Related papers: Long-range interactions of kinks
In this Letter, we address the {long-range interaction} between kinks and antikinks, as well as kinks and kinks, in $\varphi^{2n+4}$ field theories for $n>1$. The kink-antikink interaction is generically attractive, while the kink-kink…
We obtain asymptotic estimates of the interaction forces between kink and antikink in a family of field-theoretic models with two vacua in (1+1)-dimensional space-time. In our study we consider a new class of soliton solutions previously…
We study collisions of coherent structures in higher-order field-theoretic models, such as the $\phi^8$, $\phi^{10}$ and $\phi^{12}$ ones. The main distinguishing feature, of the example models considered herein, is that the collision…
We explore a class of $\phi^{4n}$ models with kink and antikink solutions that have long-range tails on both sides, specializing to the cases with $n=2$ and $n=3$. A recently developed method of an accelerating kink ansatz is used to…
We consider the interaction of solitary waves in a model involving the well-known $\phi^4$ Klein-Gordon theory, but now bearing both Laplacian and biharmonic terms with different prefactors. As a result of the competition of the respective…
We study the scattering of the $\varphi^8$ kinks off each other, namely, we consider those $\varphi^8$ kinks that have power-law asymptotics. The slow power-law fall-off leads to a long-range interaction between the kink and the antikink.…
We study interactions of kinks and antikinks of the $(1+1)$-dimensional $\varphi^8$ model. In this model, there are kinks with mixed tail asymptotics: power-law behavior at one infinity versus exponential decay towards the other. We show…
We study excitations of solitary waves -- the kinks -- in scalar models with degree eight polynomial self-interaction in (1+1) dimensions. We perform numerical studies of scattering of two kinks with an exponential asymptotic off each other…
We examine various recently proposed discretizations of the well-known $\phi^4$ field theory. We compare and contrast the properties of their fundamental solutions including the nature of their kink-type solitary waves and the spectral…
Higher-order scalar field models in two dimensions, including the $\phi^8$ model, have been researched. It has been shown that for some special cases of the minima positions of the potential, the explicit kink solutions can be found.…
We consider a rational scalar field model in (1+1)-dimensions where the long-range character of the kinks is controllable. We show via numerical simulations that kinks with long-range tails on both sides can exhibit resonance windows. The…
We study an example of higher-order field-theoretic model with an eighth-degree polynomial potential -- the $\varphi^8$ model. We show that for some certain ratios of constants of the potential, the problem of finding kink-type solutions in…
We study various properties of topological solitons (kinks) of a field-theoretic model with a polynomial potential of the twelfth degree. This model is remarkable in that it has several topological sectors, in which kinks have different…
In this work we present a new class of real scalar field models admitting strongly interactive kink solutions. Instead of the usual exponential asymptotic behavior these topological solutions exhibit a power-law one. We investigate the…
We consider the interaction of solitons in a biharmonic, beam model analogue of the well-studied $\phi^4$ Klein-Gordon theory. Specifically, we calculate the force between a well separated kink and antikink. Knowing their accelerations as a…
This paper concerns classical nonlinear scalar field models on the real line. If the potential is a symmetric double-well, such a model admits static solutions called kinks and antikinks, which are perhaps the simplest examples of…
In this letter, we show how to build bridges between field-theoretic models that have kink solutions with different asymptotic behavior. We study transformational properties of kinks in models with a real scalar field in two-dimensional…
We study final states in the scattering of kinks and antikinks of the $\varphi^8$ field-theoretic model. We use the initial conditions in the form of two, three or four static or moving kinks. In the numerical experiments we observe a…
We studied kink-antikink collisions in (1+1)-dimensional spacetime for all $Z_2$ symmetric $\phi^8$ models with four degenerate minima. Such a polynomial model has only one free parameter, allowing us to conduct an exhaustive analysis. We…
Collective coordinate methods are frequently applied to study dynamical properties of solitons. These methods simplify the field equations - typically partial differential equations - to ordinary differential equations for selected…