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TMF, 2011, Volume 167, Number 3, Pages 420–431 (Mi tmf6651)  

This article is cited in 5 scientific papers (total in 5 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

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

DOI: https://doi.org/10.4213/tmf6651

Full text: PDF file (441 kB)
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English version:
Theoretical and Mathematical Physics, 2011, 167:3, 762–771

Bibliographic databases:

Document Type: Article
Received: 23.06.2011

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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\paper Asymptotic analysis of a~model of nuclear magnetic autoresonance
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  • http://mi.mathnet.ru/eng/tmf6651
  • https://doi.org/10.4213/tmf6651
  • http://mi.mathnet.ru/eng/tmf/v167/i3/p420

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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. O. A. Sultanov, L. A. Kalyakin, “Usrednenie uravnenii Blokha”, Vestnik ChelGU, 2011, no. 14, 107–112  mathnet  mathscinet  elib
    2. 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
    3. O. A. Sultanov, “Ustoichivost modelei avtorezonansa otnositelno vozmuschenii, ogranichennykh v srednem”, Tr. IMM UrO RAN, 19, no. 3, 2013, 274–283  mathnet  mathscinet  elib
    4. O. A. Sultanov, “Stability of autoresonance models subject to random perturbations for systems of nonlinear oscillation equations”, Comput. Math. Math. Phys., 54:1 (2014), 59–73  mathnet  crossref  crossref  isi  elib  elib
    5. L. A. Kalyakin, “Analysis of a Mathematical Model for Nuclear Spins in an Antiferromagnet”, Nelineinaya dinam., 14:2 (2018), 217–234  mathnet  crossref  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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