New results on the interaction forces of kinks in a field-theoretical model with a polynomial potential
https://doi.org/10.26583/vestnik.2025.6.4
EDN: KDPKBO
Abstract
We obtain asymptotic estimates for the interaction forces between topological solitons(kinks) of the Klein–Gordon equation with a polynomial nonlinearity. This equation is the equation of motion for a real scalar field in the Lorentz-invariant (1 + 1)-dimensional φ12 model, which is important for many physical applications. The model under consideration is not integrable, so it lacks exact two-soliton solutions. Nevertheless, the dynamics of a system consisting of a kink and an antikink located at some distance from each other is important for applications. Such a configuration is not a solution to the equation of motion, but can be constructed from individual soliton solutions. The nonintegrability of the model leads to the presence of an interaction force between the kinks. In this paper, we show that attraction occurs in all cases, and the force decreases exponentially with distance. To obtain expressions for the attractive force, we used the asymptotics of the corresponding kink solutions, which in the model under consideration have an exponential nature, which, in turn, is a consequence of the type of potential of the field-theoretic model that determines the self-interaction of the scalar field.
Supporting agencies: The study was carried out within the framework of the state assignment of the Ministry of Science and Higher Education of the Russian Federation, project FSWU-2023-0031.
About the Authors
V. A. Gani
National Research Nuclear University MEPhI;
National Research Centre «Kurchatov Institute»
Russian Federation
Russian Federation
O. V. Nagornov
National Research Nuclear University MEPhI
Russian Federation
Russian Federation
References
1. Manton N., Sutcliffe P. Topological Solitons. Cambridge University Press, Cambridge U.K. 2004. 493 p. DOI:10.1017/CBO9780511617034
2. Vachaspati T. Kinks and Domain Walls: An Introduction to Classical and Quantum Solitons. Cambridge University Press, Cambridge U.K, 2006. DOI:10.1017/CBO9780511535192
3. Buijnsters F.J., Fasolino A., Katsnelson M.I. Motion of Domain Walls and the Dynamics of Kinks in the Magnetic Peierls Potential. Physical Review Letters , 2014. Vol.113. Art. id. 217202 . DOI: 10.1103/PhysRevLett.113.217202
4. Yamaletdinov R.D., Slipko V.A., Pershin Y.V. Kinks and antikinks of buckled graphene: A testing ground for phi^4 field model. Physical Review B, 2017. Vol.96. Art. id. 094306. DOI:10.1103/PhysRevB.96.094306
5. Khare A., Christov I. C., Saxena A. Successive phase transitions and kink solutions in 8 , 10 , and 12 field theories . Physical Review E, 2014. Vol.90. Art. id. 023208. DOI: 10.1103/PhysRevE.90.023208
6. Kevrekidis P.G., Cuevas-Maraver J., eds, A dynamical perspective on the 4 model: Past, present and future. Part of the Nonlinear Systems and Complexity book series, Vol. 26. Springer, 2019. 311 p.. DOI: 10.1007/978-3-030-11839-6
7. Vanderbilt D., Cohen M.H. Monoclinic and triclinic phases in higher-order Devonshire theory. Physical Review B, 2001. Vol.63. Art.id. 094108. DOI:10.1103/PhysRevB.63.094108
8. Sergienko I. A., Gufan Y. M., Urazhdin S. Phenomenological theory of phase transitions in highly piezoelectric perovskites. Physical Review B, 2002. Vol. 65. Art.id. 144104. doi :10.1103/PhysRevB.65.144104
9. Cuevas-Maraver J., Kevrekidis P. G., Williams F., eds. The sine-Gordon Model and its Applications: from Pendula and Josephson Junctions to Gravity and High-Energy Physics. Part of the Nonlinear Systems and Complexity book series ,Vol. 10. Springer Cham , 2014. 263 p. DOI: 10.1007/978-3-319-06722-3
