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Zh. Vychisl. Mat. Mat. Fiz., 2013, Volume 53, Number 12, Pages 2072–2081 (Mi zvmmf9964)  

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

Influence of dislocations on kink solutions of the double sine-Gordon equation

S. P. Popov

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

Abstract: Dependences related to the formation of kinks and their interaction with local perturbations defined as a smooth function of coordinates multiplying the sine of complete argument in the double sine-Gordon equation are studied. It is shown that there are nonstationary kink solutions remaining within the perturbation domain. These solutions consist of two separate $2\pi$-kinks oscillating about the center of the perturbation. The interactions of these kinks with $4\pi$-kinks have a complicated character depending not only on the velocity but also on the phases of the kink pairs. The transmission, capture, and reflection of kinks are investigated. The computations were based on the quasispectral Fourier method and the fourth-order Runge–Kutta method.

Key words: sine-Gordon equation, double sine-Gordon equation, kink, kink-antikink interaction, wobbler, quasi-spectral method, Runge–Kutta method.

DOI: https://doi.org/10.7868/S0044466913120120

Full text: PDF file (339 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2013, 53:12, 1891–1899

Bibliographic databases:

UDC: 519.634
Received: 17.03.2013
Revised: 11.06.2013

Citation: S. P. Popov, “Influence of dislocations on kink solutions of the double sine-Gordon equation”, Zh. Vychisl. Mat. Mat. Fiz., 53:12 (2013), 2072–2081; Comput. Math. Math. Phys., 53:12 (2013), 1891–1899

Citation in format AMSBIB
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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. 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
    2. A. M. Gumerov, E. G. Ekomasov, R. R. Murtazin, V. N. Nazarov, “Transformation of sine-Gordon solitons in models with variable coefficients and damping”, Comput. Math. Math. Phys., 55:4 (2015), 628–637  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    3. 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
    4. V. A. Gani, V. Lensky, M. A. Lizunova, “Kink excitation spectra in the (1+1)-dimensional phi(8) model”, J. High Energy Phys., 2015, no. 8, 147  crossref  mathscinet  zmath  isi  elib  scopus
    5. 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
    6. 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  scopus
    7. 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
    8. Belendryasova E. Gani V.A., “Scattering of the Phi(8) Kinks With Power-Law Asymptotics”, Commun. Nonlinear Sci. Numer. Simul., 67 (2019), 414–426  crossref  mathscinet  isi  scopus
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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