Related papers: Transitions between topologically non-trivial conf…
We consider classical dynamics of two real scalar fields within a model with the potential having a saddle point. The solitons of such model are field configurations that have the form of closed loops in the field space. We study the…
We analyze the morphological transition of a one-dimensional system described by a scalar field, where a flat state looses its stability. This scalar field may for example account for the position of a crystal growth front, an order…
We apply a very simple procedure to construct non-singular cosmological models for flat Friedmann universes filled with minimally coupled scalar fields or by tachyon Born-Infeld-type fields. Remarkably, for the minimally coupled scalar…
Oscillons are time-dependent, localized in space, extremely long-lived states in nonlinear scalar-field models, while kinks are topological solitons in one spatial dimension. In the present work, we show new classes of oscillons and…
In this work we study configurations in one-dimensional scalar field theory, which are time-dependent, localized in space and extremely long-lived called oscillons. It is investigated how the action of changing the minimum value of the…
The intrinsic non-linearities of the spin dynamics in condensed matter systems give rise to a rich phenomenology that can be strongly affected by topology. Here we study formation of magnonic solitons in the topologically nontrivial bandgap…
We construct families of one-dimensional (1D) stable solitons in two-component $\mathcal{PT}$-symmetric systems with spin-orbit coupling (SOC) and quintic nonlinearity, which plays the critical role in 1D setups. The system models light…
Production of domain walls and string-like solitons in the model with two real scalar fields and potential with at least one saddle point and a local maximum is considered. The model is regarded as 2-dimensional spatial slices of…
We consider a scalar field model with a self-interaction potential that possesses a discrete vacuum manifold. We point out that this model allows for both topological as well as non-topological solitons. In (1+1) dimensions both type of…
The subject of moving curves (and surfaces) in three dimensional space (3-D) is a fascinating topic not only because it represents typical nonlinear dynamical systems in classical mechanics, but also finds important applications in a…
The topological structure of field theory often makes inevitable the existence of stable and unstable localised solutions of the field equations. These are minima and saddle points of the energy. Saddle point solutions occurring this way…
In this work, we present a general procedure, which is able to generate new exact solitonic models in 1+1 dimensions, from a known one, consisting of two coupled scalar fields. An interesting consequence of the method, is that of the…
In theories where spacetime is a direct product of Minkowski space ($M^4$) and a d dimensional compact space ($K^d$), there can exist topological solitons that simultaneously wind around $R^3$ (or $R^2$ or $R^1$) in $M^4$ and the compact…
Non-equilibrium phase transitions of a scalar field in an expanding spacetime are discussed. These transitions are shown to lead, for appropriate potential energy functions, to a biased choice of vacuum structure which can be analytically…
We propose an extension of the classical variational theory of evolution equations that accounts for dynamics also in possibly non-reflexive and non-separable spaces. The pivoting point is to establish a novel variational structure, based…
A supersymmetric theory with several scalar superfields generically has several domain wall type classical configurations which interpolate between various supersymmetric vacua of the scalar fields. Depending on the couplings, some of these…
We consider the existence and stability of static configurations of a scalar field in a five dimensional spacetime in which the extra spatial dimension is compactified on an $S^1/Z_2$ orbifold. For a wide class of potentials with multiple…
In a smooth dynamical system, a homoclinic connection is a closed orbit returning to a saddle equilibrium. Under perturbation, homoclinics are associated with bifurcations of periodic orbits, and with chaos in higher dimensions. Homoclinic…
It is well-known that in two dimensions Turing systems produce spots, stripes and labyrinthine patterns, and in three dimensions lamellar and spherical structures or their combinations are observed. We study transitions between these states…
We discuss the structure of topological solitons in a general non-Heisenberg model of isotropic two-dimensional magnet with spin S=1, in the vicinity of a special point where the model symmetry is enhanced to SU(3). It is shown that upon…