Related papers: Interaction Between Kink and Radiation in $\phi^4$…
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 $B$.…
In this paper the interaction between the shape modes of the wobbling kinks arising in the family of two-component MSTB scalar field theory models is studied. The spectrum of the second order small kink fluctuation in this model has two…
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…
In this work, we investigate collision processes and their mechanism among chiral and nonchiral kinks in the coupled double-field $\phi^4$ model and show that the kink collisions follow the $Z_4$ abelian group operation. Unlike 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.…
In this paper we examine the scattering processes among the members of a rich family of kinks which arise in a (1+1)-dimensional relativistic two scalar field theory. These kinks carry two different topological charges that determine the…
We calculate radiative corrections to the Casimir effect for the massive complex scalar field with the $\lambda\phi^{4}$ self-interaction in $d+1$ dimensions. We consider the field submitted to four types of boundary conditions on two…
We calculate the leading order amplitude and probability for the elastic scattering of an elementary meson and a kink in the $\phi^4$ double-well model. Classically, the kink is reflectionless, and so the leading contribution arises at one…
This paper presents an analysis of the radiation seen by an observer in circular acceleration, for a magnetic spin. This is applied to an electron in a storage ring, and the subtilty of the interaction of the spin with the spatial motion of…
Exceptional dicretizations of the phi4 model are reviewed, corresponding conservation laws are reported, and the properties of static and moving discrete kinks are discussed. Different approaches to producing such discretizations are given…
At one loop, quantum kinks are described by a free theory. The nonlinearity and so the interesting phenomenology arrives at two loops, where, for example, internal excitations couple to continuum excitations. We calculate the two-loop mass…
There is a series of scalar models possessing reflectionless kinks whose linear perturbations are described by a P\"oschl-Teller potential at integer level $\sigma$. The cases $\sigma=1$ and $2$ are the well-known Sine-Gordon and $\phi^4$…
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, 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…
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…
The energy radiated by moving cracks in a discrete background is analyzed. The energy flow through a given surface is expressed in terms of a generalized Poynting vector. The velocity of the crack is determined by the radiation by the crack…
In the present work we construct kink solutions for different (parabolic and wave) variants of the fractional $\phi^4$ model, in both the sub-Laplacian and super-Laplacian setting. We establish existence and monotonicity results (for the…
We numerically investigate the production of kink-antikink pairs in a $(1+1)$ dimensional $\phi^4$ field theory subject to white noise and periodic driving. The twin effects of noise and periodic driving acting in conjunction lead to…
We consider the quantum radiation from a partially reflecting moving mirror for the massless scalar field in 1+1 Minkowski space. Partial reflectivity is achieved by localizing a delta-type potential at the mirror's position. The radiated…
In this paper we study the dynamics of $\varphi^{4}$ kinks, generated by considering a particular argument of $\varphi^{4}$ field, in the presence of class of smooth space dependent potentials ie. barriers and wells. Various type of these…