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Teoreticheskaya i Matematicheskaya Fizika, 2011, Volume 167, Number 3, Pages 420–431
DOI: https://doi.org/10.4213/tmf6651 (Mi tmf6651) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Asymptotic analysis of a model of nuclear magnetic autoresonance

L. A. Kalyakina, O. A. Sultanovb, M. A. Shamsutdinovc

a Institute of Mathematics, RAS, Ufa, Russia
b Ufa State Aircraft Technical University, Ufa, Russia
c Bashkir State University, Ufa, Russia
Full-text PDF (441 kB) Citations (7)
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DOI: https://doi.org/10.4213/tmf6651
Abstract: We study the system of three first-order differential equations arising when averaging the Bloch equations in the theory of nuclear magnetic resonance. For the averaged system, we construct an asymptotic series for the stable solution with an infinitely increasing amplitude. This result gives a key to understanding the autoresonance in weakly dissipative magnetic systems as a phenomenon of significant growth of the magnetization initiated by a small external pumping.
Keywords: nonlinear equation, perturbation, small parameter, asymptotic behavior, autoresonance, dissipation, stability.
Received: 23.06.2011
English version:
Theoretical and Mathematical Physics, 2011, Volume 167, Issue 3, Pages 762–771
DOI: https://doi.org/10.1007/s11232-011-0060-8
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: L. A. Kalyakin, O. A. Sultanov, M. A. Shamsutdinov, “Asymptotic analysis of a model of nuclear magnetic autoresonance”, TMF, 167:3 (2011), 420–431; Theoret. and Math. Phys., 167:3 (2011), 762–771
Citation in format AMSBIB
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    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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