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Zh. Vychisl. Mat. Mat. Fiz., 2017, Volume 57, Number 2, Pages 285–301 (Mi zvmmf10521)  

This article is cited in 2 scientific papers (total in 2 papers)

Asymptotic analysis of the model of gyromagnetic autoresonance

L. A. Kalyakin

Institute of Mathematics, Ufa Research Center, Russian Academy of Sciences, Ufa, Bashkortostan, Russia

Abstract: The system of ordinary differential equations that in a specific case describes the cyclotron motion of a charged particle in an electromagnetic wave is considered. The capture of the particle into autoresonance when its energy undergoes a significant change is studied. The main result is a description of the capture domain, which is the set of initial points in the phase plane where the resonance trajectories start. This description is obtained in the asymptotic approximation with respect to the small parameter that in this problem corresponds to the amplitude of the electromagnetic wave.

Key words: nonlinear oscillations, small parameter, asymptotics, autoresonance.

Funding Agency Grant Number
Russian Science Foundation 14-11-00078


DOI: https://doi.org/10.7868/S0044466916120127

Full text: PDF file (1064 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2017, 57:2, 281–296

Bibliographic databases:

Document Type: Article
UDC: 519.624
Received: 21.12.2015
Revised: 19.05.2016

Citation: L. A. Kalyakin, “Asymptotic analysis of the model of gyromagnetic autoresonance”, Zh. Vychisl. Mat. Mat. Fiz., 57:2 (2017), 285–301; Comput. Math. Math. Phys., 57:2 (2017), 281–296

Citation in format AMSBIB
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\pages 281--296
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. L. A. Kalyakin, “Adiabatic approximation for a Model of Cyclotron Motion”, Math. Notes, 101:5 (2017), 850–862  mathnet  crossref  crossref  mathscinet  isi  elib
    2. L. A. Kalyakin, “Adiabatic approximation in a resonance capture problem”, Ufa Math. J., 9:3 (2017), 61–75  mathnet  crossref  isi  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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