相关论文: On the Klein-Gordon equation and hyperbolic pseudo…
We consider a certain ultrahyperbolic equation in a Euclidean space being a generalization of Klein-Gordon-Fock equation. The behavior of solutions at points tending to infinity along timelike directions is studied. We examine the issue of…
In the paper we present a functional-discrete method for solving the Goursat problem for nonlinear Klein-Gordon equation. The sufficient conditions providing that the proposed method converges superexponentially are obtained. The results of…
In [8] it was shown that the transplant operator transforms solutions of one Vekua equation into solutions of another Vekua equation, related to the first via a Schr\"odinger equation. In this paper we demonstrate a fundamental property of…
We give a new construction based on pseudo-differential calculus of quasi-free Hadamard states for Klein-Gordon equations on a class of space-times whose metric is well-behaved at spatial infinity. In particular we construct all pure…
The interest in the Klein-Gordon equation with different potentials has increased in recent years due to its possible applications in Cosmology, Hadron Physics and High-Energy Physics. In this work we investigate the solutions of the…
In the present Chapter, we consider two prototypical Klein-Gordon models: the integrable sine-Gordon equation and the non-integrable $\phi^4$ model. We focus, in particular, on two of their prototypical solutions, namely the kink-like…
The aim of this work is to develop a global calculus for pseudo-differential operators acting on suitable algebras of generalized functions. In particular, a condition of global hypoellipticity of the symbols gives a result of regularity…
In Dunkl theory on $\mathbb{R}^{n}$ which generalizes classical Fourier analysis, we study the solution of the Klein-Gordon-equation defined by: \begin{eqnarray} \nonumber \partial_{t}^{2}u-\Delta_{k}u=-m^{2}u \ , \ \ \ u (x,0)=g(x) \ , \ \…
In this paper, we study Vekua-type operators associated with diagonal operators on compact Lie groups. Characterizations of global hypoellipticity and global solvability properties are presented on classes of Vekua-type operators with…
Green-hyperbolic operators - partial differential operators on globally hyperbolic spacetimes that (together with their formal duals) possess advanced and retarded Green operators - play an important role in many areas of mathematical…
There have been some long-standing puzzles related to the Coulomb solutions of the Klein-Gordon and Dirac equations, namely how to understand the physics underlying the weakly divergent near-the-origin behavior of the $S$-wave wave…
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…
In this note, we investigate Vekua-type periodic operators of the form $Pu=Lu-Au-B\bar u$, where $L$ is a constant coefficient partial differential operator. We provide a complete characterization of the necessary and sufficient conditions…
In investigation of boundary-value problems for certain partial differential equations arising in applied mathematics, we often need to study the solution of system of partial differential equations satisfied by hypergeometric functions and…
We study the two-dimensional stochastic sine-Gordon equation (SSG) in the hyperbolic setting. In particular, by introducing a suitable time-dependent renormalization for the relevant imaginary multiplicative Gaussian chaos, we prove local…
Building on the hyperboloidal foliation approach of Lefloch and Ma, we extend Klainerman's physical-space approach to dispersive estimates to recover the frequency-restricted $L^1$--$L^\infty$ dispersive estimates for Klein-Gordon…
An approximate solution of the Klein-Gordon equation for the general Hulth\'en-type potentials in $D$-dimensions within the framework of an approximation to the centrifugal term is obtained. The bound state energy eigenvalues and the…
We study strictly hyperbolic partial differential operators of second order with non-smooth coefficients. After modelling them as semiclassical Colombeau equations of log-type we provide a factorization procedure on some…
We consider the hyperbolic scaling of the FKPP equation and introduce two solutions of the action functional type in the limit of zero hyperbolic parameter. Furthermore, we show that the action functional of the Ablowitz-Zepetella kink is a…
We perform a high-temperature expansion of the grand potential of the restrictive primitive model of electrolytes in the frame of the extended sine-Gordon theory exposed in the companion paper. We recover a result already obtained by Stell…