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Zh. Vychisl. Mat. Mat. Fiz., 2007, Volume 47, Number 7, Pages 1208–1220 (Mi zvmmf280)  

This article is cited in 15 scientific papers (total in 15 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

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.

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English version:
Computational Mathematics and Mathematical Physics, 2007, 47:7, 1158–1170

Bibliographic databases:

UDC: 519.634
Received: 19.05.2006

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
\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
\jour Comput. Math. Math. Phys.
\yr 2007
\vol 47
\issue 7
\pages 1158--1170

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. L. A. Kalyakin, “Asymptotic analysis of autoresonance models”, Russian Math. Surveys, 63:5 (2008), 791–857  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. L. A. Kalyakin, M. A. Shamsutdinov, “Autoresonant asymptotics in an oscillating system with weak dissipation”, Theoret. and Math. Phys., 160:1 (2009), 960–967  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    3. Shamsutdinov M.A., Kalyakin L.A., Kharisov A.T., Nazarov V.N., “Avtorezonansnoe parametricheskoe vozbuzhdenie magnitnogo brizera”, Vestn. Bashkirskogo un-ta, 14:3-1 (2009), 1064–1071
    4. Aktosun T., Demontis F., van der Mee C., “Exact solutions to the sine-Gordon equation”, J. Math. Phys., 51:12 (2010), 123521  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    5. Shamsutdinov M.A., Kalyakin L.A., Kharisov A.T., “Autoresonance in a ferromagnetic film”, Technical Physics, 55:6 (2010), 860–865  crossref  adsnasa  isi  elib  scopus
    6. Shamsutdinov M.A., Kalyakin L.A., Kharisov A.T., “Upravlenie nelineinoi dinamikoi namagnichennosti maloi ferromagnitnoi chastitsy”, Izv. RAN. Ser. fiz., 74:10 (2010), 1444–1446  zmath  elib
    7. R. N. Garifullin, “Autoresonance excitation of a soliton of the nonlinear Schrödinger equation”, Proc. Steklov Inst. Math. (Suppl.), 281, suppl. 1 (2013), 59–63  mathnet  crossref  isi  elib
    8. Ekomasov E.G., Murtazin R.R., Azamatov Sh.A., “Numerical simulation of the generation of magnetic inhomogeneities in ferromagnets with inhomogeneous parameters”, Phys. Solid State, 54:8 (2012), 1584–1590  crossref  adsnasa  isi  elib  elib  scopus
    9. A. M. Gumerov, E. G. Ekomasov, F. K. Zakir'yanov, R. V. Kudryavtsev, “Structure and properties of four-kink multisolitons of the sine-Gordon equation”, Comput. Math. Math. Phys., 54:3 (2014), 491–504  mathnet  crossref  crossref  isi  elib  elib
    10. O. M. Kiselev, “Asymptotics of an autoresonance soliton”, Proc. Steklov Inst. Math. (Suppl.), 293, suppl. 1 (2016), 75–84  mathnet  crossref  mathscinet  isi  elib
    11. O. A. Sultanov, “Stability of capture into parametric autoresonance”, Proc. Steklov Inst. Math. (Suppl.), 295, suppl. 1 (2016), 156–167  mathnet  crossref  mathscinet  isi  elib
    12. Kayumov I.R., Shikhovtseva E.S., Nazarov V.N., “The Dynamics of 360 Degrees Domain Walls in Weak Ferromagnets in Autoresonant Mode”, Lett. Mater., 6:3 (2016), 173–178  crossref  isi
    13. L. A. Kalyakin, “Asymptotic analysis of the model of gyromagnetic autoresonance”, Comput. Math. Math. Phys., 57:2 (2017), 281–296  mathnet  crossref  crossref  isi  elib
    14. Marjaneh A.M., Askari A., Saadatmand D., Dmitriev S.V., “Extreme Values of Elastic Strain and Energy in sine-Gordon Multi-Kink Collisions”, Eur. Phys. J. B, 91:1 (2018)  crossref  mathscinet  isi  scopus
    15. Nazarov V.N., Ekomasov E.G., “Autoresonance Control Model of Nonlinear Dynamics of Magnetization in a Three-Layer Antiferromagnetic Structure in the Presence of Attenuation”, Lett. Mater., 8:2 (2018), 158–164  crossref  isi  scopus
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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