Related papers: An Energetically Stable Q-ball solution in 3+1 Dim…
We have examined the dynamical behavior of the kink solutions of the one-dimensional sine-Gordon equation in the presence of a spatially periodic parametric perturbation. Our study clarifies and extends the currently available knowledge on…
This work deals with charged nontopological solutions that appear in relativistic models described by a single complex scalar field in two-dimensional spacetime. We study a model which supports novel analytical configurations of the Q-ball…
The Klein-Gordon equation in the presence of a strong electric field, taking the form of the Mathieu equation, is studied. A novel analytical solution is derived for particles whose asymptotic energy is much lower or much higher than the…
This paper is concerned with strong blow-up instability (Definition 1.3) for standing wave solutions to the system of the quadratic nonlinear Klein-Gordon equations. In the single case, namely the nonlinear Klein-Gordon equation with power…
We consider compact boson stars that arise for a V-shaped scalar field potential. They represent a one parameter family of solutions of the scaled Einstein-signum-Gordon equations. We analyze the physical properties of these solutions and…
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…
A quantum-kinetic formulation of the dynamical evolution of a high-energy non-equilibrium gluon system at finite density is developed, to study the interplay between quantum fluctuations of high-momentum (hard) gluons and the low-momentum…
Global behavior of solutions is studied for the nonlinear Klein-Gordon equation with a focusing power nonlinearity and a damping term in the energy space on the Euclidean space. We give a complete classification of solutions into 5 types of…
We present a new complex non-stationary particle-like solution of the non-linear Klein-Gordon equation with several spatial variables. The construction is based on reduction to an ordinary differential equation.
We use Moeller's energy-momentum complex in order to explicitly compute the energy and momentum density distributions for an exact solution of Einstein's field equations with a negative cosmological constant minimally coupled to a static…
Generalizations of the three main equations of quantum physics, namely, the Schr\"odinger, Klein-Gordon, and Dirac equations, are proposed. Nonlinear terms, characterized by exponents depending on an index $q$, are considered in such a way…
We extended the notion of Newton-Wigner localization, already constructed in the bi-dimensional de Sitter space, to the tri-dimensional case for both principal and complementary series. We identify the one-particle subspace, generated by…
The wave equation with energy critical sources and nonlinear damping defined on a 3D bounded domain is considered. It is shown that the resulting dynamical system admits a global attractor. Under the additional assumption of strong…
We are interested in the global dynamics of a massive scalar field evolving under its own gravitational field and, in this paper, we study spherically symmetric solutions to Einstein's field equations coupled with a Klein-Gordon equation…
Recently, it has been found that a $Q$-ball can amplify waves incident upon it, due to rotation in the internal space and the interaction of the two modes in the complex scalar field. While the spherically symmetric 3D case has been…
A concept of finite-dimensional dynamical system representation is introduced. Since the solution trajectory of partial differential equations are usually represented within infinite-dimensional dynamical systems, the proposed…
We consider the codimension one asymptotic stability problem for the soliton of the focusing cubic Klein-Gordon equation on the line under even perturbations. The main obstruction to full asymptotic stability on the center-stable manifold…
We consider a modified Klein-Gordon equation that arises at ultra high energies. In a suitable approximation it is shown that for the linear potential which is of interest in quark interactions, their confinement for example,we get…
We study the focusing, cubic, nonlinear Klein-Gordon equation in 3D with large radial data in the energy space. This equation admits a unique positive stationary solution, called the ground state. In 1975, Payne and Sattinger showed that…
$\ell$-boson stars are static, spherical, multi-field self-gravitating solitons. They are asymptotically flat, finite energy solutions of Einstein's gravity minimally coupled to an odd number of massive, complex scalar fields. A previous…