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@article{ND_2024_20_1_a1, author = {M. I. Fakhretdinov and K. Y. Samsonov and S. V. Dmitriev and E. G. Ekomasov}, title = {Attractive {Impurity} as a {Generator} of {Wobbling} {Kinks}}, journal = {Russian journal of nonlinear dynamics}, pages = {15--26}, publisher = {mathdoc}, volume = {20}, number = {1}, year = {2024}, language = {en}, url = {http://geodesic.mathdoc.fr/item/ND_2024_20_1_a1/} }
TY - JOUR AU - M. I. Fakhretdinov AU - K. Y. Samsonov AU - S. V. Dmitriev AU - E. G. Ekomasov TI - Attractive Impurity as a Generator of Wobbling Kinks JO - Russian journal of nonlinear dynamics PY - 2024 SP - 15 EP - 26 VL - 20 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ND_2024_20_1_a1/ LA - en ID - ND_2024_20_1_a1 ER -
%0 Journal Article %A M. I. Fakhretdinov %A K. Y. Samsonov %A S. V. Dmitriev %A E. G. Ekomasov %T Attractive Impurity as a Generator of Wobbling Kinks %J Russian journal of nonlinear dynamics %D 2024 %P 15-26 %V 20 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/ND_2024_20_1_a1/ %G en %F ND_2024_20_1_a1
M. I. Fakhretdinov; K. Y. Samsonov; S. V. Dmitriev; E. G. Ekomasov. Attractive Impurity as a Generator of Wobbling Kinks. Russian journal of nonlinear dynamics, Tome 20 (2024) no. 1, pp. 15-26. http://geodesic.mathdoc.fr/item/ND_2024_20_1_a1/
[1] A Dynamical Perspective on the $\varphi^4$ Model: Past, Present and Future, Nonlinear Syst. Complex., 26, eds. P. Kevrekidis, J. Cuevas-Maraver, Springer, Cham, 2019, 332 pp. | MR
[2] Uspekhi Fiz. Nauk, 167:4 (1997), 377–406 (Russian) | DOI | DOI
[3] Abdullina, D. U., Bebikhov, Yu. V., Khazimullin, M. V., Kudreyko, A. A., and Dmitriev, S. V., “Atom Deposition and Sputtering at Normal Incidence Simulated by the Frenkel – Kontorova Chain”, Phys. Rev. E, 106:2 (2022), Art. 024207, 13 pp. | DOI
[4] He, J.-H., He, C.-H., and Alsolami, A. A., “A Good Initial Guess for Approximating Nonlinear Oscillators by the Homotopy Perturbation Method”, Facta Univ. Ser.: Mech. Eng., 21:1 (2023), 21–29 | MR
[5] Yamaletdinov, R. D., Slipko, V. A., and Pershin, Yu. V., “Kinks and Antikinks of Buckled Graphene: A Testing Ground for the $\varphi^4$ Field Model”, Phys. Rev. B, 96:9 (2017), Art. 094306, 5 pp. | DOI
[6] Yamaletdinov, R. D., Romańczukiewicz, T., and Pershin, Yu. V., “Manipulating Graphene Kinks through Positive and Negative Radiation Pressure Effects”, Carbon, 141 (2019), 253–257 | DOI
[7] The Sine-Gordon Model and Its Applications: From Pendula and Josephson Junctions to Gravity and High-Energy Physics, Nonlinear Syst. Complex., 10, eds. J. Cuevas-Maraver, P. Kevrekidis, F. Williams, Springer, Cham, 2014, xiii, 263 pp. | MR | Zbl
[8] Belova, T. I. and Kudryavtsev, A. E., “Quasi-Periodic Orbits in the Scalar Classical $\lambda\phi^4$ Field Theory”, Phys. D, 32:1 (1988), 18–26 | DOI | MR
[9] Marjaneh, A. M., Saadatmand, D., Zhou, K., Dmitriev, S. V., and Zomorrodian, M. E., “High Energy Density in the Collision of $N$ Kinks in the $\phi^4$ Model”, Commun. Nonlinear Sci. Numer. Simul., 49 (2017), 30–38 | DOI | MR | Zbl
[10] Takyi, I. and Weigel, H., “Collective Coordinates in One-Dimensional Soliton Models Revisited”, Phys. Rev. D, 94:8 (2016), Art. 085008, 11 pp. | DOI
[11] Zh. Èksper. Teoret. Fiz., 109:3 (1996), 1090–1099 (Russian)
[12] Malomed, B. A., “Perturbative Analysis of the Interaction of a $\varphi^4$ Kink with Inhomogeneities”, J. Phys. A, 25:4 (1992), 755–764 | DOI | MR
[13] Fei, Zh., Kivshar, Yu. S., and Vázquez, L., “Resonant Kink-Impurity Interactions in the $\varphi^4$ Model”, Phys. Rev. A, 46:8 (1992), 5214–5220 | DOI
