相关论文: Approximate kink-kink solutions for the $\phi^{6}$…
Kinks connecting zero and nonzero equilibria in the NLS equation with competing nonlinearities occur at the special values of the frequency parameter. Since they are minimizers of energy, they are expected to be orbitally stable in the time…
We borrow the form of potential of the well-known kink-bearing $\varphi^4$ system in the range between its two vacua and paste it repeatedly into the other ranges to introduce the periodic $\varphi^4$ system. The paper is devoted to…
Examining the $\phi^{4}$ and $\phi^{8}$ models within a two-dimensional framework in the flat spacetime and embracing a theory with unconventional kinetic terms, one investigates the emergence of kinks/antikinks and double-kinks/antikinks.…
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 construct new traveling wave solutions of moving kink type for a modified, driven, dynamic Frenkel-Kontorova model, representing dislocation motion under stress. Formal solutions known so far are inadmissible for velocities below a…
We add to a kink, which is a 1 dimensional structure, two transversal directions. We then check its asymptotic stability with respect to compactly supported perturbations in 3D and a time evolution under a Nonlinear Wave Equation (NLW). The…
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…
The peridynamic model of a solid does not involve spatial gradients of the displacement field and is therefore well suited for studying defect propagation. Here, bond-based peridynamic theory is used to study the equilibrium and steady…
The role played by a Lorentz-violating term on the outcomes of kink scattering in the $\phi^6$ model is investigated by using the Fourier spectral method. Impacts of the Lorentz-violating term on the critical velocities, the location of…
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…
This paper concerns classical nonlinear scalar field models on the real line. If the potential is a symmetric double-well, such a model admits static solutions called kinks and antikinks, which are perhaps the simplest examples of…
We study some properties of kink solutions of the model with non-polynomial potential obtained by deforming the well-known $\varphi^6$ field model. We consider the excitation spectrum of the kink. We also discuss the properties of the…
The maximal energy density that can be achieved in the collisions of the particle-like wave trains in the $\phi^4$ model has been investigated numerically for different wave train parameters. From these results the prediction is made on how…
In the present work we explore the competition of quadratic and quartic dispersion in producing kink-like solitary waves in a model of the nonlinear Schr{\"o}dinger type bearing cubic nonlinearity. We present the first 6 families of…
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…
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 develop a new method for proving hypocoercivity for a large class of linear kinetic equations with only one conservation law. Local mass conservation is assumed at the level of the collision kernel, while transport involves a confining…
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 investigate the dynamics of the kinks that emerge in a one-dimensional scalar field theory with an octic potential containing a quartic minimum and two quadratic minima. We show analytically that kink-antikink and kink-kink pairs…
We obtain exact traveling-wave solutions of the coupled nonlinear partial differential equations that describe the dynamics of two classical scalar fields in 1+1 dimensions. The solutions are kinks interpolating between neighboring vacua.…