Related papers: Generalized Global Defect Solutions
In this paper all the defect-type solutions in a family of scalar field theories with a real and a complex field in (1+1) dimensional Minkowski spacetime have been analytically identified. Three types of solutions have been found: (a)…
We consider multidimensional gravitational models with a nonlinear scalar curvature term and form fields in the action functional. In our scenario it is assumed that the higher dimensional spacetime undergoes a spontaneous compactification…
In this work we study the presence of kinks in models described by a single real scalar field in bidimensional spacetime. We work within the first-order framework, and we show how to write first-order differential equations that solve the…
In this paper we perform systematic investigation of all possible solutions with static compact extra dimensions and expanding three-dimensional subspace (``our Universe''). Unlike previous papers, we consider extra-dimensional subspace to…
I consider an extension of General Relativity by an auxiliary non-dynamical dimension that enables our space-time to acquire an extrinsic curvature. Obtained gravitational equations, without or with a cosmological constant, have a…
We investigate the presence of domain walls in models described by three real scalar fields. We search for stable defect structures which minimize the energy of the static field configurations. We work out explict orbits in field space and…
For given non-consistent initial conditions, we study the stability of a class of generalised linear systems of difference equations with constant coefficients and taking into account that the leading coefficient can be a singular matrix.…
The recent significant enrichment of the Order Completion Method for nonlinear Systems of PDEs resulted in the global existence of generalized solutions to a large class of such equations. In this paper we investigate the existence and…
Many current challenges involve understanding the complex dynamical interplay between the constituents of systems. Typically, the number of such constituents is high, but only limited data sources on them are available. Conventional…
Assuming the four-dimensional space-time to be a general warped product of two surfaces we reduce the four-dimensional Einstein equations to a two-dimensional problem which can be solved. All global vacuum solutions are explicitly…
The stability issue of a large class of modified gravitational models is discussed with particular emphasis to de Sitter solutions. Three approaches are briefly presented and the generalization to more general cases is mentioned.
In this work, we investigate the existence of analytic solutions of static scalar fields on Lifshitz spacetimes. We evade Derrick's theorem on curved spacetimes by breaking general covariance and use first-order formalism to obtain…
We consider the problem of critical gravitational collapse of a scalar field in 2+1 dimensions with spherical (circular) symmetry. After surveying all the analytic, continuously self-similar solutions and considering their global structure,…
We study the stability under linear perturbations of a class of static solutions of Einstein-Gauss-Bonnet gravity in $D=n+2$ dimensions with spatial slices of the form $\Sigma_{\k}^n \times {\mathbb R}^+$, $\Sigma_{\k}^n$ an $n-$manifold of…
We define and study complex structures and generalizations on spaces consisting of geodesics or harmonic maps that are compatible with the symmetries of these spaces. The main results are about existence and uniqueness of such structures.
The aim of this paper is to reconstruct and analyze the stability of some cosmological models against linear perturbations in $f(\mathcal{G},T)$ gravity ($\mathcal{G}$ and $T$ represent the Gauss-Bonnet invariant and trace of the…
Local and global phase-space descriptions and averaging methods are used to find qualitative features of solutions for the FLRW and the Bianchi I metrics in the context of scalar field cosmologies with arbitrary potentials and arbitrary…
We investigate gauge invariant cosmological perturbations in a spatially flat Friedman-Robertson-Walker universe with scalar fields. It is well known that the evolution equation for the gauge invariant quantities has exact solutions in the…
Vector fields with components which are generalized zero-forms are constructed. Inner products with generalized forms, Lie derivatives and Lie brackets are computed. The results are shown to generalize previously reported results for…
Consider the general scalar balance law $\partial_t u + \Div f(t, x,u) = F(t,x,u)$ in several space dimensions. The aim of this note is to estimate the dependence of its solutions from the flow $f$ and from the source $F$. To this aim, a…