[14] Romańczukiewicz, T., “Creation of Kink and Antikink Pairs Forced by Radiation”, J. Phys. A, 39:13 (2006), 3479–3494 | DOI | MR | Zbl
[15] Alonso Izquierdo, A., Queiroga-Nunes, J., and Nieto, L. M., “Scattering between Wobbling Kinks”, Phys. Rev. D, 103:4 (2021), Paper No. 045003, 16 pp. | MR
[16] Segur, H., “Wobbling Kinks in $\varphi^4$ and Sine-Gordon Theory”, J. Math. Phys., 24:6 (1983), 1439–1443 | DOI | MR
[17] Barashenkov, I. V. and Oxtoby, O. F., “Wobbling Kinks in $\varphi^4$ Theory”, Phys. Rev. E, 80:2 (2009), Art. 026608, 9 pp. | DOI | MR
[18] Savin, A. V. and Dmitriev, S. V., “Influence of the Internal Degrees of Freedom of Coronene Molecules on the Nonlinear Dynamics of a Columnar Chain”, Phys. Rev. E, 107:5 (2023), Paper No. 054216, 11 pp. | DOI | MR
[19] Savin, A. V., Sunagatova, I. R., and Dmitriev, S. V., “Rotobreathers in a Chain of Coupled Elastic Rotators”, Phys. Rev. E, 104:3 (2021), Paper No. 034207, 11 pp. | DOI | MR
[20] Rysaeva, L. Kh., Bachurin, D. V., Murzaev, R. T., Abdullina, D. U., Korznikova, E. A., Mulyukov, R. R., and Dmitriev, S. V., “Evolution of the Carbon Nanotube Bundle Structure under Biaxial and Shear Strains”, Facta Univ. Ser.: Mech. Eng., 18:4 (2020), 525–536
[21] Savin, A. V. and Dmitriev, S. V., “The Frequency Spectrum of Rotobreathers with Many Degrees of Freedom”, Europhys. Lett., 137:3 (2022), Art. 36005, 7 pp. | DOI
[22] Teoret. Mat. Fiz., 60:3 (1984), 395–403 (Russian) | DOI | MR
[23] Segur, H. and Kruskal, M. D., “Nonexistence of Small-Amplitude Breather Solutions in $\phi^4$ Theory”, Phys. Rev. Lett., 58:8 (1987), 747–750 | DOI | MR
[24] Oxtoby, O. F. and Barashenkov, I. V., “Resonantly Driven Wobbling Kinks”, Phys. Rev. E, 80:2 (2009), Art. 026609, 17 pp. | DOI
[25] Grimshaw, R., “Exponential Asymptotics and Generalized Solitary Waves”, Asymptotic Methods in Fluid Mechanics: Survey and Recent Advances, CISM Courses and Lect., 523, ed. H. Steinrück, Springer, Vienna, 2010, 71–120, vi, 420 pp. | MR | Zbl
[26] Pis'ma v Zh. Èksper. Teoret. Fiz., 24:5 (1976), 323–327 (Russian)
[27] Alonso-Izquierdo, A., Miguélez-Caballero, D., Nieto, L. M., and Queiroga-Nunes, J., “Wobbling Kinks in a Two-Component Scalar Field Theory: Interaction between Shape Modes”, Phys. D, 443 (2023), Paper No. 133590, 15 pp. | DOI | MR
[28] Alonso-Izquierdo, A., Nieto, L. M., and Queiroga-Nunes, J., “Asymmetric Scattering between Kinks and Wobblers”, Commun. Nonlinear Sci. Numer. Simul., 107 (2022), Paper No. 106183, 14 pp. | DOI | MR
[29] Teoret. Mat. Fiz., 159:3 (2009), 527–535 (Russian) | DOI | DOI | MR
[30] Fiz. Nizk. Temp., 47:2 (2021), 173–183 (Russian) | DOI
[31] Fiz. Nizk. Temp., 47:6 (2021), 483–490 (Russian) | DOI
[32] Alejo, M. A., Muñoz, C., and Palacios, J. M., “On Asymptotic Stability of the Sine-Gordon Kink in the Energy Space”, Commun. Math. Phys., 402:1 (2023), 581–636 | DOI | MR | Zbl
[33] Borisov, D. I. and Dmitriev, S. V., “On the Spectral Stability of Kinks in 2D Klein – Gordon Model with Parity-Time-Symmetric Perturbation”, Stud. Appl. Math., 138:3 (2017), 317–342 | DOI | MR | Zbl
[34] Saadatmand, D. and Javidan, K., “Collective-Coordinate Analysis of Inhomogeneous Nonlinear Klein – Gordon Field Theory”, Braz. J. Phys., 43:1–2 (2013), 48–56 | DOI
[35] Moradi Marjaneh, A., Simas, F. C., and Bazeia, D., “Collisions of Kinks in Deformed $\varphi^4$ and $\varphi^6$ Models”, Chaos Solitons Fractals, 164 (2022), Paper No. 112723, 14 pp. | MR
[36] Ghahraman, A., “Dynamics of $\varphi^4$ Kinks by Using Adomian Decomposition Method”, Am. J. Numer. Anal., 4:1 (2016), 8–10
