Finite states in 4 quantized dimensional gravity. The anisotropic minisuperspace Ashtekar–Klein–Gordon model (Part I). Abstract In this paper we construct the generalized Kodama state for gravity in the homogeneous anisotropic case coupled to a Klein–Gordon scalar field with constant scalar potential. The basic method is to generate an asymptotic expansion about the pure Kodama state, viewed as...

Abstract: By means of a simple transformation, we have shown that the generalized-Zakharov equations, the coupled nonlinear Klein-Gordon-Zakarov equations, the GDS, DS and GZ equations and generalized Hirota-Satsuma coupled KdV system can be reduced to the ellipticlike equations. Then, the extended projective Riccati equation expansion method is used to obtain a series of solutions including ne...

Finite states in 4 quantized dimensional gravity. The anisotropic minisuperspace Ashtekar–Klein–Gordon model (Part I). Abstract In this paper we construct the generalized Kodama state for gravity in the homogeneous anisotropic case coupled to a Klein–Gordon scalar field with constant scalar potential. The basic method is to generate an asymptotic expansion about the pure Kodama state, viewed as...

The perturbation of the Dirac sea to first order in the external potential is calculated in an expansion around the light cone. It is shown that the perturbation consists of a causal contribution, which describes the singular behavior of the Dirac sea on the light cone and contains bounded line integrals over the potential and its partial derivatives, and a noncausal contribution, which is a sm...

We develope a numerical method based on B-spline collocation method to solve linear Klein-Gordon equation. The proposed scheme is unconditionally stable. The results of numerical experiments have been compared with the exact solution to show the efficiency of the method computationally. Easy and economical implementation is the strength of this approach.  

A relativistic extension of our pseudo-shifted l–expansion technique is presented to solve for the eigenvalues of Dirac and Klein-Gordon equations. Once more we show the numerical usefulness of its results via comparison with available numerical integration data.

The modified decomposition method has been implemented for solving a coupled Klein-Gordon Schrödinger equation. We consider a system of coupled Klein-Gordon Schrödinger equation with appropriate initial values using the modified decomposition method. The method does not need linearization, weak nonlinearity assumptions or perturbation theory. The numerical solutions of coupled Klein-Gordon Schr...

An expansion method based on time fractional Sine-Gordon equation is implemented to construct some real and complex valued exact solutions the Korteweg-de Vries modified equations in forms. Compatible traveling wave transform plays a key role be able apply homogeneous balance technique set predicted solution. The relation between trigonometric hyperbolic functions allows form with multiplicatio...

in this paper, we solve a inhomogeneous fractional klein-gordon equation by the method of separating variables. we apply the method for three boundary conditions, contain dirichlet, neumann, and robin boundary conditions, and solve some examples to illustrate the effectiveness of the method.