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

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.

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English version:
Computational Mathematics and Mathematical Physics, 2009, 49:12, 2085–2091

Bibliographic databases:

UDC: 519.634

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
\Bibitem{Pop09} \by S.~P.~Popov \paper Perturbed soliton solutions of the sine-Gordon equation \jour Zh. Vychisl. Mat. Mat. Fiz. \yr 2009 \vol 49 \issue 12 \pages 2182--2188 \mathnet{http://mi.mathnet.ru/zvmmf4798} \transl \jour Comput. Math. Math. Phys. \yr 2009 \vol 49 \issue 12 \pages 2085--2091 \crossref{https://doi.org/10.1134/S0965542509120082} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000272968700008} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-74549142403} 

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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
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
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
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
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
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
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
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
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