Abstract:
We investigated numerically the dynamics of kinks of modified sine-Gordon equation in the model with localized spatial modulation of a periodic potential (or impurity). We considered the case of two identical impurities. We showed the possibility of collective effects of the influence of impurities, which are heavily dependent on the distance between them. We demonstrated the existence of a certain critical value of the distance between impurities, which has two qualitatively different scenarios of the dynamic behavior of kink.
Citation:
E. G. Ekomasov, A. M. Gumerov, “Collective influence of impurities on the dynamics of kinks of modified sine-Gordon equation”, Computer Research and Modeling, 5:3 (2013), 403–412
\Bibitem{EkoGum13}
\by E.~G.~Ekomasov, A.~M.~Gumerov
\paper Collective influence of impurities on the dynamics of kinks of modified sine-Gordon equation
\jour Computer Research and Modeling
\yr 2013
\vol 5
\issue 3
\pages 403--412
\mathnet{http://mi.mathnet.ru/crm404}
\crossref{https://doi.org/10.20537/2076-7633-2013-5-3-403-412}
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https://www.mathnet.ru/eng/crm404
https://www.mathnet.ru/eng/crm/v5/i3/p403
This publication is cited in the following 5 articles:
K. Yu. Samsonov, D. K. Kabanov, V. N. Nazarov, E. G. Ekomasov, “Lokalizovannye nelineinye volny uravneniya sinus-Gordona v modeli s tremya protyazhennymi primesyami”, Kompyuternye issledovaniya i modelirovanie, 16:4 (2024), 855–868
Tatyana V. Redkina, Arthur R. Zakinyan, Robert G. Zakinyan, “The Zakharov–Shabat Spectral Problem for Complexification and Perturbation of the Korteweg–de Vries Equation”, Axioms, 12:7 (2023), 703
S. P. Popov, “Nonautonomous soliton solutions of the modified Korteweg–de Vries-sine-Gordon equation”, Comput. Math. Math. Phys., 56:11 (2016), 1929–1937
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
S. P. Popov, “Interactions of breathers and kink pairs of the double sine-Gordon equation”, Comput. Math. Math. Phys., 54:12 (2014), 1876–1885
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