Related papers: A search on the Klein-Gordon equation
The Klein-Fock-Gordon equation is studied on the generalized Y-junction of $N$ strings with a massive center. The corresponding formulas for wave scattering and normal modes are obtained.
The scalar Klein-Gordon equation describes wave motion in a waveguide with a cut-off. For example, the displacement of an elastic cord anchored to a solid base by elastic elements can be described by the scalar Klein-Gordon equation. We…
We study linear Klein-Gordon equations with moving potentials motivated by the stability analysis of traveling waves and multi-solitons. In this paper, Strichartz estimates, local energy decay and the scattering theory for these models are…
A possible way for the consistent probability interpretation of the Klein-Gordon equation is proposed. It is assumed that some states of a scalar charged particle cannot be physically realized. The rest of quantum states are proven to have…
In the present work, we introduce a new $\mathcal{PT}$-symmetric variant of the Klein-Gordon field theoretic problem. We identify the standing wave solutions of the proposed class of equations and analyze their stability. In particular, we…
We explore the Klein-Gordon equation in the framework of crypto-Hermitian quantum mechanics. Solutions to common problems with probability interpretation and indefinite inner product of the Klein-Gordon equation are proposed.
Consider the Klein-Gordon-Zakharov equations in $\mathbb{R}^{1+2}$, and we are interested in establishing the small global solution to the equations and in investigating the pointwise asymptotic behavior of the solution. The…
In this article one will discuss the system of coupled nonlinear Klein-Gordon equations with different velocities and different masses. The nonlinearity considered is a general quadratic nonlinearity without any restriction. The method is a…
In this paper, we consider the wave equation for the Laplace operator with potential, initial data, and nonhomogeneous Dirichlet boundary condition. We establish a weak solution by using traces and extension domains. We also establish the…
Numerical simulations of the semilinear Klein--Gordon equation in the de Sitter spacetime are performed. We use two structure-preserving discrete forms of the Klein--Gordon equation. The disparity between the two forms is the discretization…
We investigate the separability of Klein-Gordon equation on near horizon of d-dimensional rotating Myers-Perry black hole in two limits : 1) generic extremal case and 2) extremal vanishing horizon case. In the first case , there is a…
In this paper we prove the validity of a long wave Whitham approximation for a system consisting of a Boussinesq equation coupled with a Klein-Gordon equation. The proof is based on an infinite series of normal form transformations and an…
In this paper we consider the Klein-Gordon-Maxwell system in the electrostatic case, assuming the fall-off large-distance requirement on the gauge potential. We are interested in proving the existence of finite energy (and finite charge)…
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…
The Klein-Gordon equation in the presence of a spatially one-dimensional Hulth\'en potential is solved exactly and the scattering solutions are obtained in terms of hypergeometric functions. The transmission coefficient is derived by the…
We point out that the free single-fermion propagator which is used in the QFT equations for two-fermion systems, has a bosonic structure, transforms to the single-boson propagator for the Klein-Gordon equation in the nonrelativistic limit,…
In this paper, we investigate the almost-periodic solutions for the one-dimensional nonlinear Klein-Gordon equation within the non-relativistic limit under periodic boundary conditions. Specifically, by employing the method introduced in…
We give the governing equations for multiple scalar fields in a flat Friedmann-Robertson-Walker (FRW) background spacetime on all scales, allowing for metric and field perturbations up to second order. We then derive the Klein-Gordon…
This paper is concerned with strong blow-up instability (Definition 1.3) for standing wave solutions to the system of the quadratic nonlinear Klein-Gordon equations. In the single case, namely the nonlinear Klein-Gordon equation with power…
The dispersive estimate plays a pivotal role in establishing the long-term behavior of solutions to the nonlinear equation, thereby being crucial for investigating the well-posedness of the equation.In this work we prove that the solutions…