Related papers: Klein-Gordon equation in $q$-deformed Euclidean sp…
We consider time-dependent Schr\"{o}dinger equations for a free nonrelativistic particle on the three-dimensional $q$-deformed Euclidean space. We determine plane wave solutions to these Schr\"{o}dinger equations and show that they form a…
The paper, classically, presents an extended Klein-Gordon field system in 3+1 dimensions with a special Q-ball solution. The Q-ball solution is energetically stable, that is, for any arbitrary small deformation above the background of that,…
We study in $\mathbb{R}^{3+1}$ a system of nonlinearly coupled Klein-Gordon equations under null condition, with (possibly vanishing) mass varying in the interval $[0, 1]$. Our goal is three folds: 1) we want to establish the global…
A detailed consideration of the Klein-Gordon equation in relativistic quantum mechanics is presented in order to offer more clarity than many standard approaches. The equation is frequently employed in the research literature, even though…
For a damped wave (or Klein-Gordon) equation on a bounded domain, with a focusing power-like nonlinearity satisfying some growth conditions, we prove that a global solution is bounded in the energy space, uniformly in time. Our result…
We study the stability of standing-waves solutions to a scalar non-linear Klein-Gordon equation in dimension one with a quadratic-cubic non-linearity. Orbits are obtained by applying the semigroup generated by the negative complex unit…
In the present paper, we show that the global solution to (partially) damped Klein-Gordon equation on the three dimensional Euclidean space with small data decays exponentially. The key ingredients in the proof are: Morawetz-type estimates…
In this paper it is shown that an equivalent to the complex Klein-Gordon equation can be obtained from the (2+3) dimensional Einstein equations coupled to a conserved energy momentum tensor. In an explicit toy model we give matching…
We study the 1D Klein-Gordon equation with variable coefficient nonlinearity. This problem exhibits an interesting resonant interaction between the spatial frequencies of the nonlinear coefficients and the temporal oscillations of the…
We give solutions of the q-deformed equations of quantum conformal Weyl gravity in terms of q-deformed plane waves.
We find a coordinate-independent wave-packet solution of the massive Klein-Gordon equation with the conformal coupling to gravity in the de-Sitter universe. This solution can locally be represented through the superposition of…
Exponentially localized solutions of the Klein-Gordon equation for two and three space variables are presented. The solutions depend on four free parameters. For some relations between the parameters, the solutions describe wave packets…
We investigate the stability and long-term behavior of spatially periodic plane waves in the complex Klein-Gordon equation under localized perturbations. Such perturbations render the wave neither localized nor periodic, placing its…
We solve the relativistic Klein--Gordon equation for a light particle gravitationally bound to a heavy central mass, with the gravitational interaction prescribed by the metric of a spherically symmetric space-time. Metrics are considered…
We present an elementary proof based on a direct calculation of the property of completeness at constant time of the solutions of the Klein-Gordon equation for a charged particle in a plane wave electromagnetic field. We also review…
We obtain a dispersive long-time decay in weighted energy norms for solutions of the Klein-Gordon equation in a moving frame. The decay extends the results of Jensen, Kato and Murata for the equations of the Schr\"odinger type. We modify…
We obtain the exact solution of the Klein-Gordon equation describing the propagation of a particle in two regions of different constant magnetic field, separated by an infinite plane wall. The continuity of the wave function and of its…
The discrete Klein-Gordon equation on a two-dimensional square lattice satisfies an $\ell^1 \mapsto \ell^\infty$ dispersive bound with polynomial decay rate $|t|^{-3/4}$. We determine the shape of the light cone for any choice of the mass…
q-deformed nonlinear field equations are constructed including Klein-Gordon and Maxwell equations. The q-deformation is interpreted as mathematical structure describing specific nonlinearity for which frequency of vibration exponentially…
Analytical solutions of the Klein-Gordon equation are obtained by reducing the radial part of the wave equation to a standard form of a second order differential equation. Differential equations of this standard form are solvable in terms…