Related papers: Long-range interaction of kinks in higher-order po…
We present and study new mechanism of interaction between the solitons based on the exchange interaction mediated by the localized fermion states. As particular examples, we consider solutions of simple 1+1 dimensional scalar field theories…
We consider the (1+1)-dimensional Lorentz-symmetric field-theoretic model with logarithmic potential having a Mexican-hat form with two local minima similar to that of the quartic Higgs potential in conventional electroweak theory with…
This paper proposes a one-dimensional lattice model with long-range interactions which, in the continuum, keeps its nonlocal behaviour. In fact, the long-time evolution of the localized waves is governed by an asymptotic equation of the…
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.…
In this paper we demonstrate that solitons of a simple real scalar field model that are {\it static and linearly stable} do exist when considered in a (3+1)-dimensional, spatially compact space-time background, the static Einstein universe,…
We propose an analytically solvable sextic potential model with non-trivial soliton solutions connecting the trivial vacua. The model does not respect parity symmetry, and like $\phi^4$ theory has two minima. The soliton solutions and the…
The nonlinear Klein-Gordon equation with a different potential that satisfies the degeneracy properties discussed in this paper possesses solitonic solutions that interact with long-range forces. We generalize the Ginzburg-Landau equation…
In this paper, we study the single kink and the kink-antikink collisions of a nonlinear beam equation bearing a fourth-derivative term. We numerically explore some of the key characteristics of the single kink both in its standing wave and…
In this work, we study kink collisions in a scalar field model with scalar-kinetic coupling. This model supports kink/antikink solutions with inner structure in the energy density. The collision of two such kinks is simulated by using the…
Interaction of asymmetric $\phi^6$ kinks with a spatially localized $\mathcal{PT}$-symmetric perturbation is investigated numerically. It has been shown that when the kink (antikink) hits the defect from the gain side, a final velocity of…
Guided by a study of kink-antikink scattering in the Gross-Neveu model and other known solutions of the Hartree-Fock approach of a particularly simple type, we demonstrate a quantitative relationship between three different problems:…
Exciton-phonon dynamics on a 1D lattice with long-range exciton-exciton interaction have been introduced and elaborated. Long-range interaction leads to a nonlocal integral term in the motion equation of the exciton subsystem if we go from…
We demonstrate that for some certain values of parameters of the $(1+1)$-dimensional $\varphi^8$ model, the kink solutions can be found from polynomial equations. For some selected values of the parameters we give the explicit formulas for…
An equation for the quasi-static soliton ansatz depending on an arbitrary set of collective variables is covariantly derived on the basis of the variational approach to the method of collective variables. The field configuration and the…
In this article, we study kink soliton configurations in interacting scalar field theories containing two fields without $SO(2)$ invariance. We study a class of such theories, the well-known Montonen-Sarker-Trullinger-Bishop model is one of…
Many solitonic configurations in field theory have localized bound states in their spectrum of linear perturbations. This opens up the possibility of having long lived excitations of these solitons that could affect their dynamics. We start…
The study of kink interactions in nonlinear Klein-Gordon models in $1+1$-dimensions has a time-honored history. Until a few years ago, it was arguably considered a fairly mature field whose main phenomenology was well understood both…
We study collisions of kinks in the one-space and one-time dimensional noncanonical nonintegrable scalar $\phi^{6}$ model. We examine the energy density of the kink, and we find that, as a function of the parameters that control the…
We study a multivariate Hawkes process with long-range interactions, where the interaction strength decays as a power-law in the distance of the particles with exponent $1+\alpha.$ Our main focus is on the long-time asymptotic behavior of…
A chain of interacting particles subject also to a nonlinear on-site potential admits stable soliton-like configurations : static kinks. The linear normal-modes around such a kink contain a discrete set of localized, gap-separated modes.…