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Such kinks have interesting features in comparison with their long-studied counterparts, which have exponential asymptotics. Thus, the \(\varphi ^8\) model, on the one hand, is not too complicated, and on the other hand, the variety of topological solitons generated by it is pretty significant.Īs already mentioned, the \(\varphi ^8\) model can have kink solutions with one or both power-law tails for more details, see, e.g. In particular, the model can have different sets of topological sectors, different asymptotic behavior of kink solutions (exponential or power-law), as well as vibrational mode(s) can be present or absent in the kink’s excitation spectrum. Depending on a specific form of the potential, the model exhibits different properties. In connection with applications, several different modifications of this model are considered. The \(\varphi ^8\) model is one of the widely used models with polynomial self-interaction (potential) of a scalar field. Nevertheless, in recent years, the number of new results in this area has not decreased see, e.g., for review. The history of the numerical study of interactions of kink solutions of nonlinear partial differential equations goes back more than half a century. This paper is devoted to the study of new phenomena in the scattering of kinks of the \(\varphi ^8\) model. The study of the properties of kink solutions is of great interest for various physical applications.
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Among the field configurations that satisfy the equations of motion, topologically nontrivial objects, including the so-called kinks (see, e.g., and ), are of particular importance.
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Many physical systems are described in terms of field-theoretic models with a real scalar field, the dynamics of which is determined by nonlinear partial differential equations.