Related papers: Kinks in higher-order polynomial models
We introduce a new class of piece-wise quadratic potentials for nonlinear wave equations with a kink solutions. The potentials allow an exact description of the spectral properties for the linearized equation at the kink. This description…
We consider a rational scalar field model in (1+1)-dimensions where the long-range character of the kinks is controllable. We show via numerical simulations that kinks with long-range tails on both sides can exhibit resonance windows. The…
We theoretically analyse the equation of topological solitons in a chain of particles interacting via a repulsive power-law potential and confined by a periodic lattice. Starting from the discrete model, we perform a gradient expansion and…
In this paper we present an elementary derivation of the semi-classical spectrum of neutral particles in a field theory with kink excitations. In the non-integrable cases, we show that each vacuum state cannot generically support more than…
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…
A Rayleigh-Schrodinger type of perturbation scheme is employed to study weak self-interacting scalar potential perturbations occurring in scalar field models describing 1D domain kinks and 3D domain walls. The solutions for the unperturbed…
In this thesis, we study interactions between topological defects in two-dimensional spacetimes. These defects are called kinks. They are solutions of scalar field theories with localized energy which propagate without losing its shape. In…
We present the explicit construction of some multi-scalar field theories in (1+1) dimensions supporting BPS (Bogomol'nyi--Prasad--Sommerfield) kink solutions. The construction is based on the ideas of the so-called extension method. In…
We give a sufficient condition, in the spirit of Kowalczyk-Martel-Munoz-Van Den Bosch \cite{KMMvdB21AnnPDE}, for the local asymptotic stability of kinks under odd perturbations. In particular, we allow the existence of quite general…
In the construction of a classical smoothed out brane world model in five dimensions, one uses a dynamically generated domain wall (a kink) to localise an effective four dimensional theory. At the level of the Euler-Lagrange equations the…
Field dynamics in a rapidly expanding system is investigated by transforming from space-time to the rapidity - proper-time frame. The proper-time dependence of different contributions to the total energy is established. For systems…
This work deals with models described by three real scalar fields in one spatial dimension. We study the case where two of the three fields engender kinematical modifications, which respond as geometrical constrictions, that can be used to…
In the present work we explore the interaction of a one-dimensional kink-like front of the sine-Gordon equation moving in 2-dimensional spatial domains. We develop an effective equation describing the kink motion, characterizing its center…
We investigate the presence of static solutions in models described by real scalar field in two-dimensional spacetime. After taking advantage of a procedure introduced sometime ago, we solve intricate nonlinear ordinary differential…
In this paper we demonstrate that solitons of a simple real scalar field model that are {\it static and linearly stable} do exist when considered in a (3+1)-dimensional, spatially compact space-time background, the static Einstein universe,…
Nonlinear cubic Euler-Lagrange equations of motion in the traveling variable are usually derived from Ginzburg-Landau free energy functionals frequently encountered in several fields of physics. Many authors considered in the past damped…
We look at BPS systems involving two interacting Sine-Gordon like fields both when one of them has a kink solution and the second one either a kink or an antikink solution. The interaction between the two fields is controlled by a parameter…
This work deals with lump-like structures in models described by a single real scalar field in two-dimensional spacetime. We start with a model that supports lump-like configurations and use the deformation procedure to construct scalar…
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…
The intrinsically relativistic problem of spinless particles subject to a general mixing of vector and scalar kink-like potentials ($\sim \mathrm{tanh} ,\gamma x$) is investigated. The problem is mapped into the exactly solvable…