Klein–Gordon oscillator with magnetic and quantum flux fields in non-trivial topological space-time

The relativistic quantum motions of the oscillator field(via the Klein–Gordon oscillator equation)under a uniform magnetic field in a topologically non-trivial space-time geometry are analyzed. We solve the Klein–Gordon oscillator equation using the Nikiforov-Uvarov method and obtain the energy profile and the wave function. We discuss the effects of the non-trivial topology and the magnetic field on the energy eigenvalues. We find that the energy eigenvalues depend on the quantum flux field tha...     

Moving potential for Dirac and Klein–Gordon equations

Using the Lorentz transformation, the Klein–Gordon and Dirac equations with moving potentials are reduced to one standard where the potential is time-independent. As application, the reflection and transmission coefficients are determined by considering the moving step with a constant velocity v. It has been found that R ± T = 1 only at x = vt. The problem of massless (2 + 1) Dirac particle is also considerered.     

Analytical approximate solution for nonlinear space-time fractional Klein Gordon equation

The fractional derivatives in the sense of Caputo and the homotopy analysis method are used to construct an approximate solution for the nonlinear space-time fractional derivatives Klein-Gordon equation. The numerical results show that the approaches are easy to implement and accurate when applied to the nonlinear space-time fractional derivatives KleinGordon equation. This method introduces a promising tool for solving many space-time fractional partial differential equations. This method is efficient and powerful in solving wide classes of nonlinear evolution fractional order equations.     

Klein–Gordon and Dirac Equations with Thermodynamic Quantities

We study the thermodynamic quantities such as the Helmholtz free energy, the mean energy and the specific heat for both the Klein–Gordon, and Dirac equations. Our analyze includes two main subsections: (1) statistical functions for the Klein–Gordon equation with a linear potential having Lorentz vector, and Lorentz scalar parts (2) thermodynamic functions for the Dirac equation with a Lorentz scalar, inverse-linear potential by assuming that the scalar potential field is strong (A ? 1). We restrict ourselves to the case where only the positive part of the spectrum gives a contribution to the sum in partition function. We give the analytical results for high temperatures.     

The Klein–Gordon–Zakharov equations with the positive fractional power terms and their exact solutions

In this paper, the famous Klein–Gordon–Zakharov (KGZ) equations are first generalized, and the new special types of KGZ equations with the positive fractional power terms (gKGZE) are presented. In order to derive exact solutions of the new special gKGZE, subsidiary higher-order ordinary differential equations (sub-ODEs) with the positive fractional power terms are introduced, and with the aid of the sub-ODE, exact solutions of four special types of the gKGZE are derived, which are the bell-type solitary wave solution, the algebraic solitary wave solution, the kink-type solitary wave solution and the sinusoidal travelling wave solution, provided that the coefficients of gKGZE satisfy certain constraint conditions.     

Stability study of a model for the Klein–Gordon equation in Kerr space-time

The current early stage in the investigation of the stability of the Kerr metric is characterized by the study of appropriate model problems. Particularly interesting is the problem of the stability of the solutions of the Klein–Gordon equation, describing the propagation of a scalar field of mass $\mu $ in the background of a rotating black hole. Rigorous results prove the stability of the reduced, by separation in the azimuth angle in Boyer–Lindquist coordinates, field for sufficiently large masses. Some, but not all, numerical investigations find instability of the reduced field for rotational parameters $a$ extremely close to $1$ . Among others, the paper derives a model problem for the equation which supports the instability of the field down to $a/M \approx 0.97$ .     

Bright and singular soliton solutions of the conformable time-fractional Klein–Gordon equations with different nonlinearities

Finding the exact solutions of nonlinear fractional differential equations has gained considerable attention, during the past two decades. In this paper, the conformable time-fractional Klein–Gordon equations with quadratic and cubic nonlinearities are studied. Several exact soliton solutions, including the bright (non-topological) and singular soliton solutions are formally extracted by making use of the ansatz method. Results demonstrate that the method can efficiently handle the time-fractional Klein–Gordon equations with different nonlinearities.     

Bifurcation analysis and the travelling wave solutions of the Klein–Gordon–Zakharov equations

In this paper, we investigate the bifurcations and dynamic behaviour of travelling wave solutions of the Klein–Gordon–Zakharov equations given in Shang et al, Comput. Math. Appl. 56, 1441 (2008). Under different parameter conditions, we obtain some exact explicit parametric representations of travelling wave solutions by using the bifurcation method (Feng et al, Appl. Math. Comput. 189, 271 (2007); Li et al, Appl. Math. Comput. 175, 61 (2006)).     

