We study a system of nonlinear Klein-Gordon equations with viscoelastic and degenerate damping in bounded domain. prove the global existence exponential growth solutions negative initial energy.

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

We study here instability problems of standing waves for the nonlinear Klein-Gordon equations and solitary waves for the generalized Boussinesq equations. It is shown that those special wave solutions may be strongly unstable by blowup in finite time, depending on the range of the wave’s frequency or the wave’s speed of propagation and on the nonlinearity.

A system of coupled Klein-Gordon equations is suggested to model onedimensional nonlinear wave processes in a bi-layer. The type of coupling depends on the type of the interface and constitutes an arbitrary element of the Lie group classification problem, which is solved for these equations. The classification results are used to find conservation laws and particular invariant solutions.

We propose a set of nonlinear integral equations to describe on the excited states of an integrable the spin 1 chain with anisotropy. The scaling dimensions, evaluated numerically in previous studies, are recovered analytically by using the equations. This result may be relevant to the study on the supersymmetric sine-Gordon model.

The Coulomb potential is derived in " one space-one time " dimension, and introduced into Dirac and Klein-Gordon equations. The equations are solved, and somewhat surprising result-nonexistence of bound state solutions in the lower dimension-discussed and identified as another fine example of the " Klein paradox " .

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.

We define, in a consistent way, non-local pseudo-differential operators acting on a space of analytic functionals. These operators include the fractional derivative case. In this context we show how to solve homogeneous and inhomogeneous equations associated with these operators. We also extend the formalism to d-dimensional space-time solving, in particular, the fractional Wave and Klein-Gordo...

The nonlinear coupled Klein-Gordon-Schr dinger equations describes a system of conserved scalar nucleons interacting with neutral scalar Mesons coupled with Yukawa interaction method . In this paper we derive a finite element scheme to solve these equations, we test this method for stability and accuracy, many numerical tests have been given to show the validity of the scheme.