Related papers: Dispersion relation of the non-linear Klein-Gordon…
We numerically solve the Klein-Gordon equation at second order in cosmological perturbation theory in closed form for a single scalar field, describing the method employed in detail. We use the slow-roll version of the second order source…
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…
In this paper, we build a Gibbs measure for the 1d cubic Klein-Gordon equation on $\mathbb R$ with a decreasing non linearity, in the sense that the non linearity $f^3$ is multiplied by $\chi$ where $\chi$ is a sufficiently integrable non…
We derive the long-time decay in weighted norms for solutions of the discrete 3D Schr\"odinger and Klein-Gordon equations.
We consider the nonlinear damped Klein-Gordon equation \[ \partial_{tt}u+2\alpha\partial_{t}u-\Delta u+u-|u|^{p-1}u=0 \quad \text{on} \ \ [0,\infty)\times \mathbb{R}^N \] with $\alpha>0$, $2 \le N\le 5$ and energy subcritical exponents…
We study the one-dimensional nonlinear Klein-Gordon (NLKG) equation with a convolution potential, and we prove that solutions with small $H^s$ norm remain small for long times. The result is uniform with respect to $c \geq 1$, which however…
In this brief communication, we present an exact analytic nonlinear dispersion relation (NLDR) for the dust acoustic waves using the Korteweg-de Vries (KdV) model. The NLDR agrees with the spectrum of spatio-temporal evolution obtained from…
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…
In this article we will develop some techniques aimed at the strong couplings in two-dimensional wave-Klein-Gordon system. We distinguish the roles of different type of decay factors and develop a method which permits us to "exchange" one…
We discuss an O(N) exension of the Sine-Gordon (S-G)equation which allows us to perform an expansion around the leading order in large-N result using Path-Integral methods. In leading order we show our methods agree with the results of a…
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…
Blowing-up solutions of Klein-Gordon equations with gauge variant semilinear terms are considered in Friedmann-Lema\'itre-Robertson-Walker spacetimes. Effects of spatial expansion or contraction on the solutions are studied through the…
The method of optimal prediction is applied to calculate the future means of solutions to the Klein-Gordon equation. It is shown that in an appropriate probability space, the difference between the average of all solutions that satisfy…
We consider the deformation of the Whitham system for the non-linear Klein-Gordon equation having the Lorentz-invariant form. Using the Lagrangian formalism of the initial system we obtain the first non-trivial correction to the Whitham…
Dispersive approaches provide model independent description of meson-meson scattering. We first review here the use of dispersion relations to obtain a model independent unitarization of Chiral Perturbation Theory amplitudes, that establish…
Dispersion relations are nonperturbative formulas that relate the ultraviolet and infrared behavior of an observable with wide-ranging applications applications in linear response theory, quantum field theory scattering amplitudes, and…
In additional to the parity ($\mathcal{P}$) symmetric, time reversal ($\mathcal{T}$) symmetric, and $\mathcal{PT}$ symmetric nonlocal integrable systems, some other types of nonlocal integrable Klein-Gordon models with the space-time…
A fundamental non-classical fourth-order partial differential equation to describe small amplitude linear oscillations in a rotating compressible fluid, is obtained. The dispersion relations for such a fluid, and the different regions of…
Consider, in dimension 3, a system of coupled Klein-Gordon equations with different speeds, and an arbitrary quadratic nonlinearity. We show, for data which are small, smooth, and localized, that a global solution exists, and that it…
We prove small data global existence and scattering for quasilinear systems of Klein-Gordon equations with different speeds, in dimension three. As an application, we obtain a robust global stability result for the Euler-Maxwell equations…