[37] Lizunova, M. A., Kager, J., de Lange, S., and van Wezel, J., “Kinks and Realistic Impurity Models in $\varphi^4$-Theory”, Int. J. Mod. Phys. B, 36:05 (2022), Art. 2250042, 12 pp. | DOI
[38] Saadatmand, D., Dmitriev, S. V., Borisov, D. I., and Kevrekidis, P. G., “Interaction of Sine-Gordon Kinks and Breathers with a Parity-Time-Symmetric Defect”, Phys. Rev. E, 90:5 (2014), Art. 052902, 10 pp. | DOI | MR
[39] Pis'ma v Zh. Èksper. Teoret. Fiz., 101:7 (2015), 550–555 (Russian) | DOI
[40] Saadatmand, D., Borisov, D. I., Kevrekidis, P. G., Zhou, K., and Dmitriev, S. V., “Resonant Interaction of $\phi^4$ Kink with PT-Symmetric Perturbation with Spatially Periodic Gain/Loss Coefficient”, Commun. Nonlinear Sci. Numer. Simul., 56 (2018), 62–76 | DOI | MR | Zbl
[41] Saadatmand, D., Dmitriev, S. V., Borisov, D. I., Kevrekidis, P. G., Fatykhov, M. A., and Javidan K., “Kink Scattering from a Parity-Time-Symmetric Defect in the $\phi^4$ Model”, Commun. Nonlinear Sci. Numer. Simul., 29:1–3 (2015), 267–282 | DOI | MR | Zbl
[42] Dmitriev, S. V., Suchkov, S. V., Sukhorukov, A. A., and Kivshar, Yu. S., “Scattering of Linear and Nonlinear Waves in a Waveguide Array with a $\mathrm{PT}$-Symmetric Defect”, Phys. Rev. A, 84:1 (2011), Art. 013833, 5 pp. | DOI
[43] Askari, A., Moradi Marjaneh, A., Rakhmatullina, Zh. G., Ebrahimi-Loushab, M., Saadatmand, D., Gani, V. A., Kevrekidis, P. G., and Dmitriev, S. V., “Collision of $\phi^4$ Kinks Free of the Peierls – Nabarro Barrier in the Regime of Strong Discreteness”, Chaos Solitons Fractals, 138 (2020), Art. 109854, 12 pp. | DOI | MR
[44] Dmitriev, S. V., Kevrekidis, P. G., Malomed, B. A., and Frantzeskakis, D. J., “Two-Soliton Collisions in a Near-Integrable Lattice System”, Phys. Rev. E (3), 68:5 (2003), Art. 056603, 7 pp. | DOI | MR
[45] Saadatmand, D., Dmitriev, S. V., and Kevrekidis, P. G., “High Energy Density in Multisoliton Collisions”, Phys. Rev. D, 92:5 (2015), Art. 056005, 11 pp. | DOI | MR
[46] Kevrekidis, P. G. and Weinstein, M. I., “Dynamics of Lattice Kinks”, Phys. D, 142:1–2 (2000), 113–152 | DOI | MR | Zbl
[47] Lizunova, M., Kager, J., de Lange, S., and van Wezel, J., “Emergence of Oscillons in Kink-Impurity Interactions”, J. Phys. A, 54:31 (2021), Paper No. 315701, 9 pp. | DOI | MR
[48] Romańczukiewicz, T. and Shnir, Y., “Oscillons in the Presence of External Potential”, J. High Energ. Phys., 2018:1 (2018), Art. 101, 24 pp. | MR
[49] Dorey, P. and Romańczukiewicz, T., “Resonant Kink – Antikink Scattering through Quasinormal Modes”, Phys. Lett. B, 779 (2018), 117–123 | DOI
[50] Fakhretdinov, M. I., Samsonov, K. Yu., Dmitriev, S. V., and Ekomasov, E. G., “Kink Dynamics in the $\varphi^4$ Model with Extended Impurity”, Russian J. Nonlinear Dyn., 19:3 (2023), 303–320 | MR | Zbl
[51] Piette, B. and Zakrzewski, W. J., “Scattering of Sine-Gordon Kinks on Potential Wells”, J. Phys. A, 40:22 (2007), 5995–6010 | DOI | MR | Zbl
[52] Ekomasov, E. G., Nazarov, V. N., and Samsonov, K. Yu., “Changing the Dynamic Parameters of Localized Breather and Soliton Waves in the sine-Gordon Model with Extended Impurity, External Force, and Decay in the Autoresonance Mode”, Russian J. Nonlinear Dyn., 18:2 (2022), 217–229 | MR | Zbl
[53] Gumerov, A. M., Ekomasov, E. G., Kudryavtsev, R. V., and Fakhretdinov, M. I., “Excitation of Large-Amplitude Localized Nonlinear Waves by the Interaction of Kinks of the Sine-Gordon-Equation with Attracting Impurity”, Russian J. Nonlinear Dyn., 15:1 (2019), 21–34 | MR | Zbl
[54] Schiesser, W. E., The Numerical Method of Lines: Integration of Partial Differential Equations, Acad. Press, Cambridge, Mass., 1991, 326 pp. | MR | Zbl