10. Kudryavtsev A. E. Solitonlike solutions for a Higgs scalar field. JETP Letters, 1975. Vol. 22. Iss.3 pp.82.
11. Belova T.I., Kudryavcev A.E. Solitony i ih vzaimodejstviya v klassicheskoj teorii polya [Solitons and their interactions in classical field theory]. Uspekhi fizicheskih nauk, 1997. Vol.167. Pp.377-406. (in Russian) DOI: 10.3367/UFNr.0167.199704b.0377
12. Khare A., Saxena A. Logarithmic potential with super-super-exponential kink profiles and tails. Physica Scripta, 2020. Vol.95. Art.id. 075205. DOI: 10.1088/1402-4896/ab8eeb
13. Khare A., Saxena A. Wide class of logarithmic potentials with power-tower kink tails. Journal of Physics A: Mathematical and Theoretical, 2020. Vol. 53. Art.id. 315201 . DOI: 10.1088/1751-8121/ab84ac
14. Kumar P., Khare A., Saxena A. A minimal nonlinearity logarithmic potential: Kinks with super-exponential profiles. International Journal of Modern Physics B, 2021. Vol.35(08). Art.id. 2150114. DOI:10.1142/S0217979221501149
15. Blinov P.A., et al. Kinks in higher-order polynomial models. Chaos, Solitons and Fractals, 2022. Vol.165(07), 112805. DOI:10.1016/j.chaos.2022.112805
16. Dorey P., Mersh K., Romanczukiewicz T., Shnir Y. Kink-antikink collisions in the phi^6 model. Physical Review Letters, 2011. Vol. 107, 091602 . DOI:10.1103/PhysRevLett.107.091602
17. Adam C. , et al. Multikink scattering in the 6 model revisited. Physical Review D, 2022. Vol.106, 125003. DOI: 10.1103/PhysRevD.106.125003
18. Christov I. C., et al. Kink-antikink collisions and multi-bounce resonance windows in higher-order field theories. Communications in Nonlinear Science and Numerical Simulation, 2021. Vol.97. 105748. DOI: 10.1016/j.cnsns.2021.10574897:105748
19. Demirkaya A.,et al. Kink dynamics in a parametric φ6 system: a model with controllably many internal modes J. High Energy Phys.,2017 (12), 071 (2017). DOI: 10.1007/JHEP12(2017)07
20. Mohammadi M., Dehghani R., Kink-antikink collisions in the periodic φ4 model. Communications in Nonlinear Science and Numerical Simulation, 2021. Vol.94. art. id. 105575. DOI: 10.1016/j.cnsns.2020.105575
21. Mohammadi M., Momeni E. Scattering of kinks in the Bφ4 model. Chaos, Solitons and Fractals, 2022. Vol.165(P2). Art.id. 112834. DOI:10.1016/j.chaos.2022.112834
22. Alonso-Izquierdo A.,. Nieto L.M, Queiroga-Nunes J. Scattering between wobbling kinks. Physical Review D, 2021. Vol.103. Art.id. 045003. DOI: 10.1103/PhysRevD.103.045003
23. Bazeia D. , González León M.A., Losano L., Guilarte J. M Deformed defects for scalar fields with polynomial interactions. Physical Review D, 2006. Vol.73, Art.id. 105008. DOI: 10.1103/PhysRevD.73.105008
24. Marjaneh A.M. , et al. Kink Dynamics in a High-Order Field Model. Journal of Nonlinear Science, 2025. Vol. 35, art. number 99. DOI: 10.1007/s00332-025-10196-x
Review
For citations:
Gani V.A., Nagornov O.V. New results on the interaction forces of kinks in a field-theoretical model with a polynomial potential. Vestnik natsional'nogo issledovatel'skogo yadernogo universiteta "MIFI". 2025;14(6):492-499. (In Russ.) https://doi.org/10.26583/vestnik.2025.6.4. EDN: KDPKBO
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