In this article we will develop some techniques aimed at the strong couplings in two-dimensional wave-Klein-Gordon system. We distinguish roles of different type decay factors and a method which permits us to “exchange” one into other. Then global existence result model problem is established. also give sketch Klein-Gordon-Zakharov system establish associate result.

We give an explicit construction of a positive-definite invariant inner-product for the Klein-Gordon fields, thus solving the old problem of the probability interpretation of Klein-Gordon fields without having to restrict to the subspaces of the positivefrequency solutions. Our method has a much wider domain of application and enjoys a remarkable uniqueness property. We explore its consequences...

We give an explicit construction of a positive-definite invariant inner-product for the Klein-Gordon fields, thus solving the old problem of the probability interpretation of Klein-Gordon fields without having to restrict to the subspaces of the positive-frequency solutions. Our method has a much wider domain of application and enjoys a remarkable uniqueness property. We explore its consequence...

We present a new step in the foundation of quantum field theory with the tools of scale relativity. Previously, quantum motion equations (Schrödinger, Klein–Gordon, Dirac, Pauli) have been derived as geodesic equations written with a quantum-covariant derivative operator. Then, the nature of gauge transformations, of gauge fields and of conserved charges have been given a geometric meaning in t...

In this paper we study the multiplicity of positive solutions for nonlinear elliptic equations on R . The number of solutions is greater or equal than the number of disjoint intervals on which the nonlinear term is negative. Applications are given to multiplicity of standing waves for the nonlinear Schrödinger, Klein-Gordon and Klein-Gordon-Maxwell equations.

In this paper, nonlinear Klein-Gordon equation with quadratic term is solved by means of an analytic technique, namely the Homotopy analysis method (HAM).Comparisons are made between the Adomian decomposition method (ADM), the exact solution and homotopy analysis method. The results reveal that the proposed method is very effective and simple.

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.

We re-examine the dynamical stability of the nakedly singular, static, spherically symmetric solutions of the Einstein-Klein Gordon system. We correct an earlier proof of the instability of these solutions, and demonstrate that there are solutions to the massive Klein-Gordon system that are perturbatively stable.