We study the evolution of fronts in a nonlinear wave equation with global feedback. This equation generalizes the Klein-Gordon and sine-Gordon equations. Extending previous work, we describe the derivation of an equation governing the front motion, which is strongly nonlinear, and, for the two-dimensional case, generalizes the damped Born-Infeld equation. We study the motion of one- and two-dim...

We analyse three nite diierence approximations of the nonlinear Klein{Gordon equation and show that they are directly related to symplectic mappings. Two of the schemes, the Perring{Skyrme and Ablowitz{Kruskal{Ladik, are long established and the third is a new, higher order accurate scheme. We test the schemes on travelling wave and periodic breather problems over long time intervals, and compa...

The numerical solution of the one-dimensional nonlinear Klein-Gordon equation on an unbounded domain is studied in this paper. Split local absorbing boundary (SLAB) conditions are obtained by the operator splitting method, then the original problem is reduced to an initial boundary value problem on a bounded computational domain, which can be solved by the finite difference method. Several nume...

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.

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.

The long-time asymptotics is analyzed for all finite energy solutions to a model U(1)invariant nonlinear Klein-Gordon equation in one dimension, with the nonlinearity concentrated at a point. Our main result is that each finite energy solution converges as t→ ±∞ to the set of “nonlinear eigenfunctions” ψ(x)e−iωt. Résumé. Attraction Globale vers des Ondes Solitaires pour l’Équation de KleinGordo...