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Zh. Vychisl. Mat. Mat. Fiz., 2009, Volume 49, Number 12, Pages 2182–2188 (Mi zvmmf4798)  

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

Perturbed soliton solutions of the sine-Gordon equation

S. P. Popov

Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333, Russia

Abstract: Soliton solutions of the sine-Gordon classical equation are numerically studied. It is shown that considerable perturbations in these solutions lead to the formation of new solution forms that exhibit soliton properties in interactions. The study is performed for kinks and breathers obtained by solving problems with suitable initial data. The underlying numerical technique combines the fourth-order Runge–Kutta method with the quasi-spectral Fourier method.

Key words: sine-Gordon equation, soliton, breather, wobbler, kink, Runge–Kutta method, quasi-spectral Fourier method.

Full text: PDF file (1399 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2009, 49:12, 2085–2091

Bibliographic databases:

UDC: 519.634
Received: 17.04.2009

Citation: S. P. Popov, “Perturbed soliton solutions of the sine-Gordon equation”, Zh. Vychisl. Mat. Mat. Fiz., 49:12 (2009), 2182–2188; Comput. Math. Math. Phys., 49:12 (2009), 2085–2091

Citation in format AMSBIB
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\by S.~P.~Popov
\paper Perturbed soliton solutions of the sine-Gordon equation
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\yr 2009
\vol 49
\issue 12
\pages 2182--2188
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\yr 2009
\vol 49
\issue 12
\pages 2085--2091
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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. Golbabai A., Arabshahi M.M., “On the behavior of high-order compact approximations in the one-dimensional sine-Gordon equation”, Phys Scripta, 83:1 (2011), 015015  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    2. Aero E.L., Bulygin A.N., Pavlov Yu.V., “New approach to the solution of the classical sine-Gordon equation and its generalizations”, Differ Equ, 47:10 (2011), 1442–1452  crossref  mathscinet  zmath  isi  elib  elib  scopus
    3. Ekomasov E.G., Murtazin R.R., Bogomazova O.B., Gumerov A.M., “One-Dimensional Dynamics of Domain Walls in Two-Layer Ferromagnet Structure with Different Parameters of Magnetic Anisotropy and Exchange”, J. Magn. Magn. Mater., 339 (2013), 133–137  crossref  adsnasa  isi  elib  scopus
    4. S. P. Popov, “Interactions of breathers and kink pairs of the double sine-Gordon equation”, Comput. Math. Math. Phys., 54:12 (2014), 1876–1885  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    5. S. P. Popov, “Numerical analysis of soliton solutions of the modified Korteweg–de Vries–sine-Gordon equation”, Comput. Math. Math. Phys., 55:3 (2015), 437–446  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    6. S. P. Popov, “Scattering of solitons by dislocations in the modified Korteweg de Vries–sine-Gordon equation”, Comput. Math. Math. Phys., 55:12 (2015), 2014–2024  mathnet  crossref  crossref  mathscinet  isi  elib
    7. E. G. Ekomasov, R. K. Salimov, “Pseudo-spectral Fourier method as applied to finding localized spherical soliton solutions of $(3 + 1)$-dimensional Klein–Gordon equations”, Comput. Math. Math. Phys., 56:9 (2016), 1604–1610  mathnet  crossref  crossref  isi  elib
    8. S. P. Popov, “Nonautonomous soliton solutions of the modified Korteweg–de Vries-sine-Gordon equation”, Comput. Math. Math. Phys., 56:11 (2016), 1929–1937  mathnet  crossref  crossref  isi  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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