steklov Inst. Math. (Suppl.), 2005no. , suppl. 1, S107–S122  mathnet  mathscinet  zmath  elib
    3. L. A. Kalyakin, Yu. Yu. Bagderina, “Asymptotics for the solution of averaged equations for the system of coupled oscillators”, J. Math. Sci., 151:1 (2008), 2699–2709  mathnet  crossref  mathscinet  zmath  elib  elib
    4. 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
    5. Dobrokhotov S.Yu., Minenkov D.S., “On Various Averaging Methods for a Nonlinear Oscillator with Slow Time-dependent Potential and a Nonconservative Perturbation”, Regular & Chaotic Dynamics, 15:2–3 (2010), 285–299  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    6. S. Yu. Dobrokhotov, D. S. Minenkov, “Remark on the phase shift in the Kuzmak–Whitham ansatz”, Theoret. and Math. Phys., 166:3 (2011), 303–316  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    7. “Arlen Mikhailovich Ilin (k vosmidesyatiletiyu so dnya rozhdeniya)”, Ufimsk. matem. zhurn., 4:2 (2012), 3–12  mathnet  mathscinet
    8. L. A. Kalyakin, “Analysis of the Bloch equations for the nuclear magnetization model”, Proc. Steklov Inst. Math. (Suppl.), 281, suppl. 1 (2013), 64–81  mathnet  crossref  isi  elib
    9. Starkov I.A., Pakhomov O.V., Starkov A.S., “Asymptotic Solution of the Heat Conduction Equation With Weak Nonlinearity and Rapidly Oscillating Heat Source”, Proceedings of the International Conference Days on Diffraction 2015, IEEE, 2015, 338–341  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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