The aim of this paper is to prove the existence nonlinear Klein-Gordon equations coupled with Born-Infeld theory by using variational methods.

In this paper, we establish exact solutions for the timefractional Klein-Gordon equation, and the time-fractional HirotaSatsuma coupled KdV system. The Hes semi-inverse and the Kudryashov methods are used to construct exact solutions of these equations. We apply Hes semi-inverse method to establish a variational theory for the time-fractional Klein-Gordon equation, and the timefractional Hirota...

We discuss several aspects of singularities of the solutions of the partial differential equations of Klein–Gordon, Schrödinger and Dirac. In particular we analyze the fold type singularity, of the first and higher orders, and the related characteristic equations. We also consider the field equations as reduction of homogenous equations in higher dimensions, and discuss how singularities of the...

In this paper, we study the existence and uniqueness of global solution for a Klein–Gordon equations system with mixed boundary conditions. We, also, analyze asymptotic behavior solution.

Abstract: Haar wavelet method for solving the Klein–Gordon and the sine-Gordon equations has been implemented. Application to partial differential equations is exemplified by solving the sine-Gordon equation. The efficiency of the method is demonstrated by five numerical examples. Computer simulation is carried out for problems the exact solution of which is known. This allows us to estimate th...

We study the 2D coupled wave–Klein-Gordon systems with semilinear null nonlinearities Q0 and Qαβ. The main result states that solution to system exists globally provided initial data is small in some weighted Sobolev space, which does not necessarily have compact support, we also asymptotic behavior of solution. In particular, show optimal time decay scattering major difficulties lie slow natur...