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Zh. Vychisl. Mat. Mat. Fiz., 2015, Volume 55, Number 4, Pages 631–640 (Mi zvmmf10190)  

This article is cited in 8 scientific papers (total in 8 papers)

Transformation of sine-Gordon solitons in models with variable coefficients and damping

A. M. Gumerova, E. G. Ekomasova, R. R. Murtazina, V. N. Nazarovb

a Bashkir State University, ul. Zaki Validi 32, Ufa, 450076, Bashkortostan, Russia
b Institute of Physics of Molecules and Crystals, Ufa Research Center, Russian Academy of Sciences, pr. Octyabrya 151, Ufa, 450075, Russia

Abstract: The dynamics of sine-Gordon solitons in the presence of an external force, damping, and a spatially modulated periodic potential is studied. Numerical methods are used to show the possibility of generating localized nonlinear waves of the soliton and breather types. Their evolution is investigated, and the dependences of the amplitude and the oscillation frequency on the parameters of the system are found.

Key words: kink, breather, soliton, sine-Gordon equation, spatially modulated periodic potential.

DOI: https://doi.org/10.7868/S0044466915040031

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English version:
Computational Mathematics and Mathematical Physics, 2015, 55:4, 628–637

Bibliographic databases:

UDC: 519.634
MSC: Primary 82D25; Secondary 35C08, 35L71, 82D40
Received: 16.06.2014
Revised: 06.10.2014

Citation: A. M. Gumerov, E. G. Ekomasov, R. R. Murtazin, V. N. Nazarov, “Transformation of sine-Gordon solitons in models with variable coefficients and damping”, Zh. Vychisl. Mat. Mat. Fiz., 55:4 (2015), 631–640; Comput. Math. Math. Phys., 55:4 (2015), 628–637

Citation in format AMSBIB
\by A.~M.~Gumerov, E.~G.~Ekomasov, R.~R.~Murtazin, V.~N.~Nazarov
\paper Transformation of sine-Gordon solitons in models with variable coefficients and damping
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2015
\vol 55
\issue 4
\pages 631--640
\jour Comput. Math. Math. Phys.
\yr 2015
\vol 55
\issue 4
\pages 628--637

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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. E. G. Ekomasov, A. M. Gumerov, R. V. Kudryavtsev, “On the possibility of the observation of the resonance interaction between kinks of the sine-Gordon equation and localized waves in real physical systems”, JETP Letters, 101:12 (2015), 835–839  mathnet  crossref  crossref  isi  elib  elib
    2. E. G. Ekomasov, A. M. Gumerov, R. R. Murtazin, “Interaction of sine-Gordon solitons in the model with attracting impurities”, Math. Meth. Appl. Sci., 40:17, SI (2017), 6178–6186  crossref  mathscinet  zmath  isi
    3. J. A. Gonzalez, A. Bellorin, M. A. Garcia-Nustes, L. E. Guerrero, S. Jimenez, L. Vazquez, “Arbitrarily large numbers of kink internal modes in inhomogeneous sine-Gordon equations”, Phys. Lett. A, 381:24 (2017), 1995–1998  crossref  mathscinet  zmath  isi
    4. E. G. Ekomasov, A. M. Gumerov, R. V. Kudryavtsev, “Resonance dynamics of kinks in the sine-Gordon model with impurity, external force and damping”, J. Comput. Appl. Math., 312 (2017), 198–208  crossref  mathscinet  zmath  isi
    5. A. M. Marjaneh, A. Askari, D. Saadatmand, S. V. Dmitriev, “Extreme values of elastic strain and energy in sine-Gordon multi-kink collisions”, Eur. Phys. J. B, 91:1 (2018)  crossref  mathscinet  isi
    6. E. G. Ekomasov, A. M. Gumerov, R. V. Kudryavtsev, S. V. Dmitriev, V. N. Nazarov, “Multisoliton dynamics in the sine-Gordon model with two point impurities”, Braz. J. Phys., 48:6 (2018), 576–584  crossref  isi  scopus
    7. V. A. Delev, O. A. Skaldin, E. S. Batyrshin, V. N. Nazarov, E. G. Ekomasov, “Kink-antikink interaction in a linear defect of the electroconvective structure of a nematic”, JETP Letters, 109:2 (2019), 87–91  mathnet  crossref  crossref  isi  elib
    8. A. M. Gumerov, E. G. Ekomasov, R. V. Kudryavtsev, M. I. Fakhretdinov, “Excitation of Large-Amplitude Localized Nonlinear Waves by the Interaction of Kinks of the Sine-Gordon Equation with Attracting Impurity”, Rus. J. Nonlin. Dyn., 15:1 (2019), 21–34  mathnet  crossref  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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