相关论文: Weighted energy decay for magnetic Klein-Gordon eq…
Recently, it has been shown that the generalized symmetric Woods-Saxon potential energy, in which surface interaction terms are taken into account, describes the physical processes better than the standard form. Therefore in this study, we…
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 are interested in the Klein-Gordon-Zakharov system in $\mathbb{R}^{1+2}$, which is an important model in plasma physics with extensive mathematical studies. The system can be regarded as semilinear coupled wave and Klein-Gordon equations…
In this paper, we study the global well-posedness and scattering problem in the energy space for both focusing and defocusing the Klein-Gordon-Hartree equation in the spatial dimension $d \geq 3$. The main difficulties are the absence of an…
We study long-time dynamics of small even perturbations of the soliton in 1D quadratic Klein-Gordon equation. The soliton possesses both an internal mode and the unstable mode. On a codimension-one manifold of fine-tuned initial data the…
We consider the Klein-Gordon equation on the exterior of the toric anti de-Sitter Schwarzschild black hole with Dirichlet, Neumann and Robin boundary conditions at $\mathcal{I}$. We define a non-degenerate energy for the equation which…
In this paper, we study the scattering theory for the defocusing energy-critical Klein-Gordon equation with a cubic convolution $u_{tt}-\Delta u+u+(|x|^{-4}\ast|u|^2)u=0$ in the spatial dimension $d \geq 5$. We utilize the strategy in [S.…
We study the three-dimensional Dirac and Klein-Gordon equations with scalar and vector potentials of equal magnitudes as an attempt to give a proper physical interpretation of this class of problems which has recently been accumulating…
We study the asymptotics of the Schr\"odinger equation with time-dependent potential in dimension one. Assuming that the potential decays sufficiently rapidly as $|x| \to \infty$, we prove that the solution can be written as the sum of a…
We show that for a one-dimensional Schr\"odinger operator with a potential whose first moment is integrable the scattering matrix is in the unital Wiener algebra of functions with integrable Fourier transforms. Then we use this to derive…
This paper proves the existence of a bounded energy and integrated energy decay for solutions of the massless Vlasov equation in the exterior of a very slowly rotating Kerr spacetime. This combines methods previously developed to prove…
We construct the causal (forward/backward) propagators for the massive Klein-Gordon equation perturbed by a first order operator which decays in space but not necessarily in time. In particular, we obtain global estimates for…
We prove decay with respect to some Lebesgue norms for a class of Schr\"odinger equations with non-local nonlinearities by showing new Morawetz inequalities and estimates. As a byproduct, we obtain large-data scattering in the energy space…
We seek to introduce a mathematical method to derive the Klein-Gordon equation and a set of relevant laws strictly, which combines the relativistic wave functions in two inertial frames of reference. If we define the stationary state wave…
The wave Schrodinger and, to clarify one interesting point encountered in the calculations, Klein-Gordon equations are solved exactly for a single neutron moving in a central Woods-Saxon plus an additional potential that provides a…
The effective mass Klein-Gordon equation in one dimension for the Woods-Saxon potential is solved by using the Nikiforov-Uvarov method. Energy eigenvalues and the corresponding eigenfunctions are computed. Results are also given for the…
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…
Based on the Coulomb gauge, the accurate Klein-Gordon equation in static scalar and vector potentials was derived from Klein-Gordon equation in electromagnetic environment. The correct equation developed in this comment demonstrates that…
We consider long time evolution of small solutions to general multispeed Klein-Gordon systems in 3+1 dimensions. We prove that such solutions are always global and scatter to a linear flow, thus extending previous partial results. The main…
We prove global in time dispersion for the wave and the Klein-Gordon equation inside the Friedlander domain by taking full advantage of the space-time localization of caustics and a precise estimate of the number of waves that may cross at…