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The approximate solution of the Klein-Gordon equation for a real scalar field of mass $\mu$ in the geometry of a Kerr black hole obtained by Detweiler \cite{Detweiler:1980uk} is widely used in the analysis of the stability of black holes as…
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…
We study the 1D Klein-Gordon equation with variable coefficient cubic nonlinearity. This problem exhibits a striking resonant interaction between the spatial frequencies of the nonlinear coefficients and the temporal oscillations of the…
This article presents the generalization of a zero spin hydrogen atom to a relativistic atomic model of hydrogen with dyons using the Klein--Gordon equation. The derivation of the Klein--Gordon equation for the particle of relative motion…
We present a new axially symmetric monochromatic free-space solution to the Klein-Gordon equation propagating with a superluminal group velocity and show that it gives rise to an imaginary part of the causal propagator outside the light…
We develop a novel and powerful method of exactly calculating various transport characteristics of waves in one-dimensional random media with (or without) coherent absorption or amplification. Using the method, we compute the probability…
We find the relation between the energy of the absorbed photon and the threshold current at which the resistive state appears in the current-carrying superconducting film with the probability about unity. In our calculations we use the…
We study long-time dynamics of small even perturbations of the soliton in 1D quadratic Klein-Gordon equation. The soliton possesses both an internal mode and the unstable mode. On a codimension-one manifold of fine-tuned initial data the…
A shifted - l expansion technique is introduced to calculate the energy eigenvalues for Klein-Gordon (KG) equation with Lorentz vector and/or Lorentz scalar potentials. Although it applies to any spherically symmetric potential, those that…
We consider a U(1)-invariant nonlinear Klein-Gordon equation in dimension one or larger, self-interacting via the mean field mechanism. We analyze the long-time asymptotics of finite energy solutions and prove that, under certain generic…
We establish the global existence and scattering for small and localized solutions of the Klein-Gordon-Schr\"{o}dinger system in three dimensions. The system consists of coupled semilinear Schr\"{o}dinger and Klein-Gordon equations with…
The one-dimensional Klein-Gordon equation is investigated with the most general Lorentz structure for the external potentials. The analysis and calculation of the reflection and transmission coefficients for the scattering of particles in a…
Klein-Gordon Equation has been solved in four dimension. The potential has been chosen to be any arbitrary field Potential.
In this paper the solution of the hyperbolic Klein-Gordon thermal equation are obtained and discussed. The analytical form of the solution - Green functions are calculated for one and three dimensional cases. It is shown that only in three…
The Klein paradox of Klein-Gordon (KG) equation is discussed to show that KG equation is self-consistent even at one-particle level and the wave function for antiparticle is uniquely determined by the reasonable explanation of Klein…
By applying continuity and boundary conditions, the reflection and transmission coefficients of one-dimensional time-independent Schr\"odinger equation with a symmetric barrier-type shifted Deng-Fan potential are obtained and discussed. The…
We consider the fractional Klein-Gordon equation in one spatial dimension, subjected to a damping coefficient, which is non-trivial and periodic, or more generally strictly positive on a periodic set. We show that the energy of the solution…
In 1928, P. Dirac proposed a new wave equation to describe relativistic electrons. Shortly afterwards, O. Klein solved a simple potential step problem for the Dirac equation and stumbled upon an apparent paradox - the potential becomes…
Analog gravity models of black holes and exotic compact objects provide a unique opportunity to study key properties of such systems in controlled laboratory environments. In contrast to astrophysical systems, analog gravity systems can be…
We introduce the Dunkl--Klein--Gordon (DKG) equation in 2D by changing the standard partial derivatives by the Dunkl derivatives in the standard Klein--Gordon (KG) equation. We show that the generalization with Dunkl derivative of the…