Related papers: On the kink-kink collision problem of for the $\ph…
This manuscript is the first of a series of two papers that study the problem of elasticity and stability of the collision of two kinks with low speed $v$ for the nonlinear wave equation known as the $\phi^{6}$ model in dimension $1+1$. In…
We consider the nonlinear wave equation known as the $\phi^{6}$ model in dimension 1+1. We describe the long time behavior of all the solutions of this model close to a sum of two kinks with energy slightly larger than twice the minimum…
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 kink scattering processes in the (1+1)-dimensional $\varphi^6$ model in the framework of the collective coordinate approximation. We find critical values of the initial velocities of the colliding kinks. These critical velocities…
We study simultaneous collisions of two, three, and four kinks and antikinks of the $\phi^6$ model at the same spatial point. Unlike the $\phi^4$ kinks, the $\phi^6$ kinks are asymmetric and this enriches the variety of the collision…
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…
We study the scattering of the $\varphi^8$ kinks with power-law asymptotics. We found two critical values of the initial velocity, $v_{cr}^{(1)}$ and $v_{cr}^{(2)}$, which separate different regimes of the kink-antikink collision. At the…
We study the properties of a relativistic model with logarithmic nonlinearity. We show that such model allows two types of solutions: topologically trivial (gaussons) and topologically non-trivial (kinks), depending on a sign of the…
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 kink-antikink collisions in the one-dimensional non-integrable scalar phi^6 model. Although the single-kink solutions for this model do not possess an internal vibrational mode, our simulations reveal a resonant scattering…
In this work we consider kink-antikink collisions for some classes of $(1,1)$-dimensional nonlinear models. We are particularly interested to investigate in which aspect the presence of a general kinetic content in the Lagrangian could be…
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…
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…
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…
We study the kink motion for the one-dimensional stochastic Allen-Cahn equation and its mass conserving counterpart. Using a deterministic slow manifold, in the sharp interface limit for sufficiently small noise strength we derive an…
We study excitation spectra of BPS-saturated topological solutions -- the kinks -- of the $\varphi^8$ scalar field model in $(1+1)$ dimensions, for three different choices of the model parameters. We demonstrate that some of these kinks…
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…
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 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…
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…