Related papers: Some novel considerations about the collective coo…
We investigate the propagation of fronts in an inhomogeneous medium within the framework of the $\phi^4$ model. The inhomogeneity is modeled either as an interface separating regions with different dissipation or as a finite layer with…
For most discretisations of the $\phi^4$ theory, the stationary kink can only be centered either on a lattice site or midway between two adjacent sites. We search for exceptional discretisations which allow stationary kinks to be centered…
Some recent investigations of the thermal equilibrium properties of kinks in a $1+1$-dimensional, classical $\Phi^4$ field theory are reviewed. The distribution function, kink density, correlation function, and certain thermodynamic…
We investigate kink-antikink scattering in the $\lambda \phi^4$ model in the presence of an additional scalar field, $\psi$, that is in its quantum vacuum and interacts with $\phi$ via a $\xi \phi^2\psi^2$ term where $\xi$ is the coupling.…
In this paper, we explored a class of potentials with three minima that support kink solutions exhibiting one long-range tail. We analyzed antikink-kink interactions using an effective Lagrangian based on collective coordinates and compared…
We study a model described by a single real scalar field in the two-dimensional space-time. The model is specified by a potential which is non-polynomial and supports analytical kink-like solutions that are similar to the standard kink-like…
We study boundary scattering in the $\phi^4$ model on a half-line with a one-parameter family of Neumann-type boundary conditions. A rich variety of phenomena is observed, which extends previously-studied behaviour on the full line to…
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.…
We compare the classical scattering of kinks in (1+1) Higgs model with its analogous noncommutative counterpart. While at a classical level we are able to solve the scattering at all orders finding a smooth solution, at a noncommutative…
Motivated by applications to acoustic imaging, the present work establishes a framework to analyze scattering for the one-dimensional wave, Helmholtz, Schr\"odinger and Riccati equations that allows for coefficients which are more singular…
It was recently proposed a novel discretization for nonlinear Klein-Gordon field theories in which the resulting lattice preserves the topological (Bogomol'nyi) lower bound on the kink energy and, as a consequence, has no Peierls-Nabarro…
We study a generalized $\phi^4$ model that gives rise to BPS kink/antikink configurations with compacton-like profiles. One observes that the positive parameter controlling the generalizing function promotes an infinity degenerescence of…
We investigate the propagation of a wave--packet in the $\phi^4$ model. We solve the time-dependent equation of motion for two distinct initial conditions: The wave-packet in a trivial vacuum background and in the background of the kink…
The deformed model $\tilde{\varphi}^{(6)}$ is introduced based on the $\varphi^4$ model using a deformation functional $F[\varphi]$ including a free parameter $a$. The kink solutions in different sectors and their internal modes are…
The $CP^2$ model, with and without a generalized Hopf term, is studied using the collective coordinate approximation. In the spirit of this approximation, an ansatz is given which in previous numerical studies was seen to give a good…
In this talk I summarize a recently proposed mechanism to understand pi pi scattering to 1 GeV. The model is motivated by the 1/Nc expansion to QCD, and includes a current algebra contact term and resonant pole exchanges. Chiral symmetry…
We analyze the perturbative Relativistic Moduli Space approach, where the amplitudes of the Derrick modes are promoted to collective coordinates. In particular, we analyse the possibility to calculate the critical velocity, i.e., the…
A first order equation for a static ${\phi}^4$ kink in the presence of an impurity is extended into an iterative scheme. At the first iteration, the solution is the standard kink, but at the second iteration the kink impurity generates a…
The topological defects of the lambda phi^4 theory, kink and antikink, are studied in the Hartree approximation. This allows us to discuss quantum effects on the defects in both stationary and dynamical systems. The kink mass is calculated…
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…