Related papers: Klein-Gordon oscillator in a topologically nontriv…
From a study of an oscillator in a $4D$ NC spacetime, we establish the Hamilton equations of motion. The formers are solved to give the oscillator position and momentum coordinates. These coordinates are used to build a metric similar to…
This paper is concerned with an investigation of the quantum mechanical dynamics of massive, spinless relativistic Klein-Gordon particle in the space-time generated by a rotating cosmic string. The equations of motion are found by the use…
We present explicit solutions of the signum-Gordon scalar field equation which have finite energy and are periodic in time. Such oscillons have a strictly finite size. They do not emit radiation.
We prove existence and multiplicity of Cantor families of small amplitude time periodic solutions of completely resonant Klein-Gordon equations on the sphere $\mathbb{S}^3$ with quadratic, cubic and quintic nonlinearity, regarded as toy…
We investigate the solution of the Klein-Gordon equation for a charged scalar particle in an electromagnetic plane wave background with $k^2>0$, which can be realized in a medium with a refractive index $n<1$. We reduce the equation of…
We consider the U(1)-invariant nonlinear Klein-Gordon equation in discrete space and discrete time, which is the discretization of the nonlinear continuous Klein-Gordon equation. To obtain this equation, we use the energy-conserving…
In this article we consider a system of two Klein-Gordon equations, set on the $d$-dimensional box of size $L$, coupled through quadratic semilinear terms of strength $\varepsilon$ and evolving from well-prepared random initial data. We…
We study the scalar perturbations of rotating black holes in framework of extra dimensions type Randall-Sundrum(RS).
We prove that finite energy solutions to the nonlinear Schroedinger equation and nonlinear Klein--Gordon equation which have the compact time spectrum have to be one-frequency solitary waves. The argument is based on the generalization of…
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 consider the quantum mechanical problem of the motion of a spinless charged relativistic particle with mass$M$, described by the Klein-Fock-Gordon equation with equal scalar $S(\vec{r})$ and vector $V(\vec{r})$ Coulomb plus ring-shaped…
This dissertation discusses solutions to the nonlinear Klein-Gordon equation with symmetric and asymmetric double-well potentials, focusing on the collapse and collision of bubbles and critical phenomena found therein. A new method is…
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…
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 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 this research contribution, we explore the relativistic quantum dynamics of spin-0 scalar particles within a curved space-time background containing topological defects, while incorporating the effects of rainbow gravity. The Klein…
In this work, we study the Klein-Gordon oscillator with equal scalar and vector potentials in a topologically charged Ellis-Bronnikov wormhole space-time background. The behaviour of a relativistic oscillator field is studied with a…
We use the Klein-Gordon equation in a curved spacetime to construct the relativistic analog of the Schr\"odinger-Newton problem, where a scalar particle lives in a gravitational potential well generated by its own probability distribution.…
Klein-Gordon equations describe the dynamics of waves/particles in sub-atomic scales. For a system of nonlinear Klein-Gordon equations, a systematic analysis of the time evolution for their spatially uniform solutions has been performed…
We consider the conformal wave equation on the Einstein cylinder with a defocusing cubic non-linearity. Motivated by a method developed by Rostworowski-Maliborski on the existence of time periodic solutions to the spherically symmetric…