Related papers: Collective coordinate model of kink-antikink colli…
In this work, kink-antikink collision in a two-dimensional Lorentz-violating $\phi^4$ model is considered. It is shown that the Lorentz-violating term in the proposed model does not affect the structure of the linear perturbation spectrum…
We present a numerical study of the process of the kink-antikink collisions in the coupled one-dimensional two-component $\phi^4$ model. Our results reveal two different soliton solutions which represent double kink configuration and…
For kink-antikink scattering within the \phi^4 non--linear field theory in one space and one time dimension resonance type configurations emerge when the relative velocity between kink and antikink falls below a critical value. It has been…
We consider a two-dimensional Lorentz-invariant field model with a $\phi^{4}$ potential modified by a term that introduces asymmetries at the manifold space. In this framework, the model recovers its original symmetry only when $p=0$. The…
We study topological kinks and their interactions in a family of scalar field models with a double well potential parametrized by the mass of small perturbations around the vacua, ranging from the mass of the $\phi^4$ Klein-Gordon model all…
In this work we consider a model where the potential has two topological sectors connecting three adjacent minima, as occurs with the $\phi^6$ model. In each topological sector, the potential is symmetric around the local maximum. For…
Extending a recent effective theory formulation for the dynamics of kinks in the sine-Gordon model [1], we propose an analogous effective description of $\phi^4$ kinks. Three different reduced models based on the kink position, width and…
We study kink-antikink scattering in a one-parameter variant of the $\phi^4$ theory where the model parameter controls the static intersoliton force. We interpolate between the limit of no static force (BPS limit) and the regime where the…
We have investigated the head-on collision of a two-kink and a two-antikink pair that arises as a generalization of the $\phi^4$ model. We have evolved numerically the Klein-Gordon equation with a new spectral algorithm whose accuracy and…
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,…
The symmetric dynamics of two kinks and one antikink in classical (1+1)-dimensional $\phi^4$ theory is investigated. Gradient flow is used to construct a collective coordinate model of the system. The relationship between the discrete…
Kink-antikink scattering in the $\phi^4$ model is investigated in the limit when the static inter-soliton force vanishes. We observe the formation of spectral walls and, further, identify a new phenomenon, the vacuum wall, whose existence…
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…
The moduli space approximation to kink dynamics permits a relativistic generalization if the Derrick scaling parameter is used as a collective coordinate. We develop a perturbative approach to the resulting relativistic moduli space by…
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 show that constrained $CP^1$ instantons, combined with the Relativistic Moduli Space approach, can accurately describe kink-antikink collisions in the $\phi^4$ model.
We study kink-antikink collisions in a model which interpolates smoothly between the completely integrable sine-Gordon theory, the $\phi^4$ model, and a $\phi^6$-like model with three degenerate vacua. We find a rich variety of behaviours,…
We investigate the role that quasinormal modes can play in kink-antikink collisions, via an example based on a perturbation of the $\phi^4$ model. We find that narrow quasinormal modes can store energy during collision processes and return…
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 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…