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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2007, Volume 47, Number 7, Pages 1208–1220 (Mi zvmmf280)  
This article is cited in 18 scientific papers (total in 18 papers)

Autoresonance excitation of a breather in weak ferromagnetics

R. N. Garifullina, L. A. Kalyakina, M. A. Shamsutdinovb

a Institute of Mathematics and Computing Center, Ufa Research Center, Russian Academy of Sciences, ul. Chernyshevskogo 112, Ufa, 450077, Russia
b Bashkir State University
Full-text PDF (1850 kB) Citations (18)
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Abstract: A mathematical model of the magnetodynamics of a weak ferromagnetic in an external magnetic field with variable frequency is studied. Conditions for the appearance of autoresonance are found under which the amplitude of the local magnetic inhomogeneities is considerably increased. Mathematically, the problem is to analyze the solutions to the sine-Gordon equation subject to a specific nonautonomous perturbation. For the perturbed equation, asymptotic solutions in the form of a breather with a slowly varying amplitude and a phase shift are constructed. The solutions whose amplitude increases with time from small values to quantities of order one are associated with the autoresonance phenomenon.
Key words: nonlinear magnetodynamics equations, perturbation method, method of small parameter, asymptotics, autoresonance.
Received: 19.05.2006
English version:
Computational Mathematics and Mathematical Physics, 2007, Volume 47, Issue 7, Pages 1158–1170
DOI: https://doi.org/10.1134/S0965542507070081
Bibliographic databases:
Document Type: Article
UDC: 519.634
Language: Russian
Citation: R. N. Garifullin, L. A. Kalyakin, M. A. Shamsutdinov, “Autoresonance excitation of a breather in weak ferromagnetics”, Zh. Vychisl. Mat. Mat. Fiz., 47:7 (2007), 1208–1220; Comput. Math. Math. Phys., 47:7 (2007), 1158–1170
Citation in format AMSBIB
\Bibitem{GarKalSha07}
\by R.~N.~Garifullin, L.~A.~Kalyakin, M.~A.~Shamsutdinov
\paper Autoresonance excitation of a~breather in weak ferromagnetics
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2007
\vol 47
\issue 7
\pages 1208--1220
\mathnet{http://mi.mathnet.ru/zvmmf280}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2378141}
\transl
\jour Comput. Math. Math. Phys.
\yr 2007
\vol 47
\issue 7
\pages 1158--1170
\crossref{https://doi.org/10.1134/S0965542507070081}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-34547700233}
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    • This publication is cited in the following 18 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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