Multibreather stability in discrete Klein–Gordon equations: Beyond nearest neighbor interactions

We present results on multibreather stability in one-dimensional nonlinear Klein–Gordon chains. Our analysis is based on Aubry?s band theory and perturbation theory. First, we provide an alternative proof of the stability of multibreathers in a chain with nearest neighbor interactions only. Then, we extend our analysis to the case of interactions with up to three neighbors. For next-nearest neighbor and third-nearest neighbor interactions we also extend the theory to study the stability properties of recently found multibreathers that have nonstandard phase shifts (not equal to 0 or π).     

Exact Analytical Solution of the Klein–Gordon Equation in the Generalized Woods–Saxon Potential

The exact analytical solution of the Klein–Gordon equation for the spin-0 particles in the generalized Woods–Saxon potential is presented. The bound state energy eigenvalues and corresponding wave functions are obtained in the closed forms. The correlations between the potential parameters and energy eigenvalues are examined for π0particles.     

Exact Solutions of the Klein–Gordon Equation with Hylleraas Potential

We present the exact solution of the Klein–Gordon with Hylleraas Potential using the Nikiforov–Uvarov method. We obtain explicitly the bound state energy eigenvalues and the corresponding eigen function for s-wave. The wave functions obtained are expressed in terms of Jacobi polynomials.     

Davey–Stewartson equations in (3 + 1) dimensions with an infinite-dimensional symmetry algebra

Letters in Mathematical Physics - This article is devoted to discovering Lie symmetry algebra of a (3 + 1)-dimensional Davey–Stewartson system which appears in the field of plasma physics. It...     

q-nonlinear Schrodinger and q-nonlinear Klein–Gordon equations in the frame work of GUP

In this work, we first introduce a nonlinear Schrodinger and a nonlinear Klein–Gordon equations. Then we deform these equations to a the q-nonlinear Schrodinger and q-nonlinear Klein–Gordon equations. This is done using the formalism of generalized uncertainty principle (GUP). We also study the deformed nonlinear solutions.     

A local energy-preserving scheme for Klein Gordon Schrdinger equations

A local energy conservation law is proposed for the Klein–Gordon–Schr ¨odinger equations, which is held in any local time–space region. The local property is independent of the boundary condition and more essential than the global energy conservation law. To develop a numerical method preserving the intrinsic properties as much as possible, we propose a local energy-preserving(LEP) scheme for the equations. The merit of the proposed scheme is that the local energy conservation law can hold exactly in any time–space region. With the periodic boundary conditions, the scheme also possesses the discrete change and global energy conservation laws. A nonlinear analysis shows that the LEP scheme converges to the exact solutions with order O(τ2+ h2). The theoretical properties are verified by numerical experiments.     

A singularity theorem for Einstein–Klein–Gordon theory

Hawking’s singularity theorem concerns matter obeying the strong energy condition (SEC), which means that all observers experience a nonnegative effective energy density (EED), thereby guaranteeing the timelike convergence property. However, there are models that do not satisfy the SEC and therefore lie outside the scope of Hawking’s hypotheses, an important example being the massive Klein–Gordon field. Here we derive lower bounds on local averages of the EED for solutions to the Klein–Gordon equation, allowing nonzero mass and nonminimal coupling to the scalar curvature. The averages are taken along timelike geodesics or over spacetime volumes, and our bounds are valid for a range of coupling constants including both minimal and conformal coupling. Using methods developed by Fewster and Galloway, these lower bounds are applied to prove a Hawking-type singularity theorem for solutions to the Einstein–Klein–Gordon theory, asserting that solutions with sufficient initial contraction at a compact Cauchy surface will be future timelike geodesically incomplete. These results remain true in the presence of additional matter obeying both the strong and weak energy conditions.     

A Klein–Gordon particle captured by embedded curves

In the present work, a Klein–Gordon particle with singular interactions supported on embedded curves on Riemannian manifolds is discussed from a more direct and physical perspective, via the heat kernel approach. It is shown that the renormalized problem is well-defined, and the ground state energy is unique and finite. The renormalization group invariance of the model is discussed, and it is observed that the model is asymptotically free.     

The extended conformal Einstein field equations with matter: The Einstein–Maxwell field

A discussion is given of the conformal Einstein field equations coupled with matter whose energy–momentum tensor is trace-free. These resulting equations are expressed in terms of a generic Weyl connection. The article shows how in the presence of matter it is possible to construct a conformal gauge which allows to know a priori the location of the conformal boundary. In vacuum this gauge reduces to the so-called conformal Gaussian gauge. These ideas are applied to obtain (i) a new proof of the stability of Einstein–Maxwell de Sitter-like spacetimes; (ii) a proof of the semi-global stability of purely radiative Einstein–Maxwell spacetimes.