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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2014, Volume 54, Number 12, Pages 1954–1964
DOI: https://doi.org/10.7868/S0044466914120126 (Mi zvmmf10125) 		 
This article is cited in 12 scientific papers (total in 12 papers)

Interactions of breathers and kink pairs of the double sine-Gordon equation

S. P. Popov

Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333, Russia
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DOI: https://doi.org/10.7868/S0044466914120126
Abstract: The double sine-Gordon equation is considered in the case of a small parameter multiplying the half-angle sine. It is shown that initial distributions consisting of combinations of kink solutions to the sine-Gordon equation decompose into breathers, single kinks, and kink-kink (kink-anti-kink) long-lived pairs. The interactions of kink pairs with each other and with breathers in bifurcation modes characterized by considerable variations in the kink velocities, frequencies, and oscillation amplitudes are studied. The numerical simulation is based on the quasi-spectral Fourier method and the fourth-order Runge–Kutta method.
Key words: sine-Gordon equation, double sine-Gordon equation, kink, antikink, breather, kink-anti-kink interaction, numerical simulation, quasi-spectral Fourier method, Runge–Kutta method.
Received: 21.11.2013
Revised: 11.06.2014
English version:
Computational Mathematics and Mathematical Physics, 2014, Volume 54, Issue 12, Pages 1876–1885
DOI: https://doi.org/10.1134/S0965542514120112
Bibliographic databases:
Document Type: Article
UDC: 519.634
Language: Russian
Citation: S. P. Popov, “Interactions of breathers and kink pairs of the double sine-Gordon equation”, Zh. Vychisl. Mat. Mat. Fiz., 54:12 (2014), 1954–1964; Comput. Math. Math. Phys., 54:12 (2014), 1876–1885
Citation in format AMSBIB
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    • This publication is cited in the following 12 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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