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
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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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