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.

We develop the local theory of surfaces immersed in the pseudo-Galilean space, a special type of Cayley-Klein spaces. We define principal, Gaussian, and mean curvatures. By this, the general setting for study of surfaces of constant curvature in the pseudo-Galilean space is provided. We describe surfaces of revolution of constant curvature. We introduce special local coordinates for surfaces of...

We prove the global well-posedness and we study the linear response for a system of two coupled equations composed of a Dirac equation for an infinite rank operator and a nonlinear wave or Klein-Gordon equation.

In this paper we obtain a global characterization of the dynamics of even solutions to the one-dimensional nonlinear Klein-Gordon (NLKG) equation on the line with focusing nonlinearity |u|u, p > 5, provided their energy exceeds that of the ground state only sightly. The method is the same as in the three-dimensional case [15], the major difference being in the construction of the center-stable ...

Exponentially localized solutions of the Klein-Gordon equation for two and three space variables are presented. The solutions depend on four free parameters. For some relations between the parameters, the solutions describe wave packets filled with oscillations whose amplitudes decrease in the Gaussian way with distance from a point running with group velocity along a straight line. The solutio...

Nonlinear dynamics of wave packets in parity-time-symmetric optical lattices near the phase-transition point is analytically studied. A nonlinear Klein-Gordon equation is derived for the envelope of these wave packets. A variety of phenomena known to exist in this envelope equation are shown to also exist in the full equation, including wave blowup, periodic bound states, and solitary wave solu...

An asymptotic nonlinear theory of the two superposed magnetic fluids is presented taking into account the spatial as well as temporal effects. A generalized formulation of the evolution equation governing the amplitude is developed which leads to the nonlinear Klein-Gordon equation. The various stability criteria are derived from this equation. Obtained also are the bell shaped soliton and the ...

We construct small amplitude breathers in 1D and 2D Klein–Gordon infinite lattices. We also show that the breathers are well approximated by the ground state of the nonlinear Schrödinger equation. The result is obtained by exploiting the relation between the Klein Gordon lattice and the discrete Non Linear Schrödinger lattice. The proof is based on a Lyapunov-Schmidt decomposition and continuum...