Related papers: Kink manifolds in a three-component scalar field t…
The Brans-Dicke scalar-tensor cosmological models are studied in both Einstein and Jordan frames, using hydrodynamical and self-interacting scalar field representations of the energy-momentum tensor, leading to the same background…
Recent programs on conformal bootstrap suggest an empirical relationship between the existence of non-trivial conformal field theories and non-trivial features such as a kink in the unitarity bound of conformal dimensions in the conformal…
For a given complex n-fold M we present an explicit construction of all complex (n+1)-folds which are principal holomorphic T2-fibrations over M. For physical applications we consider the case of M being a Calabi-Yau 2-fold. We show that…
An algebraic interpretation of the bivariate Krawtchouk polynomials is provided in the framework of the 3-dimensional isotropic harmonic oscillator model. These polynomials in two discrete variables are shown to arise as matrix elements of…
I review some recent results on four-manifold invariants which have been obtained in the context of topological quantum field theory. I focus on three different aspects: (a) the computation of correlation functions, which give explicit…
Many solitonic configurations in field theory have localized bound states in their spectrum of linear perturbations. This opens up the possibility of having long lived excitations of these solitons that could affect their dynamics. We start…
The Artificial Axon is a unique synthetic system, based on biomolecular components, which supports action potentials. Here we consider, theoretically, the corresponding space extended system, and discuss the occurrence of solitary waves, or…
A topological monopole-like field configuration exists for Yang-Mills gauge fields in a 4+1 dimensions. When the extra dimension is compactified to 3+1 dimensions with periodic lattice boundary conditions, these objects reappear in the low…
The dynamics of the Brans-Dicke theory with a scalar field potential function is investigated. We show that the system with a barotropic matter content can be reduced to an autonomous three-dimensional dynamical system. For an arbitrary…
This thesis studies moduli spaces of singular connections on 3-manifolds and manifolds with cylindrical ends. A Chern-Simons functional is defined for singular connections on 3-manifolds which are singular along a knot. The critical points…
We investigate the linear classical stability of Bogomol'nyi-Prasad-Sommerfield (BPS) on three domain wall solutions in a system of three coupled real scalar fields, for a general positive potential with a square form. From a field…
We derive several new Bogomol'nyi (self-dual) equations in two-species $U(1)\times U(1)$ gauge theories governed by the Born--Infeld nonlinear electrodynamics. By identifying appropriate Born--Infeld type Higgs potentials, we show that the…
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…
Three solutions of the Brans-Dicke theory with a self-interacting quartic potential and perfect fluid distribution are presented for a spatially flat geometry. The physical behavior is consistent with the recent cosmological scenario…
We study the existence of solitary-wave solutions and some of their properties for a general multicomponent long-wave-short-wave interaction system. The system considered here describes the nonlinear interaction of multiple short waves with…
In this paper the whole kink varieties arising in several massive non-linear Sigma models whose target space is the torus ${\mathbb S}^1\times{\mathbb S}^1$ are analytically calculated. This possibility underlies the construction of…
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 demonstrate that for some certain values of parameters of the $(1+1)$-dimensional $\varphi^8$ model, the kink solutions can be found from polynomial equations. For some selected values of the parameters we give the explicit formulas for…
We consider the (1+1)-dimensional Lorentz-symmetric field-theoretic model with logarithmic potential having a Mexican-hat form with two local minima similar to that of the quartic Higgs potential in conventional electroweak theory with…
The existence of stationary solitary waves in symmetric and non-symmetric complex potentials is studied by means of Melnikov's perturbation method. The latter provides analytical conditions for the existence of such waves that bifurcate…