We consider a system of coupled Klein-Gordon equations, which models one-dimensional nonlinear wave processes in two-component media. We find both linear and nonlinear solutions involving the exchange of energy between the different components of the system. The solutions are a continuum generalization of the classical example of energy exchange in Mandelshtam’s system of coupled pendulums. PAC...

E.H. DOHA1,a, A.H. BHRAWY2,3,b, D. BALEANU4,5,6,c, M.A. ABDELKAWY3,d 1Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt, E-mail: [email protected] 2Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia, E-mail: [email protected] 3Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef 62511, E...

The linear and non-linear Klein-Gordon equations are considered. fractional complex transform is used to convert the on a continuous space/time fractals ones Cantor sets, resultant solved by local reduced differential method. Three examples given show effectiveness of technology.

We construct infinitely many real-valued, time-periodic breather solutions of power-type nonlinear wave equations. These are obtained from critical points a dual functional and they weakly localized in space. Our abstract framework allows to find similar existence results for the Klein-Gordon equation or biharmonic

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.

We are interested in studying the coupled wave and Klein-Gordon equations with null quadratic nonlinearities R2+1. aim to establish small data global existence result, addition, we also illustrate sharp pointwise asymptotic behaviour of solution system. The initial not required have compact support, this is achieved by applying Alinhac's ghost weight method both equations.

In this paper we prove standard and reversed Strichartz estimates for the Klein--Gordon equation in $\mathbb{R}^{3+1}$. Instead of Fourier theory, our analysis is based on fundamental solutions free equations fractional integrations. final part paper, apply study a semilinear equation.

In the present paper, we establish existence and orbital instability results of cnoidal periodic waves for quintic Klein-Gordon nonlinear Schrödinger equations. The spectral analysis corresponding linearized operator is established by using Floquet theory. determined applying an abstract result due to Shatah Strauss.

In this paper, we find the exact solutions of some nonlinear evolution equations by using ( ′ G )expansion method. Four nonlinear models of physical significance i.e. the symmetric regularized longwave equation, the Klein-Gordon-Zakharov equations, the Burgers-Kadomtsev-Petviashvili equation and the nonlinear Schrödinger equation with a cubic nonlinearity are considered and obtained their exact...