Related papers: Transitions between topologically non-trivial conf…
The equilibrium configuration of an engineering structure, able to withstand a certain loading condition, is usually associated with a local minimum of the underlying potential energy. However, in the nonlinear context, there may be other…
It has recently been found that bosonic excitations of ordered media, such as phonons or spinons, can exhibit topologically nontrivial band structures. Of particular interest are magnon and triplon excitations in quantum magnets, as they…
A saddle to saddle-focus homoclinic transition when the stable leading eigenspace is 3-dimensional (called the 3DL bifurcation) is analyzed. Here a pair of complex eigenvalues and a real eigenvalue exchange their position relative to the…
The aim of this paper is to study dynamical and topological properties of a flow in the region of influence of an isolated non-saddle set or a $W$-set in a manifold. These are certain classes of compact invariant sets in whose vicinity the…
Recently it has been discovered that some nonlinear evolution equations in 2+1 dimensions, which are integrable by the use of the Spectral Transform, admit localized (in the space) soliton solutions. This article briefly reviews some of the…
Oscillons are long-lived, spatially localized field configurations, which are supported by attractive non-linearities in the scalar potential. We study oscillons comprised of multiple interacting fields, each having an identical potential…
The relation between thermodynamic phase transitions in classical systems and topological changes in their configuration space is discussed for two physical models and contains the first exact analytic computation of a topologic invariant…
In this lecture we outline the main results of our investigations of certain field-theoretic systems which have V-shaped field potential. After presenting physical examples of such systems, we show that in static problems the exact ground…
In various supersymmetric extensions of the Standard Model there appear non-topological solitons due to the existence of U(1) global symmetries associated with Baryon and/or Lepton quantum numbers. Trilinear couplings (A-terms) in the…
This work concerns scalar field theories with topologically nontrivial vacuum manifold in rotationally symmetric backgrounds of arbitrary dimension. Lagrangians with canonical and generalized kinetic terms are considered, and a Bogomol'nyi…
Magnetic solitons are nonlinear, local excitations in magnetic systems. In this study, we theoretically and numerically investigate the properties and generation of one-dimensional (1D) topologically trivial magnetic solitons in…
We study the evolution of mixed scalar as well as spinor fields within the context of the classical field theory. The initial condition problem is solved and the fields distributions, exactly accounting for the initial conditions, are…
Three-dimensional convex bodies can be classified in terms of the number and stability types of critical points on which they can balance at rest on a horizontal plane. For typical bodies these are nondegenerate maxima, minima, and…
We examine the various linkings in space-time of ``ball-like'' and ``ring-like'' topological solitons in certain nonlinear sigma models in 2+1 and 3+1 dimensions. By going to theories where soliton overlaps are forbidden, these linkings…
Logistic growth process with nonlocal interactions is considered in one dimension. Spontaneous breakdown of translational invariance is shown to take place at some parameter region, and the bifurcation regime is identified for short and…
Inspired by the well known sine-Gordon equation, we present a symmetric coupled system of two real scalar fields in $1+1$ dimensions. There are three different topological soliton solutions which be labelled according to their topological…
Oscillons are spatially stationary, quasi-periodic solutions of nonlinear field theories seen in settings ranging from granular systems, low temperature condensates and early universe cosmology. We describe a new class of oscillon in which…
Standard two-dimensional orientation-field based phase-field models rely on a continuous scalar field to represent crystallographic orientation. The corresponding order parameter space is the unit circle, which is not simply-connected. This…
We examine some general properties of a certain class of scalar filed theory models containing non-topological soliton solutions in the context of brane world models with compact large extra dimensions. If a scalar field is allowed to…
We use the model of L. Randall et al to investigate the stability of allowed quantum field configurations. Firstly, we find that due to the topology of this 5 dimensional model, there are 2 possible configurations of the scalar field,…