Related papers: Fractional Klein-Gordon equation for linear disper…
A Langevin equation with a special type of additive random source is considered. This random force presents a fractional order derivative of white noise, and leads to a power-law time behavior of the mean square displacement of a particle,…
This paper is devoted to the numerical analysis of a piecewise constant discontinuous Galerkin method for time fractional subdiffusion problems. The regularity of weak solution is firstly established by using variational approach and…
Elliptic pseudoanalytic function theory was considered independently by Bers and Vekua decades ago. In this paper we develop a hyperbolic analogue of pseudoanalytic function theory using the algebra of hyperbolic numbers. We consider the…
In this article we will prove the global existence of a type of wave-Klein-Gordon system in $2+1$ spacetime dimension. Some technical tools such as conformal energy estimate on hyperboloid, normal form transform on Klein-Gordon equations…
In this article we propose a scheme for solving the coupled time-fractional nonlocal diffusion problem. The scheme consist of fractional Crank-Nicolson method with Galerkin finite element method (FEM) and Newton's method. We derive \emph{a…
We solve the Klein-Gordon and Dirac equations in an open cosmological universe with a partially horn topology in the presence of a time dependent magnetic field. Since the exact solution cannot be obtained explicitly for arbitrary…
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…
We obtain a dispersive long-time decay in weighted energy norms for solutions of the 3D Klein-Gordon equation with generic potential. The decay extends the results obtained by Jensen and Kato for the 3D Schredinger equation. For the proof…
We consider the evolution of narrow-band wave trains of finite amplitude in a nonlinear dispersive system which is described by the Klein--Gordon equation with arbitrary polynomial nonlinearity. We use a new perturbative technique which…
We present the exact solution of the Klein-Gordon equation in D-dimensions in the presence of the noncentral equal scalar and vector pseudoharmonic potential plus the new ring-shaped potential using the Nikiforov-Uvarov method. We obtain…
For the $1+1$ dimensional damped stochastic Klein-Gordon equation, we show that random singularities associated with the law of the iterated logarithm exist and propogate in the same way as the stochastic wave equation. This provides…
A de Broglie-Bohm like model of Klein-Gordon equation, that leads to the correct Schrodinger equation in the low-speed limit, is presented. Under this theoretical framework, that affords an interpretation of the quantum potential, the main…
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…
The massless Klein--Gordon equation on arbitrary curved backgrounds allows for solutions which develop "tails" inside the light cone and, therefore, do not strictly follow null geodesics as discovered by DeWitt and Brehme almost sixty years…
We find three exact solutions to the Klein-Gordon equation in 1-1 dimensional space-time for different time dependent potentials. In two cases we consider a time dependent scalar potential and in one case a time dependent electric…
We have investigated the reality of exact bound states of complex and/or PT-symmetric non-Hermitian exponential-type generalized Hulthen potential. The Klein-Gordon equation has been solved by using the Nikiforov-Uvarov method which is…
In this article, the new exact travelling wave solutions of the time-and space-fractional KdV-Burgers equation has been found. For this the fractional complex transformation have been implemented to convert nonlinear partial fractional…
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 deal with some extensions of the space-fractional diffusion equation, which is satisfied by the density of a stable process (see Mainardi, Luchko, Pagnini (2001)): the first equation considered here is obtained by adding an exponential…
In this paper, the famous Klein-Gordon-Zakharov equations are firstly generalized, the new special types of Klein-Gordon-Zakharov equations with the positive fractional power terms (gKGZE) are presented. In order to derive the exact…