this paper studies the perturbed klein-gordon equation by the aid of several methods of integrability. there are six forms of nonlinearity that are considered in this paper. the parameter domains are thus identified.

Laplace operators perturbed by meromorphic potential on the Riemann and separated type Klein surfaces are constructed and their indices are calculated by two different ways. The topological expressions for the indices are obtained from the study of spectral properties of the operators. Analytical expressions are provided by the Heat Kernel approach in terms of the functional integrals. As a res...

A solution of the nonlinear Klein-Gordon equation perturbed by a parametric driver is studied. The frequency of the parametric perturbation varies slowly and passes through a resonant value. It yields a change in a solution. We obtain a connection formula for the asymptotic solution before and after the resonance.

In this paper we present numerical solutions by the fourth order implicit finite difference scheme to nonlinear Klein-Gordon-Schrödinger equations with a perturbed term. We discuss the accuracy and stability of the scheme. Numerical tests are used to assess the performance of the scheme.

In this paper, the auxiliary ordinary differential equation is employed to solve the perturbed Klein–Gordon equation with quadratic nonlinearity in the (1+1)-dimension without local inductance and dissipation effect. By using this method, we obtain abundant new types of exact traveling wave solutions.