Related papers: Scattering of kinks in the $B\varphi^{4}$ model
The resonant interaction of the $\phi^4$ kink with a periodic $\mathcal{PT}$-symmetric perturbation is observed in the frame of the continuum model and with the help of a two degree of freedom collective variable model derived in PRA 89,…
Antikink-kink ( $\bar{\rm K} $$ {\rm K}$) collisions in the $\phi^6$ model exhibit resonant scattering although the $\phi^6$ kinks do not support any bound states to which energy could be transferred. In Phys. Rev. Lett. 107 (2011) 091602…
This paper investigates a model containing $\phi^4$ kinks interacting with fermions. The fermion back-reaction is included in the equations of motion, which affects the kink-antikink collisions. We show that the fermion field generates a…
We study boundary scattering in the $\phi^4$ model on a half-line with a one-parameter family of Neumann-type boundary conditions. A rich variety of phenomena is observed, which extends previously-studied behaviour on the full line to…
We present a dynamical picture of kink-anti-kink scattering in a pair of special, Frankensteinian potentials made of piece-wise quadratic and linear pieces. Specifically, we focus on models that support kinks without skin and core regions.…
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 the kink scattering in a two-component scalar field theory model in (1+1)-Minkowskian space-time is addressed. The potential term $U(\phi_1,\phi_2)$ is given by a polynomial of fourth degree in the first field component and of…
This study explores the scattering dynamics of kinks within a nonlinear system governed by a parameterized potential $U_\lambda(\chi)$, examining the distinct behaviors of small and large kinks across a range of $\lambda$ values and initial…
We consider an enlarged $(1+1)$-dimensional model with two real scalar fields, $\phi$ and $\chi$ whose scalar potential $V(\phi,\chi)$ has a standard $\chi^4$ sector and a sine-Gordon one for $\phi$. These fields are coupled through a…
In this work, we investigate the dynamics of a scalar field in the nonintegrable $\displaystyle \phi ^{4}$ model, restricted to the half-line. Here we consider singular solutions that interpolate the Dirichlet boundary condition…
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 study a scalar field model in a two dimensional space-time with a generalized $\phi^4_G$ potential which has four minima, obtaining novel kink solutions with well defined properties although the potential is non-analytical at the origin.…
We present a model of two-kinks resulting from an explicit composition of two standards kinks of the $\phi^4$ model based on the procedure of Ref. \cite{uchiyama}. The two-kinks have an additional parameter accounting for the separation of…
We propose a toy model to reproduce the fractal structure of kink and antikink collisions on one topological sector of $\phi^6$ theory. Using the toy model, we investigate the missing bounce windows observed in the fractal structure, and…
We study the elasticity of the collision of two kinks with an incoming low speed $v\in (0,1)$ for the nonlinear wave equation in dimension $1+1$ known as the $\phi^{6}$ model. We prove for any $k\in\mathbb{N}$ that if the incoming speed $v$…
We investigate kink-antikink collisions in a model characterized by two scalar fields in the presence of geometric constrictions. The model includes an auxiliary function that modifies the kinematics associated with one of the two fields.…
In this paper, we study the $\phi^4$ kink scattering from a spatially localized $\mathcal{PT}$-symmetric defect and the effect of the kink's internal mode (IM) is discussed. It is demonstrated that if a kink hits the defect from the gain…
We consider a class of topological defects in $(1,1)$-dimensions with a deformed $\phi^4$ kink structure whose stability analysis leads to a Schr\"odinger-like equation with a zero-mode and at least one vibrational (shape) mode. We are…
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…
Recent studies have emphasized the important role that a shape deformability of scalar-field models pertaining to the same class with the standard $\phi^4$ field, can play in controlling the production of a specific type of breathing bound…