Related papers: $\lambda\phi^{4}$ Kink and sine-Gordon Soliton in …
We give an exhaustive, non-perturbative classification of exact travelling-wave solutions of a perturbed sine-Gordon equation (on the real line or on the circle) which is used to describe the Josephson effect in the theory of…
We consider effectively one-dimensional planar and radial kinks in two-dimensional nonlinear Klein-Gordon models and focus on the sine-Gordon model and the $\phi^4$ variants thereof. We adapt an adiabatic invariant formulation recently…
Various approaches to quantum gravity, such as string theory, predict a minimal measurable length and a modification of the Heisenberg Uncertainty Principle near the Plank scale, known as the Generalized Uncertainty Principle (GUP). Here we…
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…
Recently, scattering of a Klein-Gordon particle in the presence of mixed scalar-vector generalized symmetric Woods-Saxon potential was investigated for the spin symmetric and the pseudo-spin symmetric limits in one spatial dimension. In…
We consider a discrete nonlinear Klein-Gordon equations with damping and external drive. Using a small amplitude ansatz, one usually approximates the equation using a damped, driven discrete nonlinear Schr\"odinger equation. Here, we show…
We consider the one-dimensional nonlinear Klein-Gordon equation with a double power focusing-defocusing nonlinearity \begin{equation*} \partial_{t}^{2}u-\partial_{x}^{2}u+u-|u|^{p-1}u+|u|^{q-1}u=0,\quad \mbox{on}\ [0,\infty)\times…
The numerical approximation of the semilinear Klein--Gordon equation in the $d$-dimensional space, with $d=1,2,3$, is studied by analyzing the consistency errors in approximating the solution. By discovering and utilizing a new cancellation…
We propose in this paper a quantization scheme for real Klein-Gordon field in de Sitter spacetime. Our scheme is generally covariant with the help of vierbein, which is necessary usually for spinor field in curved spacetime. We first…
The implications of manifestly covariant formulation of relativistic quantum mechanics depending on a scalar evolution parameter, canonically conjugated to the variable mass, is still an unsettled issue. In this work we find a complete set…
A system consisting of a point material particle and a scalar field described by the nonlinear Klein-Gordon equation has been considered. It has been shown that, when taking into account relativistic effects, in the case of small rest…
Existence of a minimal measurable length, as an effective cutoff in the ultraviolet regime, is a common feature of all approaches to the quantum gravity proposal. It is widely believed that this length scale will be of the order of the…
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…
We study the Klein-Gordon (KG) oscillator with a Cornell-type scalar confinement in (2+1)-dimensional G\"{u}rses space-time backgrounds and report their exact solutions. The effect of the vorticity parameter $\Omega$ on the energy levels is…
The existence of a minimum observable length and/or a maximum observable momentum is in agreement with various candidates of quantum gravity such as string theory, loop quantum gravity, doubly special relativity and black hole physics. In…
Inspired by the generalized uncertainty principle (GUP), which adds gravitational effects to the standard description of quantum uncertainty, we extend the exact uncertainty principle (EUP) approach by Hall and Reginatto [J. Phys. A: Math.…
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…
We consider the dynamics of even solutions of the one-dimensional nonlinear Klein-Gordon equation $\partial_t^2 \phi - \partial_x^2 \phi + \phi - |\phi|^{2\alpha} \phi =0$ for $\alpha>1$, in the vicinity of the unstable soliton $Q$. Our…
The first-order loop quantum gravity correction of the simplest, classical general-relativistic Friedmann Hamiltonian constraint, emerging from a holomorphic spinfoam cosmological model peaked on homogeneous, isotropic geometries, is…
In this paper, we present topological defects in $(1,1)$ dimensions, described by an extended nonlinear $O(3)$ sigma model. We consider spherical coordinates $(\phi,\chi)$ in the $S^2$ isotopic space and a potential $V(\phi,\chi)$. For…