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Teoreticheskaya i Matematicheskaya Fizika, 2003, Volume 137, Number 1, Pages 142–152
DOI: https://doi.org/10.4213/tmf1757 (Mi tmf1757) 		 
This article is cited in 19 scientific papers (total in 19 papers)

Asymptotic Behavior of Solutions of Equations of Main Resonance

L. A. Kalyakin

Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences
Full-text PDF (236 kB) Citations (19)
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DOI: https://doi.org/10.4213/tmf1757
Abstract: We investigate a system of two first-order differential equations that appears when averaging nonlinear systems over fast one-frequency oscillations. The main result is the asymptotic behavior of a two-parameter family of solutions with an infinitely growing amplitude. In addition, we find the asymptotic behavior of another two-parameter family of solutions with a bounded amplitude. In particular, these results provide the key to understanding autoresonance as the phenomenon of a considerable growth of forced nonlinear oscillations initiated by a small external pumping.
Keywords: nonlinear equations, asymptotic behavior, WKB approximation.
English version:
Theoretical and Mathematical Physics, 2003, Volume 137, Issue 1, Pages 1476–1484
DOI: https://doi.org/10.1023/A:1026065025429
Bibliographic databases:
Language: Russian
Citation: L. A. Kalyakin, “Asymptotic Behavior of Solutions of Equations of Main Resonance”, TMF, 137:1 (2003), 142–152; Theoret. and Math. Phys., 137:1 (2003), 1476–1484
Citation in format AMSBIB
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\paper Asymptotic Behavior of Solutions of Equations of Main Resonance
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\pages 142--152
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\transl
\jour Theoret. and Math. Phys.
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\vol 137
\issue 1
\pages 1476--1484
\crossref{https://doi.org/10.1023/A:1026065025429}
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  • https://doi.org/10.4213/tmf1757
  • https://www.mathnet.ru/eng/tmf/v137/i1/p142
    • This publication is cited in the following 19 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
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    Full-text PDF :198
    References:64
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