Invariant solutions of Liouville's equation in Robertson-Walker space-times

We find all solutions of Liouville's equation in Robertson-Walker space-times that are either spatially homogeneous or isotropic or both. Some of these solutions depend on constants of motion that are not generated by Killing vectors. We indicate how these solutions may be used to find Einstein-Liouville solutions.     

The Lorentz-Dirac equation in curved spaces

The Teitelboim-Plebañski method of average field is used to obtain the Lorentz-Dirac equation with gravitation.     

The hypergeneralized Heun equation in quantum field theory in curved space-times

We show for the first time the role played by the hypergeneralized Heun equation (HHE) in the context of quantum field theory in curved space-times. More precisely, we find suitable transformations relating the separated radial and angular parts of a massive Dirac equation in the Kerr-Newman-deSitter metric to a HHE.     

Similarity solutions of the cubic nonlinear Klein-Gordon equation

Using the direct method introduced by Clarkson and Kruskal recently, we obtain the similarity reductions of the cubic nonlinear Klein-Gordon equation whenz=0.     

Classification of F algebras and noncommutative integration of the Klein-Gordon equation in Riemannian spaces

The method of noncommutative integration of linear differential equations [A. V. Shapovalov and I. V. Shirokov, Izv. Vyssh. Uchebn. Zaved. Fiz., No. 4, 116; No. 5, 100 (1991)] is used to integrate the Klein-Gordon equation in Riemannian spaces. The situation is investigated where the set of noncommuting symmetry operators of the Klein-Gordon equation consists of first-order operators and one second-order operator and forms a so-called F algebra, which generalizes the concept of a Lie algebra. The F algebra is a quadratic algebra in the given situation. A classification of four- and five-dimensional F algebras is given. The integration of the Klein-Gordon equation in a Riemannian space, which does not admit separation of variables, is demonstrated in a nontrivial example.V. V. Kuibyshev State University, Tomsk. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 45–50, January, 1993.     

Klein-Gordon方程Q球解中能量稳定性和扰动研究

本文研究了一种复标量场模型中的双层Q球解,在解析形式下计算了Q球荷和能量. 同时,分析了其能量稳定性质,通过Klein-Gordon 方程获得了Q球能量的扰动表达式. 另外,还讨论了Q球暗物质产生的物理效应. 关键词： Klein-Gordon方程 Q球解 能量稳定性与扰动 暗物质     

Separation of variables and symmetry operators for the conformally invariant Klein-Gordon equation on curved spacetime

The separability of the conformally invariant Klein-Gordon equation and the Laplace-Beltrami equation are contrasted on two classes of Petrov type D curved spacetimes, showing that neither implies the other. The second-order symmetry operators corresponding to the separation of variables of the conformally invariant Klein-Gordon equation are constructed in both classes and the most general second-order symmetry operator for the conformally invariant Klein-Gordon operator on a general curved background is characterized tensorially in terms of a valence two-symmetric tensor satisfying the conformal Killing tensor equation and further constraints.     

Hartmann势的Klein-Gordon方程束缚态解及递推关系

给出了在Hartmann型标量势与矢量势相等的条件下其Klein-Gordon方程束缚态解.结果表明 ，径向波函数可用广义Laguerre多项式表示，其角向波函数可用Legendre多项式表示.另外 ，给出了径向波函数关于角量子数l和量子数n的二类新递推关系. 关键词： Hartmann势 Klein-Gorgon方程 束缚态 递推关系     

Quasiclassical solutions of the Klein-Gordon equation in a space-time with closed time-like curves

A formulation of the Cauchy problem for the Klein-Gordon equation in a space-time with a wormhole is studied. It is shown that if closed time-like curves pass through the Cauchy surface, then a global solution exists in the high-frequency (quasiclassical) limit only if the initial data satisfy nonlocal consistency conditions. In the simplest case these conditions determine a discrete spectrum of frequencies (energies of a quasiclassical scalar particle). Zh. éksp. Teor. Fiz. 113, 3–11 (January 1998)     

Periodic travelling and non-travelling wave solutions of the nonlinear Klein-Gordon equation with imaginary mass

Exact solutions, including the periodic travelling and non-travelling wave solutions, are presented for the nonlinear Klein-Gordon equation with imaginary mass. Some arbitrary functions are permitted in the periodic non-travelling wave solutions, which contribute to various high dimensional nonlinear structures.     

The direct Lyapunov method and the stability of certain solutions of the nonlinear Klein-Gordon equation

Central Scientific-Research Institute of Measurement Apparatus. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 34, No. 3, pp. 333–335, March, 1991.     

On the path integral for diffusion in curved spaces

The Onsager-Machlup Lagrangian for diffusion processes in curved spaces is determined by evaluating the covariant path integral by means of a spectral analysis of smooth trajectories in Riemannian normal coordinates. The Lagrangian involves a novel curvature scalar potential term $\text{v=?}\text{(}\text{1}\text{8}\text{)}\text{R}$. The present treatment replaces an earlier one.     

Approximate solutions of Klein-Gordon equation with improved Manning-Rosen potential in D-dimensions using SUSYQM

In this paper, we present solutions of the Klein–Gordon equation for the improved Manning–Rosen potential for arbitrary l state in d-dimensions using the supersymmetric shape invariance method. We obtained the energy levels and the corresponding wave functions expressed in terms of Jacobi polynomial in a closed form for arbitrary l state. We also calculate the oscillator strength for the potential.     

Positive definite particle densities for the positive frequency solutions of the klein gordon equation with arbitrary mass

In this paper it is shown that the set of kernels introduced previously by Gerlach, Gromes and Petzold can be enlarged considerably. The paper concludes with a remark on the theory of massless particles.     

Remark on nonexistence of global solutions of the initial-boundary-value problem for the nonlinear Klein-Gordon equation

Sufficient conditions are given so that the solutions of the initial-boundary-value problem for the nonlinear Klein-Gordon equation do not exist for allt>0.     

Trajectory length constraint and the Klein-Gordon equation

It is shown that the relativistic constraint of the length of possible trajectories in the method of integrals over the trajectories results in the Klein-Gordon equation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 63–65, December, 1984.     

On the invariance properties of the Klein-Gordon equation with external electromagnetic field

Abstarct Here we attempt to find the nature of the external electromagnetic field such that the KG equation with external electromagnetic field is invariant. Lie’s extended group method is applied to obtain the class of external electromagnetic field which admits the invariance of the KG equation. Though, the field potential only explicitly appears in the equation, the constraints for the invariance are only on the electromagnetic field. since deceased.