Related papers: Kink-antikink collisions in a weakly interacting $…
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 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…
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 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 show that thick spectral walls exist in antikink-kink collisions in the $\phi^6$ model. In this model, they are triggered by the so-called $delocalized$ $modes$ which do not exist in the single-soliton sector but emerge in antikink-kink…
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…
We review recent works on modeling of dynamics of kinks in 1+1 dimensional $\phi^4$ theory and other related models, like sine-Gordon model or $\phi^6$ theory. We discuss how the spectral structure of small perturbations can affect the…
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…
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…
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…
During defect-antidefect scattering, bound modes frequently disappear into the continuous spectrum before the defects themselves collide. This leads to a structural, nonperturbative change in the spectrum of small excitations. Sometimes the…
In this study, based on the $\varphi^4$ model, a new model (called the $B\varphi^4$ model) is introduced in which the potential form for the values of the field whose magnitudes are greater than $1$ is multiplied by the positive number $B$.…
The fractal velocity pattern in symmetric kink-antikink collisions in $\phi^4$ theory is shown to emerge from a dynamical model with two effective moduli, the kink-antikink separation and the internal shape mode amplitude. The shape mode…
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…
The transition from integrable to non-integrable highly-dispersive nonlinear models is investigated. The sine-Gordon and $\phi^4$-equations with the additional fourth-order spatial and spatio-temporal derivatives, describing the higher…
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…
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…
In this work we study kink-antikink and antikink-kink collisions in hyperbolic models of fourth and sixth order. We compared the patterns of scattering with known results from polynomial models of the same order. The hyperbolic models…
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…
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…