Related papers: (2+3) dimensional geometrical dual of the complex …
In this paper we construct an invariant probability measure concentrated on $H^2(K)\times H^1(K)$ for a general cubic Klein-Gordon equation (including the case of the wave equation). Here $K$ represents both the $3$-dimensional torus or a…
Within this article one finds the statement of the Klein-Gordon problem within the real Hilbert space formalism ($\mathbbm R$HS) in terms of complex wave functions, and in terms of quaternionic wave functions as well. The complex…
Approximate analytical solutions of a two-term potential are studied for the relativistic wave equations, namely, for the Klein-Gordon and Dirac equations. The results are obtained by solving of a Riemann-type equation whose solution can be…
In this work a static solution of Einstein-Cartan (EC) equations in 2+1 dimensional space-time is given by considering classical spin-1/2 field as external source for torsion of the space-time. Here, the torsion tensor is obtained from…
We propose a natural family of higher-order partial differential equations generalizing the second-order Klein-Gordon equation. We characterize the associated model by means of a generalized action for a scalar field, containing…
Several types of static solutions to Einstein's equations coupled with antisymmetric tensor fields are found in $(2+N+1)$-dimensional spacetime. The solutions describe a product of a three-dimensional radially symmetric spacetime and an…
We discuss general properties of the conservation law associated with a local symmetry. Using Noether's theorem and a generalized Belinfante symmetrization procedure in 3+1 dimensions, a symmetric energy-momentum (pseudo) tensor for the…
In this study, we replace the standard partial derivatives in the Klein-Gordon equation with Dunkl derivatives and obtain exact analytical solutions for the eigenvalues and eigenfunctions of the Dunkl-Klein-Gordon equation in higher…
We study the 2D coupled wave-Klein-Gordon systems with semi-linear null nonlinearities $Q_0$ and $Q_{\alpha\beta}$. The main result states that the solution to the 2D coupled systems exists globally provided that the initial data are small…
The infinite-dimensional family of exact solutions of the Klein--Gordon equation is constructed by the hypercomplex method.
We review recent results on global attractors of U(1)-invariant dispersive Hamiltonian systems. We study several models based on the Klein-Gordon equation and sketch the proof that in these models, under certain generic assumptions, the…
In this paper, we consider a semiclassical version of the fractional Klein-Gordon equation on the lattice, $h{\mathbb{Z}}^n.$ Contrary to the Euclidean case that was considered in [2], the discrete fractional Klein-Gordon equation is…
In (3 + 1) spacetime dimensions the Rainich conditions are a set of equations expressed solely in terms of the metric tensor which are equivalent to the Einstein-Maxwell equations for non-null electromagnetic fields. Here we provide the…
It is shown that in the two-dimensional space-time the dynamic system, described by the free Klein-Gordon equation, turns to the dynamic system, described by the free Dirac equation, provided the current and the energy-momentum tensor are…
I propose a generalization of the Klein-Gordon equation in the framework of AdS space-time and exhibit a four parameter family of solutions among which there is a two parameter family of time-dependent bound states.
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…
The covariant Klein-Gordon equation requires twice the boundary conditions of the Schrodinger equation and does not have an accepted single-particle interpretation. Instead of interpreting its solution as a probability wave determined by an…
Exact solutions are presented of the Klein-Gordon equation of a charged particle moving in a classical monochromatic electromagnetic plane wave in a medium of index of refraction n < 1. The solutions are expressed in terms of Ince…
For the $1+1$ dimensional nonlinear damped stochastic Klein-Gordon equation driven by space-time white noise, we prove that the second-order increments of the solution can be approximated, after scaling with the diffusion coefficient, by…
We obtain a dispersive long-time decay in weighted energy norms for solutions of the 3D Klein-Gordon equation with generic potential. The decay extends the results obtained by Jensen and Kato for the 3D Schredinger equation. For the proof…